The subject of the present invention relates to a method and a system making it possible to perform a global collaborative readjustment taking into account a set of mobile units belonging to one and the same group as well as landmarks of unknown positions, but which are visible to several mobile units.
The invention can be used for cartographic readjustment with conventional tools for taking readings (angular reading by visual pointing and/or distance reading with a telemeter) on geographical landmarks but also for locating one or more radio transmitters with mobile radio units configured to take readings (radio goniometry and/or telemetry).
The word “landmark” designates a notable fixed object of the known environment of the system.
By extension, the word “radio landmark” designates a radio transmitter.
The latter is not known to the system which seeks to locate it.
The term group is used to designate a set of mobile units, or platforms which are pro- grammed to communicate with one another and to exchange information.
The word “visible” is used to specify that a landmark is detected (visually or by radio if it is a radio landmark) and that the platform is capable of taking readings on this landmark.
In the rest of the description, the word node designates equivalently a platform and/or a landmark.
The term readjustment is used to designate a repositioning of a platform.
Landmark-based readjustment is a known technique for allowing a mobile node to read- just its position, that is to say improve the accuracy of its geolocation.
One of the technical problems posed is the inability for readjustment of nodes or of groups of nodes when the positions of the landmarks are not known.
Landmark-based readjustment relies on the measurement of direction of landmarks (go- niometry), optionally supplemented with distance measurements (telemetry) and a geolocation algorithm which optionally takes into account the accuracies of measurements and, more rarely,
the position inaccuracy of the landmarks.
The inaccuracies are generally characterized by the person skilled in the art by an uncertainty interval, a probable circular error “Circular Error Prob- ability, CEP” at x % or by a variance.
Figure 1 illustrates a solution known from the prior art for the readjustment of a single platform PTF, on landmarks of known position.
The technique performs a relocation of a plat-
form PTF; by triangulation on three landmarks AM, of known positions by taking a reading of the directions of the landmarks, followed by a triangulation.
The technical teaching of the patent application US 2012/0081248 Al relates to a system and a method to locate a mobile station.
For this purpose, US 2012/0081248 Al performs tele- metry measurements on the received RF signals, classifies the RF signals according to a predeter-
mined parameter criterion and, depending on the performed telemetry measurements and the clas- sification of the received signals, the method will determine a position of a mobile.
The technical teaching of the patent application US20110059752 A1 describes a method for estimating the location of mobile stations in a network.
The method is limited to cooperative radio transmitters on which distance measurements are performed.
One of the drawbacks of the schemes known from the prior art is the inability to use the landmark if the position of the latter is not known.
The invention relates to a method of collaborative readjustment according to claim 1. According to one embodiment, the state vector is estimated by maximizing the probabil- ity: 1 1 pa plmju) = TF än CP -3lm- ru) [me — ka) with N being the Ca of the observation vector, B the covariance matrix of the measurements, Hu) , the global observation function of u, T the transpose.
The state vector can also be estimated by minimizing the quadratic form: T OG) =[m— ha] Bm hw] with N being the dimension of the observation vector, B the covariance matrix of the measurements, h(x) , the global observation function of u, T the transpose.
In this case, the Gauss-Newton algorithm is used and the method executes the following steps: Expansion of the state vector A(u) to first order: h(a) = bay) + Hur) Calculation of the Jacobian matrix H, of dimension (2M+L+K, 2M) of the global obser- vation function. dx, dy, with the position observation sub-matrix: yoy Fie TÄ; MTX Ni TÄ, i ed dt d; d; where dy = J n) +) with the distances observation sub-matrix:
H, = | on laadi lx oy, ) Jd, da x dy, Ax oy Hd, .. : where dy =, fe.) + —y,) - Initialization of H, with the 2M first components are initialized with the initial positions of the platforms; - the 21 last components are initialized by a heuristic with the num- ber of landmarks of unknown positions M, = | x id Definition of a maximum likelihood estimator by H = H, + (H "BH YH B |m - h(u,)] after linearization of the vector H,, one iterates by making a linear estimation and by defining the stopping criterion by a threshold on the norm of ee; —2:4]| corresponding to the set of the nodes so as to obtain a vector comprising: - the set of the position re-estimations for all the platforms, - a position estimation for all the landmarks. The method according to the invention is notably used to estimate positions of one or more transmitters in a network of mobile radiogoniometers while taking into account the inac- curacies in the positions of the platforms. The invention also relates to a system according to claim 4. A platform comprises, for example, a database. Other characteristics and advantages of the present invention will become better appar- ent on reading the description of exemplary embodiments given by way of non-limiting illustra- tion, together with the appended figures which represent:
. Figure 1, a solution known from the prior art, . Figure 2, a basic diagram of the method and of the system ac- cording to the invention,
. Figure 3, an example of details of the modules fitted to the plat- forms and the landmarks allowing the implementation of the invention, and
. Figure 4, a variant embodiment of the method for locating trans- mitters from mobile vehicles.
