REALIGNMENT METHOD BASED ON A PLURALITY OF REFERENCE POINTS AND ASSOCIATED COMPUTER PROGRAM PRODUCT AND REALIGNMENT DEVICE

Description

[0001] The present invention relates to a method of registration on a plurality of landmarks.

[0002] The present invention also relates to a computer program product and a recalibration device associated with this recalibration method.

[0003] More particularly, the invention is applicable when geolocating a mobile device, in particular a mobile machine such as a vehicle or an aircraft, using landmarks.

[0004] By “landmark” we mean any natural or artificial object that can be located by the mobile device and whose position is known or determinable.

[0005] According to methods already known in the state of the art, it is possible to geolocate a mobile device or to recalibrate its position determined by another means, using a plurality of landmarks.

[0006] To do this, the mobile device is generally able to measure directions (azimuths or bearings) relative to the landmarks and / or distances to them. Thus, by analyzing these measurements and the known positions of the landmarks, it is generally possible to determine or specify the position of the mobile device. More specifically, when heading information is not available, or when it is of poor precision, the device can geolocate itself using so-called bearing methods which exploit measurements of angular differences between the landmarks.

[0007] More precisely, the known bearing methods are based on angular measurements with respect to three landmarks and exploit the angular differences observed between these landmarks, either measured directly or obtained by difference between bearing measurements. Among these methods, we find in particular the Delambre method, the barycenter method, the Italian bearing method, the two capable arcs method, etc.

[0008] However, known methods are generally limited to the use of three landmarks or to the combination of results obtained by different triplets of landmarks whose positions are supposedly precisely known. Moreover, they do not directly provide an estimate of the geolocation accuracy.

[0009] WO2015078000 A1 relates to a terminal positioning method, a positioning server and a terminal, the method comprising: receiving N first wave arrival angles measured by the terminal, the first arrival angle being a direction angle of a downlink signal reaching the terminal relative to the current direction of the terminal; the N first wave arrival angles respectively correspond to N transmission points, N being an integer greater than or equal to 2; determining the location of the terminal according to the N first wave arrival angles and the location information of the N transmission points.

[0010] The aim of the present invention is to propose a solution for geolocating a mobile device by simultaneously exploiting any number of landmarks with imprecise positions but whose position uncertainty is known (this uncertainty may result from the dimensions of the landmark and / or the imprecision of the position measurement), with an optimal global statistical approach (taking into account both inaccuracies in the position of the landmarks and inaccuracies in the direction measurements, while remaining efficient and without bias).

[0011] To this end, the invention relates to a recalibration method in accordance with claim 1.

[0012] According to further advantageous aspects of the invention, the method comprises features of claims 2 to 7.

[0013] The present invention also relates to a computer program product comprising software instructions which, when implemented by computer equipment, implement the method as defined above.

[0014] The present invention also relates to a device for resetting to a plurality of landmarks when geolocating a mobile device, comprising technical means adapted to implement the method as defined previously.

[0015] These characteristics and advantages of the invention will appear on reading the description which follows, given solely as a non-limiting example, and made with reference to the appended drawings, in which: [ Figure 1 ] there figure 1 is a schematic view of a resetting device according to the invention; [ Figure 2 ] there figure 2is a flowchart of a recalibration method according to the invention, the method being implemented by the recalibration device of the figure 1 ; And [ Figure 3 ] there figure 3 is a schematic view illustrating the implementation of one of the steps of the process of the figure 2 .

[0016] In fact, it has been represented on the figure 1 , a resetting device 10 according to the invention capable of determining or specifying the position of a mobile device 12 at each instant. The mobile device 12 is capable of moving for example according to two or three degrees of freedom for example in a terrestrial reference frame.

[0017] According to an exemplary embodiment, the mobile device 12 is a mobile machine, such as for example a land vehicle or an aircraft, carrying the recalibration device 10. In the case of an aircraft, it may be an airplane or a helicopter pilotable by an operator and / or by an avionics system from the latter, or a drone pilotable from a remote control center by an operator and / or by a suitable avionics system.

[0018] According to another exemplary embodiment, the mobile device 12 is carried by an operator or by any other user and has, for example, a mobile telephone. In this case, the resetting device 10 is, for example, integrated into the mobile device 12.

[0019] The recalibration device 10 is capable of determining the position of the mobile device 12 using sighting measurements taken relative to the landmarks 14-1,...,14-N by at least some of the sensors of a plurality of sensors 16.

[0020] Each landmark 14-1,...,14-N presents a natural or artificial object arranged for example in a fixed manner on the Earth's surface according to a known position with a precision also known and identifiable from the mobile device 12. Thus, each landmark presents for example a pylon, a wind turbine, a lighthouse, a building, a mountain, a rock, etc.

[0021] Each landmark 14-1,...,14-N is for example identifiable by its own identifier. Furthermore, according to a particular embodiment of the invention, the identifier of each landmark 14-1,...,14-N makes it possible to obtain its position using for example a position database provided for this purpose. Such a database may be publicly accessible or have restricted access.

