CA2482871C - Method and apparatus for ground-based surveying in sites having one or more unstable zone(s) - Google Patents

Abstract

The invention relates to ground-based surveying on a site (2) which comprises an unstable zone (60) and at least one control point (FCP1, FCP2, FCP6, FCP7; CP1-CP3) placed outside the unstable zone, in which method at least one surveying device (TS8, TS9; ST1-ST3) is used to acquire positional data by sighting least one control point (FCP1, FCP2, FCP6, FCP7; CP1-CP3). The approach comprises: - providing at least one sighting point (UP3-UP5; A-C) within the unstable zone (60 ; 20), - using the surveying device(s) (TS8, TS9; ST1-ST3) to acquire positional data by sighting the at least one sighting point (UP3-UP5; A-C) that is located within the unstable zone (60 ; 20), and - combining the positional data acquired from: i) the at least one control point (FCP1, FCP2, FCP6, FCP7; CP1-CP3) placed outside the unstable zone and ii) at least one sighting point (UP3-UP5; A-C; within the unstable zone (60 ; 20), to produce a positional reference for the surveying device (s). The combining step can be implemented using a bundle adjustment technique.

Description

040920 ~~AP-586'7-CA
_ 2 _ l~l~~~a~~. ~.x~d ~g~para_ta~.s nor gr~tznd~~~.~e~ci ;~~a.r~r°~~~.aag in ~it~s lm~inorate ~r an~z~~ xaxasta~:~e ~c3a~a~ ~s) The present i:rwention relates to the: general field of ground-based site' surveying, anca more particularly addresses the problem of ground-based surveying in site~~
having one or more uns~able zone(s).
Ground-based survey~_ng in sites containing unstable zones can be neces:~ary when s.t is the: inst ability itself of the zone that needs to be monitored. This is the case, for instance, when it is reqLZired. tc~ check for spuriou:~
movements in hurn;~.n-m~.de structures; sLach as buildings,P
bridges, dams, roads, underground. structures, etc, e.g. to detect dangerous le~rels of movement _in all or a part of the I5 structure. 'fhe unstable zone to be monitored can also be natural, for inst~~nce an overhanging' rocl~ face, a glacier, a ground area subject to landslides, land subject to erosion, etc.
In other app:L~_ca-~ions, it may simply be necessary to 20 determine the overall contour of a site which happens to contain moving zor.~_es that also need to be mapped.
In general, ground-based sur~reyirzg of a site is conducted by initially installing a number of control points whose geograph~_c positions are accurately determined 25 and mapped on a pre-establi shed ooo:rdin~.te system covering the site, and typically corresponding to a geographical (ordnance) map coordinate grid system. These control points can be sigLzted by a displaceable :3urveying apparatus to allow the latter to ider~aify it,5 owrr. absolute position 30 on that coordina~re system. In this ~:vay~ the surveya_ng apparatus, after having determined positions of sighted known points i.n terms s.ts own, local; coordinate system, can situate its local coordinate on the pre-established coordinate system.
Clearly, the accuracy with which a surveying apparatus can be positioned or~_ the pre-established coordinate system depends directly arl the positioning ar.:cur~~Cy of the control points themselves. Far this reason, it is important far the latter to be placed an stable around. Also, as the:
absolute position a~ the surveying apparatus is generally determined by tri angulat3on techniques, it is desirable tc>
sight as many control paints as possib7.e and have those control points ~_acated over a. broad azimuthal angle range,.
However, the presence ov unstab=~ a zones within a site to be surveyed does not make it always possible to meet this requirement, given that contro7_ points placed in the unstable zones will lose their pas:i.tioning accuracy over time doe to drifts.
lvTowadays, the aforementioned displaceable surveying apparatus usually takes the farm of a motorised tata:l station, or a metsNark ay such stations cooperating over a site.
20 A total station is ef~aectzvely a combination of a:n electronic theodo:lite and distance met=re. As such, it provides the following topo~raphic:al information of a sighted remote point with respect to its measurement position: slope distance, horizontal angle (also known as 2~ azirnuthal angle) and vertical angle o Modern c~notarised., automated, laser-based total stations, when used with appropriate surveying protocols, car... yield relative positions with m_Lllimetre accuracy at ranges of several hundreds of metre: , and are thus well capable of detectir~g 30 positional drifts in many application s A total stat__on, or more generally any theodolite, can be considered as a dual axis system supporting th.e line of sight of a trarbsit/telescopea Far reducing the effect of y the mechanical misalignments on the «bservations, classic al operational procedures have been a~>plied since the first use of such instrumer~ts.
Today, a ~~ota_ station c<~n '~.ake these axis misalignments into account using an inbuilt dual axis compensator and special firmware to correct the resulting error in the measurements. However, the operational range of compensators is restricted, t~~pica:lly to about six minutes of arc range.. The operator aligns the main axis 1Q coarsely by keeping the bubble of the station inside the graduation. In case of a cornpensator 'a out of range"
signal, the staticn must be real:igneG. manually. This procedure, kno~vzz by experienced operators, is simply inappropriate whey operating a total station remotely fc~r Lang periods of ~~~_me .
The basic concept of surveying usi:r~g a total station in the general case of a st;~ble environment is illustrated schematically ire. figure 1. At an initial phase, a number of control points CPl-CP4 (four in t.:l~e example illustrated) are positioned af. scattered locations <~t a site 2 to ~>e surveyed. The exact location of each control paint i_s determined and ~cggecm in terms of :~,Y,~~ coordinate values on a specified a <~rid coordinate sy~~tem, typically the grid coordinates of a geographical map. ~. total station. TS can then sight a num:-~er of these contg:ol points to determine its absolute position on that X,Y,Z coordinate system using standard trianguJ.ation techniques. Typically, a control paint is materia:Lised by a fixedly-mou:r~ted support for a concave mirror ~f~ or other form of optical target far returning the laser beam Pram the tc~ta:L station TS .
In operatiari, the total station operator determinf=s the aforementioned range and angle data successively for each control paint CP1-CP4. These valves are stored in the «.
total statior~'s microcomputer together with the absolute=
position data for the respective coot=ro:1 points, the latter position data being pre-loaded into the total station. The total station then implements an algorithm, generally known.
as a free-statiori algorithm, to determine its absolute position from t:t~e sightings of those control points.
known example of such a free-station algorithm is the software modu~i~e installed on total stations produced by 3~eica Geosystems AG ou Switzerland arid also implemented on IO the GeoMos (registevec trademarks software. The positioning accuracy of a tota,~ station is propor~:ional to the number of control points it can exploit from its location, the angular distribuw-on of those contro-wled points, as well as the stability of the site at which they ~:re placed.
This can lead to a problem in en~r.ironments where too few control point~~ can be installed on a stable site. Such a situation can o~~cur notab~.y where several total stations are operated in a earns general awea~ calling for a correspondingly higher number of control points tc~ serve the environment they occupy.
Figure 2 il~_ust~~ates schematic~:ally an example where the above problem arises from the I>resence of an unstable zone 6 (indicated in hatched limes located centrally within a site 2 ~nrhere a number of total stations TSl-T~>3 (three in the example) need to be positioned. The control points CP1-CPS, h~.ving to be stably fixed, must be locatEed outside that unstable zone 6. This has for consequence firstly that the control points are fewer in number, and secondly that they cannot be disposed with the desired angular distribution around a given total station. In the example, the stable p.~rtion of the s?to 2 accommodates ju:~t six control poL..~ts CPl-CP6, with on.Ly two respective control points accessible for sighting by any one of the 040920 :~IAP-5867-CA

total stations i~~.-TS3. T~foreover, for each total station,, the angular dist~~i.bution of the two accessible c:ontro:l points is substantially reduced, being well below 180° in a horizontal circle around the total ;jtationo As a result, the position of the total stations may not be determined with the require accuracy or reliability.
In view of the fcregoing, i~?~e present invention provides a new pas~tion deter_minatioo~ approach. which allow.
the use of poi:r~ts at u-rzstable zones to coni:ribut~s i0 positioning data -- and thereby act effectively as Control points themselves - is~. conjunction with control points at stable portions of t:he site. In the preferred embodiments, this is achieved b~T acquiring posits.an data for the points at the unstable zones, preferably= from more than one surveying location, and by a form of triangulation technique referred to as °'bundle adjustment" or °'block adjustment" . 2~he technique of "ound.le adjustment is known in itself, but in the different field of aerial photography (photograrnmetry); where the position determination is made from a location moving relative to the ground.
More particularly, the invention relates, according to a first aspect, t« a method of ground-:ba.sed surveying on a site which comp:~~_ses an unstable zone and at least on.e control point placed outside the unstable zone, in which method at least one surveying device is used to acquire positional data blr ~ic~hting least one control point, Characterised in f:hat it further comprises the steps ofe providing at least one sight:~_ng paint within the unstable zone, - using the s°~arvey~ ng device (s) to acquire positional data by sighting the at least one sighting point that s.s located within the u?~;~table zone, a~.d - combining the ~:osi tional data aCquirc=d from: i) the at 040920 HAP-586'7-CA.
- o -least one control point placed out~~~_de the unstable zone=_ and ii) at least one sighting paint within the unstable zone to produce a positional referenoe for the surveying device ( s ) .
Preferably, r:~ore than one surveying device is used, and a plurality of surveying devices sight in common at least one common sigi2ting point that ~_s located in th~s unstable zone, arid the positional data. from the common sighting point (~°>) acawuired by the surveying devices are used as positional data in the combining step.
The combining step can compri~~e performing a bundle adjustment.
The combining step can comprise per:~orming a least squares adjustment on the positional data.
I5 The positiona..l reference can b~: the coordinate system of the control points) placed outside the unstable zone, the combining step converting the positional data of the sighting points) within the unstable zone into positional data of the coordinate system of the control point(s).
The surveying devices) can be used without resorting to a physical al:icnm~ent of its/their maim axis with respect to the direction of gravity, the method comprising a step of computing rotational angles of the mechanical axis of the device ( s ) .
The surveying device (s) can be used in a full three-dimensional reference frame.
The method can further comprise a step of associating a GPS (global positior~ing by satellite) device with at least one sighting point within the unstable zone t.o acquire coordinate values thereof, wherein the aforementioned coordinate values are exploited in the combining step.
In one embodiment, the method can comprise:

040920 HAP-586'x-CA
- providing at lease- one sighting cc~:aro='_ point accessible for sighting from 'she s~.te and locatE:d outside the unstable zone, the cantra~_ points) having at least one known positions coordinator in a fir~;t coord~_nate system, - using at least one surveys.ng devz.ce placed at a chosen location in the site to obtain a.t lE:ast one relative coordinate value of at least one the control point relatl'VE?
to the location of the surveying devuce, - providing at least one sighting point ~nr~.thin the unstable zone, - using the at least one surveying device at the chosen location to obtain relative coordinaide data of the sighting point (s) within r~-~e unstable zone rel ati~;re 'co the location of the surveying device, and I5 - determining the pasition(s) , in the first coordinate system, of the sighting point (s) 1<=sated in the unstable zone an the basis of:

- the relat~-~~e coordinate (s) of: the sighting point (s) located in the unstable None rel.atiwe to the chosen location (s) , - the relatz~,re coordinate (s) of the control point (s) outside the un:>table zor7.e relative to the chosen location(s), and - the pa sit ion coordinate ( s ) o f the control point ( s ) outside the unstable zone in the first coordinate systems Advantageously, the number of sighting control poznt(s) used is established t:o be equal to, or greater than, th.e minimum to keep a datla.m fixed, this minimum being available for the network of sighting point.=s used in the surveyed site .
The sighting ~oir~ts are typically surveying points.
Advantageously, th.e posi'~iori combining step i.s implemented using a bundle adjustment teC:hnique.

_ g _ Preferably, ~.t least one sighJV1ng point within th<~
unstable zone is sighted from more than one chosen locatioIl of a surveying device, thereby to acquire a respective=_ relative position value of that sic~htint~ point from each chosen location; and the respective relative position values are used in the position combining step.
Preferably, ~~t least one sighting point within thf~
unstable zone is sighted as a commc;n sighting point by a plurality of surveying devi,:es at different locations o:f I0 the site, and position data :! n.dicati7:~g the positicn of that common sighting point relative to the position of each th~s plurality of surveyir~.g devices is uses. in the position combining step.
The combining step can implemeni~ a model adjusted by a least squares method.
Advantageously, the model is usE~d to provideo-- coordinates ror at least one sighting point located in the unstable zone, and - parameters of the surveying device at the chosen location.
The combini~~<y step can take as position parameters only the ooordi~zates of at least 011e sz.ghting point in a coordinate system o~ the surveying device.
More than one surveying device can used on the site, whereby a plurality o:~ surveying devioes make sightings of a same sighting point and obtain posz.tion data of the latter within a commor~ time frames Advantageously, a total station is used as th.e surveying device.
The combining step can be s.mplemented with a coordinate tra.rl:sfor...nation equation. establishing a relationship between - relative coordinate data of sighted points both 040920 ~ HAP-~8~7-CA
_ g _ within and outside the unstable zone, established on a relative coordinate system of the at least one surveying device, and - a skew arlg_~e between the set of axes of the first coordinate system and the relative coordinate system.
The relationship can be established in determinant form.
The relationship can comprise a firs-L determinant containing relative coordinate data of at least one sighting point ~~ocated in the unstable zone, determined from two or more surveying positions, operating as a multiplier on a co~_um~xl vector of numerz.cal parameters of the surveying device(s).
Ac..cording to a .second aspect, the Invention relates to the application of the method according to the first aspect for establishing the position of at least one sighting point located in an unstable zone in terrri.s of a position o:n a coordinate grici system which also maps fixed control points, whereby tr..e at least one sic;hung point located i:n an unstable zone is exploitable as a sighting control point.
According to a third aspect, the invent ion relates to the application of the method according to the first aspect for establishing the position of at least one sighting point located in the unstable zone in terms of a position on a coordinate grid system to monitor evolutions in position of the at .east one sighting point.
According to a fourth aspect, the invention relates to a system for grcund-based surveying on a site which comprises an un~t<~ble zone and at least one control point placed outside thc= unstable zone, comprising at least one surveying device arrane~ed too acquire positional c'ata by sighting least one control point, characterised in that it further compris~:s:

at least one si~~hting poirzt within. the unstable zone, ate least one the surveying device being arranged to acquire positional data. by sighting at lea;~t the sighting point within the unstable zone, and - means for combining the positiona=L data acquired from: :i) the at least one control point piacE'd outside the unstablE=
zone and ii) at least one sighting point within th~~
unstable zone, 7~o produce a positio~sal reference for the surveying device(s).
The system can be configured to execute the method according to any part of the method acc:o:~°ding to the first aspect, or its application according to the second o_r third aspects.
The optional features presented abc>ve in the context of the method and uses are applica.'c~le m;xtatis mutandis to the system according to the fourth aspect.
According to a fifth aspect, the z.n.vention relates to executable code sNl~ich, when run on a data processor, executes at lea~~t the combining step of the method according to the first aspecvV.
According to a sixth aspect, tr~.e in~,rention relates to executable code, whi~:,h.r when run on a data processor, executes calculat~_ons in re~,pect of an.y part of the method according to the ~:irst, aspect .
According tc a seventh aspect, the invention relates to data carrier .,tor~~ng the executable code according t.o the fifth or sixth aspect .
According to an eighth aspect, the invention relates to processing an oppara.tus, e.g. a )?C type computer c>r functionally equivalent device, loaded with the executable code according t.o the fif th, si<~th or seventh aspects integrated in its software.
The invention and -~ is advantages sh<~11 be more clearly - _~1 -understood upon reading the following description of the preferred embodiments, given purely as non-limiting examples, in conjunction W_th the appended drawings in which:
- figure 1,. ~:lready described, is a schematic diagram showing a total station set to take measurements against a set of fixedly mounted control point~~ im a stable site, - figure 2 , ~~ 1 re~rd~r described, is a schematic diagram showing a group of tr~tal stations it t.~ie vicinity of a:n.
i0 unstable zone and a restricted number of fixedly mounted control points available to take mea;~ureirr.ents, - figure 3 i s a schematic diagram. :showing a group of total stations i-r.. the vicinity of an unstable zone and operating, inter aria, on sighting poir~.ts located within ~5 that unstable zone in accordance wit'~~i the invention, - figure ~a is a graph illwstra~~ing the relative positions of two coar_c_irate >~ystems, respectively a control points coordinate sys'~em and a theodalif~e (tota7_ station) coordinate system, 20 - figure ~b shows a ma.thema'cical expression in determinant forrrG i=or ~~onverting between the control points coordinate system and the theodalite coord,'_n.ate system of figure 4a, - figure 5 ~_s a schematic diagram showing two total 25 stations in the ~r~_cinity of an unstable zone and operating, inter aliaj on sighting points within that unstable zone, to illustrate a specific example= of: coordinate data adjustment usi~~g a bundle adj'ustme'nt technique i.n accordance with the present inventior~, 3Q - figure 6a shows a mathematical expression in determinant form giving the tran:~formation between the control points coordinate system and the theodolit:e coordinate system fcr a point Pl on stable ground, as - i2 -surveyed by total sta~.ion TS8, taken from the example of.
ffigure 5, - figure ob shows a mathematical expression in determinant form giving the transformation between the control points coordinate system anca. the theodolite coordinate system for a point P4 o:n unstable ground, a:~
surveyed by total station TSB, take:rl :From the example of figure 5, - figure oe shows a mathematic~~l expressz.on in determinant fo~__°m giv:~ ng the transformation between thc=
control points c~oordin.ate system and the theodolitE=_ coordinate system for the point P4 on unstable ground, a;s surveyed by total st an on TS9, taken from the example o:f figure 5, l5 - figure 6cL shows a mathematical expression i:n determinant for~:~ giv7_ng the transformation with bundle adjustment betweenn the control point; coordinate system and the theodolite coordinate sy;~tem for the point P4 on stable ground using the combined data from total stations "_~S8 and ~0 TS9, taken from the example of figure 5, - figure oc: shows a. mai.hernatxcal expression in determinant form givi~ag the complete mathematical for the bundle adjustment based on the fixF_=.d arad unstable points used in the conf~.c~uration connection with the set-up shown 25 in figure 5, and based on the mathE:mati~al expressions of figures 6a-6d, - figure ~ is a schematic diag_~am of a network composed of two total ;stations, fc;ur control points and three ccnnecting points, to illustrate b~~ way of an example 30 how a mathematical model according to ti2e preferred embodiments is im~>lemented, - figure B is an exarr~ple of data files produced by total stations u:~ed in the preferred embodiment of the invention, - figure 9 is an example of point coordinate values produced f rom dat a in. the preferred embodiment of the invention, - (figure 10 i.s a (first screens:hot of a Visual Basic program executed in the preferred e~tbodiment of the invention, - figure 11 is a second. screenshot of a Visual Basic program executed in the preferred embodiment of the invention, - figure 12 is data presentation of a processing report showing the: results of apply_Lng a. 2D least squarer adjustment in accordance with the preferred embodiment of the invention, - figure 1'? is a presentation of station parameters for a first total station in the preferred embodiment o:f the invention, - figure 14 is a presentation of station parameters for a second total station in the preferred embodiment of the invention, - figure 15 is a presentation of the connecting points of sighting points in a mov~.ng zone of a surveyed s te, in accordance with the preferred embodimex~.t of the invention, - figure 1~ is a presentation of position corrections after bundle adjustment for the total stations use in the preferred embodiment, - figure 1i is a schematic diagram of a configuration of total stations and points according to a second embodiment, where points within an unstable zone are al~~o equipped with CPS antenna receivers to send their coordinate data, and - figure 18 is a general flow chart showing some of the steps involved in. the procedures used in the first and 040920 I~AP-5867-CA