The method according to this invention consists, in particular, in performing simultan- cous collaborative readjustments.
The principle assumes the presence of at least one landmark perceived by at least two platforms of the collaborative network.
The re-estimation of position of the platforms is performed jointly with the landmark position estimation, for example by imple- menting a weighted least squares criterion, or a global maximum likelihood technique, these tech- niques being well known to the person skilled in the art.
Taking global account of the constraints of common landmarks, i.e., ones seen by at least two platforms, even if the positions of these landmarks are unknown, makes it possible to increase geolocation accuracy whilst no “conven-
tional” individual readjustment is possible on these landmarks of unknown positions.
Figure 2 represents an exemplary application of the invention in a group comprising at least two platforms 10,, 10,, observing two landmarks 20,, 20, of unknown positions.
The plat- forms exchange information enabling them to identify these landmarks and to ascertain the ones that they observe in common.
The identification of a landmark can be carried out through a de- scription of the landmark, a photo, etc.
Figure 3 illustrates an example of modules and of elements present in a platform and optionally in a radio landmark, which are used to implement the method according to the inven- tion.
A platform or node 10i (10, 10,) comprises at least one first communication module 11 configured to receive information or data originating from one or more other platforms, and to send information to this or these same platforms.
It also comprises a module for measuring dis- tances 12, and a device for measuring angles 13, a device 14 allowing an estimation of positions and a readjustment module 16 for readjusting the position of the platforms (for example a pro- cessor) having the function in particular of recalculating the position of the platforms and at the same time of calculating the position of a landmark, the initial position of the landmark not being known.
The landmarks utilized for a readjustment of a platform can be common to several plat- forms, i.e., the word common signifying that the platforms of a communication group will use this(these) same landmark(s) of unknown positions to recalculate their position with better accur- acy and readjust themselves, i.e., repositioning in a more accurate manner.
The readjustment in- formation (new positions obtained after the implementation of the method) will be transmitted to the platforms forming part of one and the same group so as to enable the updating of their data- base 15, by the communication medium.
In the particular case of a radio landmark 20,, the latter comprises at least one transmitter 21 (represented dashed in the figure) configured to transmit a radio signal allowing the platforms to perform distance or angle measurements on this signal, according to a principle known to the
— person skilled in the art.
One of the objectives of the present invention is to enable a platform to know its position with better accuracy so as to reposition itself.
The corrected position information for the readjus- ted platform can thereafter be transmitted to the other platforms which are in communication with it.
At the same time, the position of the landmark of initially unknown position will be calculated.
In the given example which follows, the platforms communicate by radio links.
The platforms can exchange information on the landmarks (identifier, position), label them (i.e. allot them a unique identifier at the level of the platform group) and agree to establish a 5 list of landmarks in common L {landmarks in common}. In order to properly elucidate the steps of the method which are implemented by the invention, the example which follows is given in the case of a system comprising two platforms, 101, 10), two unknown landmarks 20,, 20,, and by implementing distance and goniometry meas- urements on both landmarks.
For the calculation of a more accurate positioning, the following data is considered: : the coordinates of the platform 10,, which are known with an accuracy , where the letter designates the standard deviation, : the coordinates of the platform 10), which are known with an accuracy , the measurement of distance of the platform 10; on the landmark 20; with an accuracy , with the measurement of angle of the platform 10; on the landmark 20; with an accuracy , . Of course, without departing from the scope of the invention, the description which fol- lows remains valid in the case of two platforms and a single unknown landmark in common for executing the position readjustment.
The devices of the platforms have each performed the following measurements: e The device for measuring positions estimates the two initial posi- tions , for the platforms 10), 10,, and their respective covariances, e The device for measuring distances determines the four distance measurements (measurement between a platform and a landmark, for each platform having a landmark in common 10) 20,), 10; 20;), 10, 20;), 10, 20,)), and their respect- ive variances.