[0022] At least some of the sensors 16 are capable of determining aiming measurements in relation to each of the landmarks 14-1,...,14-N.

[0023] Advantageously according to the invention, each aiming measurement determined by the corresponding sensors 16 corresponds to a bearing measurement relative to a reference frame.

[0024] The reference frame is for example linked to the mobile device 12 and in the case of a mobile machine, has for example an axis coinciding with the heading of this machine. According to another example, the reference frame has a terrestrial reference frame.

[0025] As can be seen on the figure 1 , the recalibration device 10 comprises an input module 21, a calculation module 22 and an output module 23.

[0026] The input module 21 is connected to the sensors 16 and is capable of acquiring all of the measurements determined by these sensors 16. According to an exemplary embodiment, the input module 21 is further connected to at least one system, for example an on-board system, capable of providing a known position of the mobile device 12. This position may for example correspond to the last known position of the mobile device 12 or the position which needs to be specified.

[0027] The calculation module 22 is capable of analyzing the data acquired by the input module 21 in order to provide a result determining or specifying the position of the mobile device 12.

[0028] Finally, the output module 23 is capable of providing the result determined by the calculation module 22 to any interested system. For example, the output module 23 is capable of providing a display screen with the determined position of the mobile device 12 to display it. According to another example, the output module 23 is capable of providing this position, for example, to a precision device capable of comparing this position with that provided, for example, by a GNSS-type geolocation system, in order to provide a precise position.

[0029] Each of the modules 21 to 23 is, for example, in the form of software implemented by a suitable processor. Alternatively, at least one of these modules 21 to 23 is at least partially in the form of a programmable logic circuit, such as an FPGA (Field Programmable Gate Array) type circuit.

[0030] The recalibration process will now be explained with reference to the figure 2presenting an organizational chart of its stages and the figure 3 illustrating the implementation of at least one step of this process.

[0031] Initially, it is considered that the mobile device 12 moves near the landmarks 14-1, ..., 14-N and that in a fixed position, the sensors 16 carry out M bearing measurements with respect to at least some of the landmarks 14-1, ..., 14-N. For example, the sensors 16 carry out a bearing measurement for each of the M landmarks visible by these sensors 16. Advantageously, according to the invention, the number M can be strictly greater than 3 and, in general, can correspond to any number less than or equal to N.

[0032] During an initial step 110, the input module 21 acquires all of the M bearing measurements and transmits them to the calculation module 22. The calculation module 22 forms from these measurements a vector of bearing measurements subsequently denoted by AOA.

[0033] During the same step 110, the input module 21 also acquires the positions of the landmarks 14-1, ..., 14-N as well as the details associated with these positions. These data come, for example, from a database relating to the landmarks, as defined previously.

[0034] In the next step 120, the calculation module 22 transforms the vector of deposit measurements AOA into a vector of angular deviations ADOA. Each component ADOA ij of this vector of angular deviations ADOA corresponds to an angular difference between a pair of landmarks. In other words: ADOA ij = AOA i − AOA j , Or AOA And AOA j are different components of the measurement vector AOA.

[0035] So the component ADOA ij corresponds to an angular difference between a pair of landmarks corresponding to the indices i And j. Subsequently, by "pair of landmarks" we mean two landmarks for which an angular separation ADOA ijhas been determined. Thus, in the example described, M - 1 pairs of landmarks are therefore formed during step 120.

[0036] Generally speaking, ADOA = D . AOA , where D is a transition matrix.

[0037] The transition matrix D is for example a matrix of size (M - 1, M ) and rank M - 1.

[0038] Among all the possibilities, the matrix D is advantageously chosen according to the invention as follows: D = 1 − 1 0 … 0 0 1 − 1 ⋱ ⋮ ⋮ ⋱ ⋱ ⋱ 0 0 0 … 1 − 1 ⋅

[0039] In this case, each component ADOA ij corresponds to an angular distance between a pair of neighboring landmarks according to the order defined by the numbering of these landmarks. According to an exemplary embodiment, the landmarks are numbered according to their geographical position. This allows measurements to be carried out on a single rotation of the angular pointing instrument while respecting a pseudo-symmetry in the exploitation of the bearing measurements.

[0040] During the next step 130, which can be implemented before steps 110 and 120, the calculation module 22 verifies an observability criterion.

[0041] In particular, during this step, the calculation module 22 checks whether the respective positions of the landmarks 14-1 to 14-N and a known position of the mobile device 12 make it possible to calculate or specify a new position of the mobile device 12.

[0042] For this, the calculation module 22 determines a regression circle with center ( x̂ c , ŷ c ) and radius R̂ c This circle is determined by minimizing a mean square deviation criterion.