second embodiments.
A first embo;3iment of the invention is givers with.
reference to figures 1 to 16, and 18 where sighting points are located in stable areas and also with_Ln unstable areas.
S This embodiment does not use GPS (glob<~l position_i.ng by satellite) receiver devices to acquire po:~itional data.
A second embodiment of the invention is given with reference to figures 17 and 18, which contrasts with the first embodiment inter alia by its use of one or more GPS
i0 means cooperating with one ar more sighting points to contribute GPS data for the sur~reyinc~ apps ication.
The flow chart of figure 18 is generally applicable to both the first and second embodiments, with simple adaptation to the example and implementation of the first 15 embodiment.
Figure 3 shows the three total stations TS1-TS3 of figure 2 at the same geographical 7_ocation and exploiting the same six fi~cedly-mounted control points CP1-CP6 on stable ground, in the manner explair~ed above in tree 20 introductory portion with reference to f~~gure 2. (Specifi.c features of the total stations and cowtrol points described in the introductory portion are apps icable in the case of figure 3 and shall not be repeate.~,~. for the sake of conciseness.) 25 The situation differs by thE: fux-ther provision of sighting points inside the unstable zone 6. To distingui;~h from the fixedly-mounted control points, these control points are herea:~ter refer:_ed to as unstable points, and given the generic abbreviation Uf. In the illustrated 30 example, seven unstable points designated UP1-UP7 are distributed sub~~tantially uniformly over the entire unstable zone 60. Any one of the unstable points can be sighted by two or more of the total stations TS1-TS3.

j -r The provision of the unstable point; ir. the unstable zone ~0 allows each o' the total stations TS1-TS3 to use these points UP as control points, as explained further.
The total statioz~.s can then have access firstly to a greater number of control points (fixed and moving), anc~
secondly to a wider angular distribution of the Control points (fixed and moving), thereby potentially increasing their positioning accuracy.
Largely inspired by t:he analytical photogrammetr~~r "bundle adjustment'' (also known as "block adjustment") method, this approach allows the total stations to be used in a full 3D reference .frame. Tnstead of trying to physically align physically the instrument's main axis with the direction a=gong the gravity,. the compensai~or is disengaged and thE: rotational angles of t:he mechanical axis are computed.
The idea. is t:o u: a all - or at least: some - connection points available that overlap the different measurement sub areas of the overall site to re-compute the stations>' coordinates and the rotational angles of their mechanical axes. Some contr;~l points are still used to provide the coordinates in a common reference frame and to solve the datum defect issue, but those points can now be installE~d in a much more convenient location largely outside the unstable area.
It will be rioted that in a surveying application, the minimum number c>f kr°lown points to be used is generally determined by what is termed the "datum" . Typically for a one-dimensional (1D) network of sighting points, this minimum is one point determined in altitude (i . a . of known altitude, or z coordinate) ; for a two-d i mensional (2,D) network, this minimu~:~ is two points determined in their x and y coordinates; and for a three-dimensional network, this minimum is at least three points determined in their x, y and z coordinates, or two points determined in x and y coordinates and tr~ree points determined in z coordinate.
This minimum is the minimum number of points available for the whole network, as opposed to the points available per station used in the nei~work.
To remove the restriction of today that the total station must be located on a stable point or. have avs.ilable a number of high quality control points, the preferred embodiments consider this instrument. as a local 3D (three dimensional) axis system. The coordinates computed by.using the observations (directions and distance) are internally consistent, but transformed into the reference frame defined by the a set of control points.
For a single total station, the problem is simply a 3D
transformation also kv~own as similarity transformation or Helmert transformation, from the name of a well known German geodetic Vermar~ scientist who popularised the use of the Least Square adjustment in geodesy and surveying.
When several stations are disseminated to survey all points of interest, the proposed way to avoid th.e multiplication of control points is to make use of common paints (conn.eots.on) . Par<~meters are added to t~:.e mathematical model that relate the measurements to the common points to the transformation. The: common points may be located in an area subject to deformation so long as they can be considered stable during the time of the measurement. The idea is just to keep those common points, located also directly in the unstable area, as subtantial=_y fixed during the time of observation, which is now quite limited due to th's high 'performance of the total stations..
If a full 3D model is considered, the only reduction to be applied to the range observations is the refraction _ 17 _ correction. Usually the well-known Barrel and Sears formula based on the dry and wet temperatures (or the dry temperature and the relative wet air) observations, as well as the atmospheric; pressure, is used. That model a.ssume~~
however that the al~mospheric parametc~r..s a'~ both ex.tremitie:~
of the range are k:nowr~, which is practically impossible to achieve. Another approach proposed is to consider measure some fixed points where the distance is accurately known so that a scale factor can be directly computed and used to correct the measurements.
If the process is divided into a 2D arid 1D model, the ranges are reduced to the horizontal and, if appropriate, to sea level by applying a projection correction due to the coordinate system. For a monitoring project, even one spread accross a large area, the system is still on a local grid and the projection correction can be neglected. For 1D, the height is preferably also be reduced to a reference plane.
Observing the points in the two-face position of the ~0 telescope ca.n eliminate the remaining effect of instrumental axis misalignments. With the motorized instruments used in monitoring, this is a fast and simple procedure.
As the unstable points UPl-UP7 by definition have unknown - or ~a .least unreliably known - position coordinates, meaningful positional information is extracted from them by the combined action of.: i) sighting each one from several physically separated total stations, and ii) grouping the data. acquired from those sightings with data acquired by the same total stations from sightings taken on the fixedly-mounted control points CPl-CP6.
To this end, the embodiment implements a technique of laser bundle adju.stment/bundle adjustment applied to a set of points that comprises both the fixedly mounted control points CP1-CP 6 anc~ the unstable points U~~1-UP7.
To recall, a {laser) bundle adjustment {also known as bundle block adju~~tmerzt) car. be definedF in the field of.
photogrammetry, as a topographical infoz°mation adjL~stment technique that does not treat the absolute and relative orientations of sighted points separately, and where the basic unit considered is the pair of x and y coordinates of a sighted target, whereby computation leads directly to thsj final coordinates in a single solution.
Heretofore, bundle adjustment w<~s strictly reserved to the field of aerotriangulation photogrammetric adjustment, where the x and y coordinates in qu.esticm relate to image points on a photog-ra~;h" l:ts purpose is classically to assemble correctly pairs of pictures having common scene elements. In :.hat ~~ontext, a bundle adjustment serves essentially to determine the 3-D coordinates of point s from a 2-D image measurement.
In the new application of the bundle adjustment technique in accordance with the vprese~nt invention, th.e absolute and relGtive arien.tations of righted points are respectively those of_ the fixedly-mounted control points and those of the unstable points. All the control points are physical entities attached to the ground, and the measurements of thes_r coordinates are also taken from static, ground-based instruments, in this case a set of total stations i~:L-TS3.
The mathematical techniques covered in the literature for bundle adjustment; in photogrammetric applications can be utilised in this new application with simple adaptation.
For this reason, the mathematical methods and algor~_thms of bur~dle adjustment applicable to this application shall not be covered extensively in detail for reasons of conciseness.