The variances come into the construction of the covariance matrix B of the measurement vector m: B= E[(m-E(m)).(m-E(m))'] = E(m.m)-E(m).FE(m)', where E des- ignates the mathematical expectation.
The ith sigma, of the diagonal of B, corresponds to the variance of the ith measurement considered and the other (non-diagonal) cross terms of the covariance matrix are zero under the assumption of independences of the measurements, e The device for measuring angles will determine the four angle measurements (10; 202), 10; 20), 10, 201), 102 20,)) and their respective variances.
From these position, distance and angle measurements, the method will estimate the position of at least one platform more accurately, thereby allowing its readjustment, in particular in case of overly significant drift with respect to its initial position.
In the example which follows,
the processing relies on a position estimation implementing a criterion of maximum likelihood type, well known to the person skilled in the art.
The state vector that the method seeks to estimate consists of the set of the positions of the N platforms and the positions of the landmarks, even if these latter positions are not known initially.
We consider a state vector # consisting of the positions of the platforms (in the ex- ample: two platforms) and of the landmarks of unknown positions (in the example: two land- marks), i.e. in the example: with ,, and the sub-vectors containing the coordinates of the posi- tions.
We shall see below how this state vector is initialized.
In a general manner, we have: - M measurements of positions of the platforms, - L measurements of angles available on the nodes, at most one angle measurement for each pair of entities (platform, landmark), - K measurements of distances available on the nodes.
The number of unknown landmarks is I and the number of nodes is M+1. The observation vector m of dimension N=2M+L+K consists of the set of these meas- urements: Bh i mel i m, | W . ~*~, each observation FM, of a position corresponds to two observations X. and Vi.
The state vector H, namely the vector of the positions of the nodes= platforms and land- marks, is of dimension 2(M+D.
The measurements are assumed independent centred Gaussian and the expression for the probability density of the measurements is: 1 1 p? pm) = ——=n=|—->|[m—u)] Bm hw) Lgl? 2 where h() is the olkBAVBIB ation furiction, explained hereinafter:
The expression for the covariance matrix of the measurement noise B, of dimension 2M+L+K, is:
i ort a i i a 7! :
If the coordinates of the positions of certain platforms are not independent and are known with a covariance in the positions x,y, the sub-matrices of covariance of positions will be of the form | o? | rather than {o} © |.
a. o . 0 oi . . . The global Observation functiofi-h: m=h(), with m being the observation vector, the state vector of the positions of the nodes (platform and/or landmark) consists: - of the observation function h, for the positions, - of the observation function h, for the angles, - of the observation function hy for the distances. The notion of observation function for position h,, for angle h, and for distance ha is well known to the person skilled in the art and will not be explained. If a node i with coordinates Mi (xi, yi) is observed in a non-noisy manner, then the ob- servation function for the positions is: If the direction of a node j with coordinates Mj (xj, yj) is observed in a non-noisy manner from a node Mi (xi, yi), the observation function for the angles is: If the distance of a node j with coordinates Mj (xj, yj) is observed in a non-noisy manner from a node Mi (xi, yi) (distance between the node i and the node j), the observation function for the distances is: = Jo) +(v, yj) : Under the previous noise assumptions (noisy observation with centred Gaussian noise), the position vector & can be estimated in an optimal manner with a maximum likelihood cri- terion. The criterion then consists in maximizing the probability pm) or equivalently in min- imizing the quadratic form (Xa) = [272 — RG] BB" [172 — HG] : Accordingly, it is possible to use the Gauss-Newton algorithm, well known to those in the art, and to execute the steps described hereinafter. A first-order expansion of the state vector A(x) is performed: h(a) = (uy) + H(u— up) The Jacobian matrix H, of dimension (2M+L+K, 2M) of the global observation function is calculated: : ön ön io dx, de, 0;
The matrix H consists of the Jacobian sub-matrices of the observation functions h, h, and ha: The position observations lead to the following sub-matrices: 10 ; O i i - CE] The angular observations lead to the following sub-matrices: MTM, EX, yy, X =X di di d; i, where dy = ax) +) The distance observations lead to the following sub-matrices: H, =i... ~(x, -X, j ld, “(x - ¥.} fd, ne — CRIES ~(¥ — vy Md, eed where dy = J xP ng.
The vector is initialized in the following manner: - the 2M first components are initialized with the initial positions of the platforms (position measurements),
- the 21 last components are initialized by a heuristic, such as, for example, the intersections of the directions given by the angle measurements or the inter- sections of the circles given by the distance measurements, or else by pseudo lineariza-
tion.
This type of heuristic for initializing an unknown state is well known to the person skilled in the art: Ea Misi;
For a linearization of the problem in M, , which linearization is explained further on in the description, the gradient of the criterion Q may be written:
VO=2H B'[m—h(u,)— H(u—m,)| with 7 signifying the transpose, and the expression for the maximum likelihood estimator is:
i=u + (HB HY HB [mh H=M, + [mm — ku].
The max likelihood estimator may then be written:
H =u, + AF estimation over all the nodes, i. groups together all the position es- timations for all the nodes, with:
j y | ay - Co < dy odo MTA Ft Ma ; Lot J
TndrrY!rgt
N A-(H'B'H) H'B'
a, a corresponds to the residual, that is to say to the difference between the angle measurements and the theoretical values calculated with the observation function by taking the estimated positions as position.
The value of the covariance matrix of the estimator is:
T 1 P=(g"s)'
This estimation H; =u + AT can thereafter be iterated by making a linear estimation and by defining the stopping criterion by a threshold on the norm of as; 2; | corresponding to the set of the nodes.
Ultimately, the execution of the steps of the method generates a vector comprising:
- all the position re-estimations for all the platforms, - a position estimation for all the landmarks.
The first two components of the estimated value of the vector u give the estimation of the position of the first node and the components and give the components x, y of the jth node.
This updated position information for the platforms corresponds to the readjustment of a platform and is transmitted from a readjusted platform to the other platforms so as to optimize the situation awareness of the system, i.e., more-accurate knowledge of the positions of the platforms.
Without departing from the scope of the invention, it is possible to apply it to the loca- tion of transmitters from measurement stations whose positions are inaccurate.
The transmitters are then considered to be radio landmarks and the measurement stations to be platforms.
In this application, it is not the position readjustment of the platforms that will be sought but an estima-
tion of the position of the landmark and of its accuracy taking into account the inaccuracies in position of the platforms.
This is particularly useful for mobile goniometry networks in which the measurement stations are mobile with often significant position inaccuracies.
The latter are not taken into account in conventional triangulation methods, which may lead to significant overes- timations of accuracy and therefore to erroneous locations of transmitters.
Application of the present invention makes it possible to carry out correct estimations of transmitter locations with an estimation compliant with the accuracy of this estimation.
In order to illustrate this case of application, an example consisting only of two plat- forms seeking to locate a radio transmitter or a landmark is explained.
In this example: with the sub-vectors containing the coordinates of the positions of the two platforms.
It is assumed that each platform is a mobile goniometry station performing an angle measurement on the radio transmitter.
A first numerical example considers the following data: M=4
: (0,0) coordinates of the platform 10; which are known with an accuracy x=y= 50 m
: (2000,0) coordinates of the platform 10, which are known with an accuracy
: situated at (1000,1000) coordinates of the landmark 20; of a position unknown to the station network
: situated at (1000,-1000) coordinates of the landmark 20, of a position unknown to the station network
The standard deviation of accuracy (in x and in y) of the platforms after readjustment is
36 m, i.e. a gain of the order of 30 % on the initial accuracy.
Let us recall that individual readjust- ment is not possible on a landmark of unknown position.
Figure 4 illustrates a second numerical example with two mobile platforms seeking to locate a radio transmitter.
With two platforms and goniometry measurements on the radio trans- mitter, the method makes it possible to obtain a location taking into account the inaccuracies in
— the positions of the platforms given hereinafter.
Let:
be the coordinates of the platform 10, which are known with an accuracy be the coordinates of the platform 10, which are known with an accuracy
Aj; be the angle measurement of the platform 10; on the transmitter (landmark) 20; with an accuracy
Aj; be the angle measurement of the platform 10, on the transmitter 20, with an accur-
acy °
The available measurements are: e The two initial estimations of position: , and their respective covariances, o The two measurements of angles Aj; and A and their respective variances.
The DRMS accuracy (sguare root of the trace of the covariance matrix) of location (in x and in y) of the transmitter is 5300 m when taking into account the inaccuracies of positions of the mobile goniometers whilst it would be 1700 m with a conventional triangulation method (which considers the positions of the goniometers as anchors of perfectly known positions).
The method according to the invention advantageously makes it possible after readjust- ment to obtain positions of mobile units within a group with high accuracy.
It also makes it pos- sible to correctly estimate the accuracy of location of transmitters from radiomobile measurement stations of inaccurate positions.