_ ~0 _ The mathematical model used in. the preferred.
embodiments to implement the bundle adjustment is based on a coordinate transformation equations expressed in determinant form, as explained below with reference to figures 4a and 4b.
The example covered by the following description uses a two-dimensional coon°dinate sysj~em (x a.nd y coordinates) for simplificatio~a. it s~all be understood that the teachings are applicable mutatis ~mwtandis to a three--IO dimensional coordinate application (x; y and z coordinates) using straightforward i~nathematical adaptations. Likewise, the teachings are applicable mutat:i.s mtztandis to a one-dimensional application.
Figure 4a shows a first set of orthogonal axes l~ and Y
~5 which defines the coordinate plane against which the fixedly-mounted control points CPS.-CP6 are mapped.
Typically, this X,Y ooordinate system, hereafter referred to as the cont-ro=_ points coordinates system, is made to correspond to a ge:ogr~_phical grid.
20 Each total ~atat~_on uses its own, local, coordinate system which is independent of the control points coordinate syste~r.. The local coordinate system for a particular total station is shown fir., figure 4a as a second set of orthogonal axes x and y, hereafter referred to as 25 the theodolite coordinate system (x,y), whose origin O
coincides with the position of the total station_ The theodolite coorJinate system is at a skew (i.e. rotation) angle ~, with respect to the control points coordinate system, the skes.fJ ;~nglv being def fined as the angle subtended 30 by axis y of the theodolite coordinate system with respect to the axis Y o:~ the control point~~ coordinate system. The length segment joining the origin d to a point P shall be referred to as the vector OP_ '_ r, a There shall now be considered a common point P whose positian is ideritified in both the control point~>
coordinate system and the theodolite coordinate system.
This would be the case for a stably-mounted control point which is pre-established and mapped on the control point~~
coordinate system (giving the absolute position) and surveyea by the total station (giving the relative pasition with respect to the total station). =~f: a is the pro-'section of the vector OF' on the X axis of the first set of arthogonal axes X,Y, and sirvilarly l~ is the projection o:f the vector OP on the ~r axis of the first set of orthogonal axes X,Y (i.e. the intervals between the parallel dotted lines shown in figs~rE: 4a) , and cz is tree skew (rotation) angle of the x,y axes of the theodolite coordinate system l~ relative to the first set of orthogonal axes X,Y, then: the X and Y caordinate ~ralues of that ~~ontrol point P in the first set of arthogonal axes X,Y in terms of the theodolite caordiz~.ate system (x,.y) can be expressed in determinant farms as shown in figure 4b:
jX - ~ca + k , cos a sin a ~ x Y ~b -sina cosa~ ~ y where:
k is a scale factor.
From the above, the following gE:neralised form of linear equation can be obtained dirE~ctly:
X I 0 x y b ~ (2) Y 0 1 y -x ~ c d where:
c=k~cosa and d =k~sinrx The values c and d thereby include the scale factor k and the rotation angle ex.
The above ma~:hematzcal expression is a construct to produce linear equations that shall be used to implement the standard least squares adjustment, as explained below.
A specific ex;~mple of a surveying situation in which a bundle adjustment based on the above model can be applied IO is illustrated schematically in zigure 5., In this example, two total stations designated TS8 and TS9 are situated approximately on opposite sides of an unstable zone 60 shown in hatched lines. The surrounding area of the site 2 contains four fixedly-mounted control points FCPl, FCP2, i5 FCP6, FCP7 well outside the unstable zone 60. Total station TS8 can make a sighting on fixedly-mounted control points designated CP2 and CP?, while total station TS9 can make a sighting on fixedly-mounted control points designated CP6 and CP7.
20 In accordance wit'_n the invention, the unstable zone 60 is also provided ~nith sighting points, which are considered as unstable points. The example shows three such unstable points designated UP3, UP4 and UP5, on each of which both total stations TS8 and TS9 can make a sighting.
25 In 'nThat folZ.ows, when a control point is considered without discrimir~ating vrhether it is fixedly-mounted or unstable (also refer. red to as '°moving°' ) , it is designated simply by the letter "P'° followed by its unique identification numeral, as indicated in Figure 5.
30 The interrelation between the total stations and control points is summarised in table 1 below.

". 00920 HAp-5867-CA

Table 1: control. points sightedfor each total station (cf. figure 5) Total station Sighted control point 'type position TS8 Pl fixed known P2 fixed known P3 moving unknown p~- moving unknown P5 maving unknown TS 9 P 6 f i.xed 3cnown p~ fixed knornrn P3 moving unknown p~ moving unknown P ~ movin.g unknown ~5 In the algorithm used, the: (fixedly-mounted and unstable points a=re processed collectively as points P1 to P'7, following the principle of bundle ~.d~ustment.
This principle can be applied to derive the positions of the different points in the case~~ numbered 1 to 4 below, for instance, in the equations that follow, and in figures 6a-6e and 7, the :numerals appearing as an index t:o parameters x, y, a, b ~ c or d correspond to the unique identification numeral (suffix 8 or 9? assigned to the 2S corresponding total station concerned (respectively TS8 and TS9); the numerals appearing as a sub-index to parameters x, y, X or Y correspo_~d to the nu.mera:L assigned to the corresponding sighted control point according to table I
above.
Case 1 a determination of position of a known-posi tion point - paint p1 (Xl, Yl) , say, from tota_L Station TS8 .
The position coordinates (Xz,Y1} of point Pl are derived from the determinant equat~_on, which is a specific 040920 HAP-587-~A
- ~:3 -instance of the genera~_ form of linear equation (1) abovee f-a8-, i - ~1 0 xg yl . ~ ~~ ~ ( 3 ) 1 yg - xl ~ ~g ' h_ d as shown in figure 6a.
Case 2: determination of position. of an uraknown-position= point - ~>oint P4 (~4, Y4) , say, from total station TS8.
The position coordinates (X4,~fn) of point P4 are derived from the c~e~~erminant equation, which is likewise specific instance of the general form of -Linear equation (:L) above a ~~s 8 8 g8~
0 x4 y4 J ( 4 ) Y~ 0 1 y4 - xs / i c8 ~~s as shown in fiLgure fib.
Case 3 : determi ization of poi>i tion of an unknown position point. - ~oin.t P4 (~4,Y4) , ~~ay, from total station TS9 .
The position cocrdir~ates (X4, ~Y~) c:f point P4 are derived from the ~~eterminant. equation, which is a specific instance of the gE.neral form of linear equation (1) above:
~ -, X4~ _~l 0 x4 Y~ ~ b9 ~ (5) Y~
d.9 i as shown in =figure 6c.
Case 4: det~:ermanation of position of an unknown-position point - poir~t P4 (~4,Y4) , :gay, from total station TS8 and from tota.~ station 'S9.
The values c~f t he pos-~tion of poiz~.t P4 given by the 040920 I-iAP-5867-CA

equations of cases 2 and 3, being based on a single total station measurement. point, is subject to error.
Here, the sighting information. obi..ained from both.
total stations TS8 and TS9 is combined to cancel out this error and yield the absolute position. value of the unstable point P4, corrected by the combined contributions of total stations TS8 and TS9. Ir_i this way, control moving point P4 can thereafter serge as valid reference control point, by virtue of its pnsitiori coordinates (X.~, y4) haring been IO accurately determi~_~ed (at least within a sufficiently short timescale within w:~ich possible drifts oa:C1 be neglected) .
To obtain tha.s corrected posit:i.on coordinate (X4,~Y4) , the solutions to the abozre determinant equations (3) , (4) &
f, 5 } for cases 1 to 3 above are used to both construct the IS new determinant equation that yields implicitly the corrected coordinG.te values (X4, Y4) of moving point P4 and to determine the full range of values for the parameters of that equation, thaw set being: x~e, yes, x:49, y49, ag, b8, C8, a9 b9 d~.
20 The determinant equation that yields implicitly the corrected ooordinate values (X4, Y~) of moving point P4 is given by:
~s b~
c$
0 Z 0 x4 y~ 0 0 0 0 -1 0 ~ ~l$
0 _ 0 1 y4 -x4 0 0 0 0 0 -l~_ a9 0 0 0 0 0 x4 y4 ~ 0 -1 0 ~g ( ~ ) 0 0 0 0 0 9 -x9 0 0 0 -1 ~ c~
y4 4 ~n i i as shown in figure 6d.
25 This equation (4) effectively corresponds to a least-squares adjustme~.t~ model based on bundle adjustment techniqueso It will be observed that equatio:r~s (~), (4) & (5) have the general form ~p~-~Q~~~~~, wilE:rea [P] is a col;zmn vector expressing absolute position coordinate values c>f a point, [Q] is a det:~rmi~ant o:E fou_r c~olum.ns and t:wo rows, where the first and second columns compose a unit matrix and the third and fourth columns corr~prise position values in the theodolite coordinate system x, y, and [R] is a column vector comprising the parameters a, b, c and de By des i gnat ~.nc~ m [P3] the column vector [P] for the case of equatio:rl (4), [P4] the column vector [P] for the case ofd equation (.5), it will be ob:~erved that equation (4) can be expressed ase .:r C:
~ 1 0 0()00--1 0 n~'8 0 U 1 ~'~~0 0 0 0 0 -1 0 0 0 0 0 0 0 -I 0 ~' ~ (~) ~ 0 0 ~ 0 '~4 0 0 ~ -1 ~9 Gr -~~ i The complete ~~nathematical model derived from the above set of equations is them - z6 -x8 y8 ~ 0 0 0 0 0 0 0 0 0 0 0 y8 -x8 0 ~ 0 0 0 0 0 0 0 0 0 0 xi .yg ; 0 0 0 0 ~0 0 0 0 0 0 0 Yz - (~= 0 0 0 0 0 0 0 0 0 0 a xi 0 xg ys 1 0 0 0 0 0 -I 0 0 0 0 0 dg o ys -xs 0 _ 0 0 0 0 0 -~ 0 0 0 0 0 x4 y4 ~ 0 0 0 0 0 0 0 - 0 0 0 ~

0 y4 -x4 0 ~ 0 0 0 0 0 0 0 -1 0 0 0 xg yg 1 0 0 0 0 0 0 0 0 0 -1 0 d~

0 y3 - 0 ~ (~ 0 0 0 0 0 0 0 0 -1 cx x3 ~ 0 0 0 0 x5 y9 ~.0 -~ 0 0 0 ~ ~ r~

0 0 0 0 o y~ -xs o ~ o -~ 0 0 0 0 0 0 0 o x~ y; ~ 0 0 0 0 0 0 0 0 0 0 (~ y; - 0 i 0 0 0 0 0 0 X4 x~

0 0 0 0 x~ Y6 1 0 0 0 0 0 0 0 Y6 0 0 0 0 y6 - 0 1 0 ~ 0 0 0 0 X3 x6 0 (~ 0 0 0 .x~y3 1 ~ 0 0 0 0 -1 ~ Y3 0 0 0 0 0 y3 -x~ 0 1 0 0 0 0 0 -1 (8) 0 0 0 0 0 x~ y~ 1 0 0 0 - 0 0 0 ( 0 0 0 0 0 y4 -x4 0 ~ 0 0 C -1 0 0 a,s shown irz f figure 6e .
This complete model integrates the coordinate data of both fixed and unstable paints, as acquired by the total stations, to produce the corresponding bundle adjustment.
Specifically, the expression of equation (8) above comprises the fo:Llow:ing ccordinate data for the fixed points:
- for fixed control point FCP1 (absolute position XI, 20 Y1) coordinate data xze,yla, from total ~~tation TS8, :

- for fixed control point FCP2 {abst~lute position X2, Y2) : coordinate data x~8,y28, from total ;station TS8, - for fixed c:ontrolpoint FCP6 {absalute position X6, Y6) : coordinate data x~9,y69, from total station TS9, - for fixed control point FCP7 {absolute position X'7, Y7) : coordinate data x~g,y~9, from total station TS9, 040920 H~1P-5867-CA

- for unstable point UP3 (absolute position X3, Y3):
coordinate data x3f', y3~ and .~39, y39 i:rom total stations TS8 and TS9 respecti~rely, - for unstable paint U~'4 (absolute position X4, Y4):
coordinate data ~4~', y48 and x~9, y4s from total stations TS8 and TS9 respectively, and - for unstable point UP3 (absolute position X5, Y5) coordinate data ~,F', ys$ and x:59, ysg from total stations TS8 and TS9 respecti~.%ely.
I0 After such a bundle adjustment, a conventional observations adjustment can be performed by using the coordinate values obtained by the bundle and the ra~cv observations. The appropriateness of such a follow up bjr conventional observations adjustment depends on appli rations . In monitoring application:, it is often the case that only coordinate values are of interest.
The data acquired by the total stations TS8 and TS9 used in equation (~) can be brought together by an~r suitable communication means. For instance, the data acquisitions from each of the total stations TS8 and TS9 can be transmit~t.ed. to a central base by a radio transmission line, that central base then carrying out the calculation for determining she absolute coordinate value~~
X4, Y4 of moving point P4 using equatican (6) . I~Taturally, the aforementioned central base can also dispatch the information to ancther location for the calculation to be carried out.
Alternatively, on.e of the total stations (TSB, say) can communicate ~.ts acquired data to the other total station (TS9) , wh~ic~h itself carries out the above-mentioned calculation using the same equation (o), and/or vice versa.
This option is teasible with a modern total stations equipped with communication means, onboard calculators and software packages which can be programmed to execute such calculations. Ex~:mples of current total stations capable of effecting such a calculation are mcde-i numbers TCA1800, TCA2003, TCA1100 and TCA1200 from Leica Geasystems AG af_ Switzerland, used ~~ith the GeoMos softwara package from the same manufacturer. Mare information an t~.his total station and the GeoMos ~>oftware package ~,~an be found at the follawir~g website: htt;oo//www.leica-geosy5tems.com.
In particular, the GeoMas software package stores al'~i the station's ob:~ervations and the associated camputed x,y,z coordinates (for a three-dimensional surveying application) in aa. SQL database, by means of which the bundle adjustment can be implemented.
The GeoMos s:~ftware package acc;es se;~ all the relevant information stored in the database to perform the bundle adjustment and to ~~ransform each local sef~,s of coordinates..
The latter inclua.e the coordinate~~ used in the bundle adjustment.
The GeoMos software and the software for carrying out the bundle adjustment in accordance with the preferred embodiments are implemented in a PC that is physically separate from the total stations.
Further considerations i n respe~st of. the mathematica7_ model used in f~_rst and second embodiments are presented below.
~7bservationa, data There is a large consensus in the surveying and geodetic community to handle only the measurements in the adjustment process. Even if the coordinates are directly deduced from the measurements without any reduction prccess, this trey>d is still largely promoted. Far many years now, since the availability of distance measurement~~

- ,~9 of the same level of quality as the angular measurements, only few practitic>ners have tried to promote models that deal directly with coop=dinates . GPS ~>roce;ssing results havE:
helped to motivate that change of parads.gm.
In fact, it is~ just a transformation from polar system to Cartesian system. People involved i.n processing and analysis use the _~dea that interpretation is easier. as a justification to handle measurements only. This is not the case in deformatior_ measurements - the results are generally always expressed in the position domain_ As such, in this approacr~ t:he coordirsatea will be used as observations . In. suc~~ a case several authors use thE~
expression "pseudo-observations" ~.o c~.ifferentiate thE~
coordinates from the measurerr~ents.
IS Considering the measurements (zenithal direction Vz, horizontal direction Lrz and slalr~e distance s) the point:
coordinates Xp, Yp, Zp <~re obtained a=.:
sin T~z ~ sin ~z, =S~ sinhz~cos~z (9) Zp .r,OS ~Z
In order to apply the general law of variances, we:
need to linearize the equations as follows: which farm the' content of the fol=Lowing matrix:
sin hz - sin Hz S - cos Y~ ~ sin ~Iz S ~ sin Yz ~ cos I~z ~cc = sin Vz ~ cos Hz S ~ cos ~z ~ cos IIz - S - sin T~z ~ sin ~z ( 10 ) cos~'z 0 -S~sinVz The estimation of the observation variance is introduced as:
o-s 0 0 ~~ = 0 a-vZ 0 ( ~-1 ) z 0 0 m ~~

The variance covariance o~ the point coordinates is formulated ase - ~cc W r.~ W ~c (12) Functional yodel Any paint (.x, y, z) in a 3D Cartesian frame can be transformed into another 3D Cartesian frame (X,Y,Z) by using a similarity tra:~sform~.tion which describes the seven degrees of freedom of a solid body irt space .
I0 The seven parameters describe the three translations ( TX, Ty, TZ ) , the three rotational angles s ~~,~,x-j and "s" a scale factor.
X '~Tx co~:~.cosx --cosh-sin x- sink x Y =, Ty + s . cos ~ ~ sin x -i- sin o~ . ,rin qS . cos a~ cos r~ . coy; ~; -sin ~v ~ sin ~ . sin tc - sin ~ . cos;~ . y Z LTz sin r.~ - sin ~c - cos ~ - sin ~ - cos ~- sin ~ . cos ~ + cos ro . sin ~
- Sin K cUS CD . cos ~ z (equaticn 13) The lineari~ed form of this equation is°
K=dXa-(1+ds~.dR.~'~ (14) Or in matrix form -ds d~
X; xi 0 z; - yi i 0 0 d Y y. -zt 0 .x= Q i 0 - drs' ~ (15) zr za yr -~~ fl G~ (~ 1 d2x dTY
dTZ ~
If the corresponding (Xi,Yi,Zi) is used as a conrsection point, it should be considered also as a part of the unknown parameters.

ds d~
d ~p d~
0 - ~ xt ~ z1 - yt ~ ~ 0 - ~ 0 0 0 -~ y; -z; 0 x: 0 1 0 0 -~ o ~~X ~z6~
'0 ~ z; yl - x; G 0 0 1 0 0 -1 dTZ
To clarify the mechanism of building the fuctional model,, the Applicant designed a small network where three connected points are observed by two stations, as shown in figure 7. Datum i:~ fired by four contro:l~ points. In the figure, the three connected points are designated Point 3,.
Point 4 and Point 5 respectively. The four control points are designated Carltro~~ Point. 1, Control Point 2, Control Point 6 and Contro 1 Point '7 x~especticrely. The stations are I0 designated Station A a:ad Station P r~=.spectively.
To condense the functional model, the notations j x,.' 0 zl - y1 _ 0 0 ~~ _ ~ y~ - Zz ~ xc~ ~ 0 yi xi 0 ~~ ~ 1 is used, where the index i relatesd to t~~.e observed point,.
the index j relatE~s to the station and the index .~ relater to the existing control points.

E= 0 1 0 ~k F'k = ~'k (19) Zk '. 00920 HAP-5857-CA

T' = the Corr.eponding ~uransforrlatic>n parameters for the station j P the correspondin g the = coordinates point for :i The complete onal mod el n.ow assoc iated functi to our the is:
example D~''0 -,~ 0 0 0 0 0 0 0 Dz 0 0 -E 0 0 0 0 0 0 D ~ 0 0 - C 0 0 0 - 0 ~~' ~

3 ?, Dq 0 0 0 0 ~ 0 ~ 0 TB 0 DS () 0 0 (~ 0 - 0 0 0 E

~

0 D~ 0 0 0 - 0 0 ~ ~
~' ~, (20}

0 D~ 0 0 0 0 -E 0 0 ~ 0 0 DB 0 0 0 0 D -E 0 ~ 0 0 Dg 0 0 0 0 0 0 ---E

' ~ ~ 0 E 0 0 0 ~ 0 EZ

~ ~ 0 ~ 0 0 0 E 0 E'3 0 0 0 0 0 0 ~ ~ E ~'q St~chastiC cac~.el The corresponding variance covariance matrix is given for each point observed bye - Far a connection point determined by at least two or more stations:
(21}
PP - ~ CC ~ ~ LL CC
For existing control points, the variance (covariance} matrix is built by conditioning the elements with a mean zero vari«.nce value or relaxing some of them depending of on their stability. The process of conditioning (or of relaxing) the variance covariance matrix to reduce the influence of errors 040920 ~IAP-58c~7-C~1.

in the a_.~y control points uses the variance (covariance) ~natr3.x of the form;:
crX 0 0 APP ' 0 Cry 0 (22) 0 0 ~°z Tf the coordinates are provided by a GPS antenna co-located vtith a reflewtor,, a~. in the second embodimen t, there Will be introduced the corresponding variance (co~~~arzance) rr~atrix obtained after the real time Or pOSt proCesslng SOIL~t2ol.'1.
FICWever, It l S llnoWn that GPI produce over Giotlml.St~_C precision estimates .

~0 Thus it is ~.ecessary to scale the diagonal of the resulting variance (covariance) matrix to give a more realistic representation of the quality c>f the solution. '!=,ze estimation 7 s ~>ro~rided essentially by the basel ine range scaled by a ,priori estimator of the standard acc3,~,rao~.~ of the GPI receiver used.

~e~.s~ ~~ax~.a~s Adj~.st~t~x2~
Having defined the funs°tional and stochastic ;models, it is possible to p'_.:~oCess this set of linear equations using the Least Squares adjustment method to obtain estimates for all parameters including the transformati.c~n set for each statior_ and the coord~_natea of all connected points .
The Least squares adj ustment rrlet~lo(~ provides al l the necessary statistical information than is needed t:o qualify the resinis in terms of model performance arid screening of ~:he v~ndiT.pidual abservat ions .
The approach cor_sidered uses t:i~e B-method of testing developed by Py-ofe ssor ~3aarda and promoted by the Universitlr of Delft . This method a:lloWS for investigation of the internal and external reliability of the solution"

'. 040920 HAP-5867-CA

The use of a motorized total station equipped with automatic passi~re reflector recognition reduces considerably the I?resence of error in the observations.
Automatic target recognition {AT~t) and signal scan technologies significantly reduce sighting errors and enable twenty-four hour, day and night monitoring of targets up to approximately six kilometers away.
To investigate in near real time the validity of the adjustment model for each cycle of measurement, the ~0 Applicant invest-gated the use of a pre-adjustment using the L1 norm, which minimizes the weighted sum of the absolute residuals. The advantage of. LZ norm minimization compared to the .~_east squa~.~es is its .robustness, which means that it is less sensitive to outliers, which f~.t~
very well with the requirement for high processing speed and good quality resul~s.
A practical consideration for t~i~e monitoring n.etwor_l~:
is the number of control points considered as fixed s.nd the optimal number of connected points. For solving the norma7_ matrix based on the functior~al model., we need to have it s determinant stri~~tly greater than zero. As a minimum, there shall normally be ~t least two control points determined in 2D ~.5~.d three ir-. 1D (typAcal.ly, there would be three 3D points). Additiona=~ control points increase the reliability of_ the solution by adding redundancy. The geometry of the control is also a consideration. As always, careful network design will have a major influence on the quality of the results that are obtained from the adjustment. However, unlike with the free station method, the proposed approach allows the control to be distributed around the area by removing the need for all TPS to be able to measure three control points.

'. 040920 I3AP-587-CA

Concerning the optimal number of connected points, this can be determineca. by some empirical approach, such as having at least three connected poir-~ts per station.
However, the best approach is to use statistical inference S based on the B-method. This method provides some estimates for checking the i:nter:nal rel iabilit~r that can be used in a pre-design phase ~.o verify that the connected points will provide a sufficient contribution to the strength of the network to achie~,re the desired .result s .
Another remark concerns the numeri ca.l solution of such a linear systems. ~~~Iodern computers have sufficient computational power and memory to easily compute easily the solution to such. problems quickly. ~Iowev-er, the structure itself of the design matrix (functianal model) can help to reduce the computat i onal burden, which is advantageous for near real time processing. The question is not how to increase the processing speed, but rzow to keep the numerical stabi~Iity of the results well beyond the precision of the observations themselves and avoid insignificant numbs=_rs.
The Applicant has compared two diff=erent approaches, one based on the syrnbolic factorization of the norma=L
matrix and one on '~~he modified Gram-Cchmidt transformation,.
Both deliver the same :numerioal stab~~l~.t~ya The Gram-5'ohmidt:
transformation requires that all of the coefficients of the functional model including the zero values are stored, but with the advantage that all the variance (covariance;
values and parameters estimation a-re available simultaneously.
Figures 8 to ~_6 are diagrammat~io ~~epresentations of-_ data files, output information, and screen shots produced and by/or exploited. in the preferred embodiments.
Figure 8 sho~rs two data fi les having the same basic.

040920 HAP-58b7-CA

format, the file at the top of the figure being associated to total station '~58, and the file at the bottom of the figure being associated to total station TS9. The numerals at the lefthand column are the number suffixes of the sighting points s_ndicated in figure 5. T7-iese correspond to the sighting points sighted by the respective totaJ_ stations. The second, third. and fourth columns correspond respectively to the x, y and z coordinate values determined for the corresponding sighting points by the total station concerned.
Figure 9 srio~ws the point coordinates of the fixed reference pointsa these being indicated by their suffixe~~
on the left-hand. column, the second, third and fourth columns expressing respectively the x, y and z coordinates.
Figure 10 is a first screenshot takezn. from the monitor.
of a PC runns.ng telr=_ algorithms for implementing the preferred embodiments, showing more specificall;Y the parameters presented onscreen in connection with a selection of control points.
Figure lZ is a second screenshot, again taken from the monitor_ of a PC ru=_zning the algorithms for implementing the preferred embodime_~ts, this mime showing more specifically the parameters involved in finding cc>nnec~l~ing points.
Figure 12 is a processing report on the results of a two-dimensional (2D) least squares adjustment, using the observation eauat~_ons model. The top part of report indicates the parameters and boundary conditions, these being : the number of tot<~.1 stet ions, the number of.
connecting points, the number of equations used, the number of unknowns and the degrees of freedam.
The bottom portion of the report is a correction ana_lysss indicatin.ge the number of positive corrections, the number of nec~ati~re corrections, the number of zero corrections, the maximum correction, in metres, the minimum correction, irl metres, the variance factor, and the a posteriors standard deviatior_.
Figures 13 and 14 show the station parameters S respectively for total stations TS8 and TS9. These include the values for parameters a, b, c and d defined above, the bias scale faotor and the rotational angle. The bottom part of the figure shows the reference point identifications (in tevrns of their suffixes), together with the corresponding va~_ues for Xm and Ym in respective columns.
Figure 13 a ~ so ir...dicates the stati.oxz parameters given by the equat ions X:=a . x+b . y+c , Y =b . x- a . y-~-d .
Figure 14 is ~~ re,oresent.ation of: the connecting point~~
for the unstablE points UP3 (P3)P UP4 (P4) and UP5 (P5) identified in ~i.gure 5. Each connecting point i:~
identified in terms of the parameters ~c, Yc and Hm, where Hm is the Helrnert criterion, which provides a global quality indicator.
Figure 16 zs a representation of corrections after adjustment for' the total stations '~~58 and TS9 (in thi:~
presentation, total stations TS8 and Te~9 are dess.gnated SIB8 and SIB9 vesp~actively) . The co7_umn "target" indioate:~
the suffix of tl~E~ corresponding sigh.tir~g point, and the next two adjacent columns designate respectively the parameters Xc any ~Yc in millimetres.
Figure 17 is a diagrammatic representation of a implementation of the invention according to a second embodiment. In the example, three sighting points,, 3~ designated A, B ar~d C are implanted within an unstable zone 2D. Each sighting point A, B and C is equipped with a GPS
antenna and receiver in addition to a standard reflector 24.
The GPS receiver :?2 is arranged to be co-located with its ° 640920 HAP-5867-CA

associated reflector 2~, which is here a spherical housing type of reflector, such that the GPS coordinate values obtained. correspond substantially with those of the reflector.
The use of the precise phase-based differential GPS
receivers and processing software for. monitoring project is now very well accepted due to its ability to deliver centimetre or millimExtres-level positions in near real time. The approach described here can also use those 20 positions to provide act3_ve control points in the deformation area. In that case a GPS antenna is co-located.
with a 360° reflector and the offsets are determined. A
special procedure based on the "yhidden point target°' used in industry and surve~Ting has been adapted to ensure that the antenna phase centre and the 360° reflector centre coordinates are identical.
The measurement technology available today is mature enough to allow tile use of advanced processing models to meet and exceed the market expectations. Practical tests have been used to ~rerify this new approach.
Three control points, designated CP1, CP2 and CP3 are installed stably, outside the unstable zone 20.
Three motorised total stations, designated ST1, ST2 and ST3 are placed in a network outside the unstable zone and operate in strict local coordinate systems.
The example can correspond to a practical case of an underground civil engineering project, such as the construction of a railway tunnel. The total stations can by typically model TCA 1800 1" motorised total stations available from Leica Geosystems of Switzerland. The sighting points A, B and C constitute three connected points to provide a 3~ transfer betwween their respective GPS antenna receivers 22. The three control points CP1, CP2 and CP3 are Located at or near the entrance to the aforementioned tunnel.
Each total station ST1, ST2 and ST3 is initialised within a strict local reference frame (only approximate coordinates and orientation) with their compensator switched off and the total station's main axis unaligned to the gravity vertical.
The processing was used to prova.de a solution to bring the total station (TPS) onto a common reference frame and lfl correct for the misalignment of the vertical axes. In this example, each total station is able to measure three control points CPI, CP2 and CP3. However, trl.ls 1s not a requirement since they are able to measure common points in the deformation area.
Figure 18 is a general processing flow chart outlining the procedure which can. be implemented by the embodiments.
The point coordinates are delivered from each of the total stations or equiva~_ent used ;step S2) . Here, the chart takes the case or the three total stations A, B and C
2~ of figure 17 each depicted by a respective box.
From that data, there is performed an automatic selection ar~d extraction of all common points observed from all stations (step S~) The result of this automatic selection and extraction is used to create the design matrix, covariance (-Variance) matrix and the observation vector (step SG). For this step, there is also supplied data (step 58) in respect of the control points coordinates, which can be fixed and/or provided :oy the GPS receivers, if the latter are implemented and ut~.~lised.
From -that matrix and observation vector creation step S6, there is carried out an Iterative Least Squares adjustment (step S~0).

The result of the Least Squares djustment i~~ used to update transformation parameters and as_1 connected points coordinates (step S12}.
If the Least Sq~.xares Adjustment satisfies a determined corwergence criterion (step S14), then the transformation parameters are applied to all other measured (monitoring) points (step S16}. If this criterion. is not satisfied, the procedure returns to the Iterative Least Squares Adjustment of step S10 for another calculation cycle. The iteration is repeated unti~_ the c~ri terion of step S14 i~> satisfied.
A concrete example of how this procedure is applied to the application of figure 17 is described below.
The coordinates of the GPS antennas 22 co-located to the reflectors 22 for each of the sighting points A, B and C
(here designated "GPS A'° , '°GPS B'i and "GPS C"
respectively): are given in the table below.
.~ GpS R GPS B ~ GPS t:
i X X858.6823 856.5066 854.0894 267 . 7&42 262 . 528:L~ 266 . '7709 Z ;190.3'783 190.3775 190.3957 j In the first step the measurements from each total station (TPS) are processed independently in the reference frame of that total station. The resulting coordinates are presented in the following tables.
Station A ~ B C 3. 2 3 i X 858.6842 856.5128 854.0738 854.6375 856.5948 Y 297.737~~1262.5380 266.8269 264.1719 268.0451 Z 190.3813 190.3710 190.3888 ~~ -158.7635 259.1138 fl40920 ~-IA~-5867-CA

~~~t~.on.~ i ~ c ~. ~ ~ 3 i 858.6837j856.6073 854.0906858.9941 856.5885 '~1 297 . 7655 { 262 266 > 7 i27 264 268 . 0375 . 5299 . 3069 Z 190.3780!190.3775 190.3956 158.7420 159.1205 ~tatior A ~ ~ , C ~i 2 3 i 3 ' i I

_ 856.6059 854.0890 858.9941 854.6991 858.6830 ~' 297.7641 '262.5278 266.7714 264.3043' 264.1287 190.3783 ~~90.3775 190.3957 158.'7418 158.7700 The above coorc~~.=zates are then raced in the network adjustment as measurements to compute tie final coordinates and the transformation parameters fc>r each total station.
The results of tr~e adjustment are summari2ed below.
Summary of the adjustment-l~Tumber of Stations . 3 lvlumber of Target points . 6 Number of equations r 54 Number of parameters . 39 Degree of freedom . 1.5 Variance Factor after a~.~;ustment . 3.O1F-06 Standard Deviation Weight I3nit . 0.0017 m.
Parameters ~ts.tioxa 1 8~tat~.ox~. 2 Station 3 Scale factor 0.999'76821 0.99988355 0.99986597 Rotation -0.00031 -0.00033 -0.00032 along X
' Rotation 0.00068 0.0006t~ 0.00063 i along Y

q 040920 FiAP-5867-CA
r6 2 iRotation 10.01812 1 0.0001E> 0.00022 along Z j Shift X 4.92010 0.02621 0.05498 Shift Y X15.52807 -0.16952 -0.21656 Shift ~ 0.'70873 0.62505 0.64657 The final adjusted coordinates are computed asa Final ~. ~ C 1 2 3 X 858.6823 856.60E6 854,0894 858.9'741 854.6801 856.5676 Y 297.7642 262.5281 266.'7709 264.2950 264.1178 268.0252 Z 190.3783 190.37'75190.3957 158."7449 158.7759 159.1236 With the corresponding a posteriors standard deviation:
Quality A 4 ~ ~ C ~ 1 2 8 i 0.0000 10.0000 iG.0000 0026 0.0026 0.0025 ~y 0.0000 0.0000 0.0021 0.0021 0.0000 0.0021 0.0000 0.0000 0.0000 0.0017 0.0017 0.0016 After the processing of all coordinates, the measurements of ali total stations (TPS) are brought onto a common reference frame. The results show very good coherence and. a precis~.on well withir_ the specification of the instrument used. This practical exampJ_e shows the suitability of concept notably for deformation monitoring, where the TPS may not be placed on stable control, so that changing coordinates and alignment of the vertical axis are a concern.
The concept allows the use the of automatic total stations for monitoring when no stable monuments are available to place the instrL:ments and goad control points 040.20 HAP-5867-CA
_ g 3 ._ are in short supply. The embodiments use a combination of control and common points located in the deformation area (but which can be considered fixed during the measurement phase) to compute transformation parameters to combine the measurements from multiple TPS.
This approach allows alsoprovides a flexible way to introduce new stations into a network, even temporarily, without unnecessary long initialisation.
Considering the use of a total station unaligned to I0 the gravity vertical, this approach introduces a new concept of analytical total station. Mixing GPS
coordinates results with total station coordinates in this approach permits monitoring in areas where no stable control is available.
~5 In summary, with todays advanced instrumentation, the users ohallenge ~s to review the mathematical models used traditionally to process the observations and take full advantage of the latest technology.
The mathematical concepts presented above in a 20 simple case of two or thre total stations sighting in common a set of unstable points can be straightforwardly extrapolated to any number. IvT of total stations or equivalent surveying devices sighting a group of fixed points and unstable points extended i:n. three dimensions (x, 25 y, z) . It is not necessary for each of the N total stations to sight each of the mo~r~ng or fixed points sighted by the ether total stations. In the embodiment a moving point exploited in the bundle adjustment is sighted by two or more total stations, the latter also sighting at 30 Least one fixedly-mounted control point and the moving point becomes a valid control paint.
The timescale over which the sightings are to be effected will depend oxl the estimated rate o:E movement of '- 040920 HAP-5867-CA

the unstable points to be used and on the accuracy required.
In typical applications, the u~~stable points evolve in their position over very small distances - typically a few millimetres or centimetres - in a relatively long timescale, typically of the order of several weeks or months, possibly years. It will be noted that where time constraints allow, it is possible to replace the provision of two or more total stations operating in parallel in s. common timeframe at different locations by a single total station made to take sightings at those different positions. The invention has many applications for surveying from land-based apparatus, and is well-suited to surveying in the following situations:
- when it is required to monitor positional drifts of ~5 an identified point, the drift being caused e.g. by progressive changes in a natural contour, for instance due to earthquakes, ground compaction, erosion etc, or in a man made structure, for instance in the case of stress-induced distortions ir~ a dam or bridge, sinking foundations in a building, etc . Cften , it is inconveazient or impossible to be physically present at stash points to effect precise positional measurements at repeated time intervals to track possible positional variations. Here, the invention makes it possible to process the moving point or points to be monitored in terms of the above-described moving point (s) , thereby allowing highly accurate measurements to be obtained; and/or - when the presence of unstable areas in a site to be surveyed does not make it practically possible to install a sufficient number of stably-mounted Control points for sighting from differerit surveying points in the site. Here, the invention makes it possible to install exploitable control points even on the unstable areas of the site, these unstable points nevertheless becoming effective as reference control points by virtue of the approach taught by the present invention. In this way, the total.. area of the site, i.ncludir~g the moving ~onesr can be adequately surveyed.
~'he invewti:n has many benefits including:
- the fact that the coordinates of 'anstable points can be computed from sightings generating completely different local coordinate :~ y and z values, 1~ - it allows stations making thE~ sightir.~gs to be set even with the same mutual coordine.tes, - it can work with a minimum number of control points and some common points located in a deformation area, - in the preferred embodiment, it can be implemented 15 with a model adjusted by a least squares technique which provides both i) coordinates for the common points and ii) parameters for each station, - it can be implemented as a da'r_a snooping procedure applicable to detect any unstable point measured by several 20 stations, either simultaneously or within a predetermined timescale (in which case a same station can be used to provide sightings at different locations, as explained above ) , - all of the other points computed from each station 25 can be transformed using the station°s parameters, - it can be implementea. a mode which uses only the coordinates, and not the raw observations (angles and distance), - it can provide a model which also handles Z
3~ coordinate to prov~_de a 2.5D modelling, - with all the coordinates in the same datum, it enabl es to perform a conventional 3I3 adjustment using the raw observations if needed.

The illustrated examples are based on an installed "network" of motorized total stations around (and on) a site for monitoring unstable points. The stations°
coordinates are re-computed at givers intervals by using some control points located outside the unstable zone. At least some stations carp measure some selected common points in the unstable zone substantially at the same time (ar within a time interval in which a movement in the unstable 1~ area is sufficierstly small), as well as some control points.
The thus-obtained information is used for the processing of each station.
It shall be clear to the skilled person that the invention can be implemented in many different ways and in 95 many different applications. depending on applications, the model can be applied zn a one, two o:e~ three-dimensional coordinate system. In particular, many va.riat:Lons are possible as a function of the sc>ftware, firmware and hardware possibilities at disposal.

Claims (26)

What is claimed is:

1. Method of ground-based surveying on a site (2) which comprises an unstable zone (60;
20) and at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone, in which method at least one surveying device (TS8, TS9; ST1 ST3) is used to acquire positional data by sighting at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3), characterised in that it further comprises the steps of:
providing at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), using said surveying device(s) (TS8, TS9; ST1 ST3) to acquire positional data by sighting said at least one sighting point (UP3 UP5; A C) that is located within said unstable zone (60; 20), and combining the positional data acquired from: i) said at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone and ii) at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), to produce a positional reference for said surveying device(s).

2. Method according to claim 1, wherein more than one surveying device (TS8, TS9; ST1 ST3) is used, and wherein said more than one surveying devices sight in common at least one common sighting point (UP3 UP5; A C) that is located in said unstable zone (60; 20), and wherein said positional data from the common sighting point(s) acquired by said surveying devices are used as positional data in said combining step.

3. Method according to claim 1, wherein said combining step comprises performing a bundle adjustment.

4. Method according to claim 1, wherein said combining step comprises performing a least squares adjustment on said positional data.

5. Method according to claim 1, wherein said positional reference is a coordinate system of said control point(s) (FCP1, FCP2, FCP6, FCP7; CP1 CP3) that are placed outside said unstable zone, said combining step converting the positional data of said sighting point(s) (UP3 UP5; A
C) within said unstable zone (60; 20) into positional data of said coordinate system of said control point(s).

6. Method according to claim 1, wherein said surveying device(s) (TS8, TS9;
ST1 ST3) is/are used without resorting to a physical alignment of its/their main axis with respect to the direction of gravity, said method comprising a step of computing rotational angles of a mechanical axis of said surveying device(s).

7. Method according to claim 1, wherein surveying device(s) (TS8, TS9; ST1 ST3) is/are used in a full three-dimensional reference frame.

8. Method according to claim 1, further comprising a step of associating a GPS (global positioning by satellite) device (22) with at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20) to acquire coordinate values thereof, and wherein said GPS coordinate values are exploited in said combining step.

9. Method according to claim 1, wherein: said control point(s) have at least one known position coordinate ((XL Y1), (X2, Y2), (X6, Y6), (X7, Y7)) in a first coordinate system (X,Y), said at least one surveying device (TS8, TS9) is placed at a chosen location in said site to obtain at least one relative coordinate value of at least one said control point relative to the location of said surveying device, said said at least one surveying device (TS8, TS9) is used at said chosen location to obtain relative coordinate data of said sighting point(s) (UP3 UP5) within said unstable zone relative to the location of said surveying device, and in said combining step, the position(s), in said first coordinate system (X,Y), of said sighting point(s) located in said unstable zone are determined on the basis of: said relative coordinate(s) of said sighting point(s) located in said unstable zone relative to said chosen location(s), said relative coordinate(s) of said control point(s) outside said unstable zone relative to said chosen location(s), and said position coordinate(s) ((X1,Y1), (X2, Y2), (X6, Y6), (X7, Y7)) of said of said control point(s) outside said unstable zone in said first coordinate system.

10. Method according to claim 1, wherein the number of sighting control point(s) used is established to be equal to, or greater than, the minimum to keep a datum fixed, said minimum being number of points being available for a network of sighting points used in the surveyed site.

11. Method according to claim 1, wherein at least one sighting point (UP3 UP5) within said unstable zone (60) is sighted from more than one chosen location of said surveying device (TS8, TS9), thereby to acquire a respective relative position value of that sighting point (UP3 UP5) from each said chosen location, and wherein said respective relative position values are used in said combining step.

12. Method according to claim 1, wherein at least one sighting point (UP3 UP5) within said unstable zone (60) is sighted as a common sighting point by a plurality of surveying devices (TS8, TS9) at different locations of said site (2), and wherein position data indicating the position of that common sighting point (UP3 UP5) relative to the position of each a said plurality of surveying devices is used in said combining step.

13. Method according to claim 1, wherein said combining step implements a model adjusted by a least squares method.

14. Method according to claim 9, wherein said combining step implements a model adjusted by a least squares method that is used to provide: coordinates for a said at least one sighting point (UP3--UP3) located in said unstable zone (60), and parameters of said surveying device (TS8, TS9) at said chosen location.

15. Method according to claim 1, wherein said combining step takes as position parameters only the coordinates of said at least one sighting point (UP3 UP5) in a coordinate system of said surveying device (TS8, TS9).

16. Method according to claim 1, wherein more than one surveying device (TS8, TS9) is used on said site (2), whereby said more than one surveying devices make sightings of a same sighting point (UP3 UP3) and obtain position data of the latter within a common time frame.

17. Method according to claim 1, wherein a total station (TS8, TS9) is used as said surveying device.

18. Method according to claim 9, wherein said combining step is implemented with a coordinate transformation equation establishing a relationship between:
relative coordinate data of sighted points both within and outside said unstable zone (60), established on a relative coordinate system (x,y) of said at least one surveying device (TS8, TS9), and a skew angle (a) between the set of axes of said first coordinate system (X,Y) and said relative coordinate system (x,y).

19. Method according to claim 18, wherein said relationship is established in determinant form.

20. Method according to claim 19, wherein said relationship comprises a first determinant containing relative coordinate data of at least one sighting point (UP3 UP5) located in said unstable zone (60), determined from two or more surveying positions, operating as a multiplier on a column vector of numerical parameters of said surveying device(s) (TS8, TS9).

21. The method according to claim 1 including the step of establishing the position of at least one sighting point (UP3 UP5) located in an unstable zone (60) in terms of a position on a coordinate grid system which also maps fixed control points (CP), whereby said at least one sighting point (UP3 UP5) located in an unstable zone (60) becomes exploitable as a sighting control point.

22. The method according to claim 1 including the step of establishing the position of at least one sighting point (UP3 UPS) located in the unstable zone (60) in terms of a position on a coordinate grid system to monitor evolutions in position of said at least one sighting point.

23. System for ground-based surveying on a site (2) which comprises an unstable zone (60;
20) and at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone, comprising at least one surveying device (TS8, TS9; ST1 ST3) arranged to acquire positional data by sighting least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3), characterised in that it further comprises: at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), at least one said surveying device (TS8, TS9; ST1 ST3) being arranged to acquire positional data by sighting at least said sighting point within said unstable zone, and means for combining the positional data acquired from: i) said at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone and ii) at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), to produce a positional reference for said surveying device(s).

24. System according to claim 23, further configured to execute a method of ground-based surveying on a site (2) which comprises an unstable zone (60; 20) and at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone, in which method at least one surveying device (TS8, TS9; ST1 ST3) is used to acquire positional data by sighting least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3), characterised in that it further comprises the steps of: providing at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), using said surveying device(s) (TS8, TS9; ST1 ST3) to acquire positional data by sighting said at least one sighting point (UP3 UP5; A C) that is located within said unstable zone (60; 20), and combining the positional data acquired from: i) said at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone and ii) at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), to produce a positional reference for said surveying device(s), wherein more than one surveying device (TS8, TS9; ST1 ST3) is used, and wherein a plurality of surveying devices sight in common at least one common sighting point (UP3 UP5; A C) that is located in said unstable zone (60; 20), and wherein said positional data from the common sighting point(s) acquired by said surveying devices are used as positional data in said combining step.

25. A computer readable non-transitory medium having stored thereon computer executable code which, when run on a data processor, executes the method of claim 1.

26. A computer readable non-transitory medium according to claim 25, which, when run on the data processor, executes calculations in respect of a method of ground-based surveying on a site (2) which comprises an unstable zone (60; 20) and at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone, in which method at least one surveying device (TS8, TS9; ST1 ST3) is used to acquire positional data by sighting least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3), characterised in that it further comprises the steps of: providing at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), using said surveying device(s) (TS8, TS9; ST1 ST3) to acquire positional data by sighting said at least one sighting point (UP3 UP5; A C) that is located within said unstable zone (60; 20), and combining the positional data acquired from: i) said at least one control point (FCP1, FCP2, FCP6, FCP7; CP1 CP3) placed outside said unstable zone and ii) at least one sighting point (UP3 UP5; A C) within said unstable zone (60; 20), to produce a positional reference for said surveying device(s).