[0043] In other words, this circle is determined using the following expression: x ^ c y ^ c R ^ c = min x c y c R c C x ^ c y ^ c R ^ c = = min x c y c R c 1 ∑ i = 0 M 1 σ i 2 ∑ i = 0 M 1 σ i 2 x i − x c 2 + y i − y c 2 − R c 2 , Or x 0 , y0 is the known position of the mobile device 12, for example in a terrestrial reference frame; σ 0 is the standard deviation of the known position of the mobile device 12 (here we consider location accuracies defined by probable circular errors “ECP” at 1 sigma); ( xi, yi ) is the position of the landmark associated with the index i, 1 ≤ i ≤ M in the same terrestrial reference point; and σ i is the standard deviation of the position of the landmark associated with the index i .

[0044] This minimum is determined for example by applying a gradient descent method of the function C , that is, using the expressions ∂ C ∂ x c , ∂ C ∂ y c And ∂ C ∂ R c .

[0045] The observability criterion is met when at least one of the positions of the landmarks 14-1 to 14-N or the known position of the mobile device 12 is at least a predetermined distance from the regression circle. This then means that these positions do not belong to the same circle and the system composed of the landmarks 14-1 to 14-N and the mobile device 12 is therefore observable.

[0046] In other words, the system is observable when: max i x i − x c 2 + y i − y c 2 − R c > α max i σ i Or α max i σ i is said predetermined distance; and α is a margin coefficient (which can be set to 10 according to an example of implementation).

[0047] The calculation module 22 implements the following steps 140 and 150 when the observability criterion is met. Otherwise, the method is, for example, implemented again when the mobile device 12 is in a different position.

[0048] During step 140, the calculation module 22 determines an initial approximation, subsequently denoted by X, of the position of the mobile device 12.

[0049] In particular, according to the invention, this initial approximation X is determined by minimizing the mean square deviation of a pseudo linear observation model which is interpreted as the "average" intersection point of a plurality of iso-curves. In other words, said initial approximation X is determined as a representative point of the intersection points of a plurality of iso-curves. This representative point is obtained by minimizing a mean square deviation criterion of a linear observation module, explained in detail later, and can be seen as an “average” point of said intersection points.

[0050] Each iso-curve represents an arc of a circle between a pair of landmarks such that the angle referred to the center of the circle is twice the angular difference perceived by the mobile device between this pair of landmarks.

[0051] In other words, with reference to the figure 3 , each iso-curve, defined from a pair ( A k 1 , A k 2) of landmarks perceived from an angle ADOA Yes 1, Yes 2 , represents an arc of a circle joining A k 1 to A k 2 of which the center C 1 is located on the perpendicular bisector of the chord ( A k 1 , A k 2) at a distance such that the angle ϕ 1 = ( A k 1 , C 1 , A k 2) is worth twice the angular deviation ADOA Yes 1 ,Ak 2 between this pair of bitters.

[0052] The determination of such an initial approximation X is illustrated schematically in the figure 3 in the case of two pairs of landmarks ( A k 1 , A k 2 ) and ( A k 3 , A k 4) . In the example of this figure 3 , the arc of the circle between the pair of landmarks ( A k 1 , A k 2) is of angle ϕ 1 which is equal to twice the angular deviation ADOA k 1 k 2 between this pair of landmarks, and the arc of a circle between the pair of landmarks ( A k 3 , A k 4) is of angle ϕ 2 equal to twice the angular deviation ADOA k 3 k 4 between this pair of landmarks. The center of the arc of a circle between the pair of landmarks ( A k 1 , A k 2) is denoted by C 1 and the center of the arc of a circle between the pair of landmarks (A k 3 , A k 4) is denoted by C 2. Thus, in this example, the initial approximation X, that is, the point representing the point of intersection of the illustrated circular arcs, is the point of intersection itself of these arcs. It is clear that in the presence, for example, of a third circular arc, the points of intersection of these arcs would not necessarily coincide with each other because of the inaccuracies of the measurements and the positions of the landmarks. In this case, the initial approximation X would be determined as an "average" point of intersection of the points of intersection of each pair of arcs, according to the observation model explained below.

[0053] To determine the initial approximation X, the calculation module 22 determines for each constructed circular arc, the coordinates C of its center and its radius you .

[0054] Each ray youis determined using the following equality: d i = d 2 1 + 1 tan ϕ 2 Or d is the distance separating the pair of landmarks forming the corresponding arc of a circle; ϕ is the ADOA angle measured between this pair of landmarks.

[0055] The coordinates C can be determined using also the values ​​of d and of ϕ depending on the chosen marker.

[0056] Then, to determine the point of intersection X, the calculation module 22 uses the following vector relationship, defined for each pair of circular arcs with centers C And C j , and rays you And DJ : f d i d j = A d i d j . X , with f d i d j = C i C j → . OC j → + 1 2 d i 2 − C i C j 2 − d j 2 , A d i d j = C i C j → , Or O is the center of the chosen reference point.

[0057] The previous vector relationship therefore defines a “pseudo” linear observation model of X (deduced from the rays you and centers C, themselves deduced from the initial measurements). In particular, f ( d ) = A ( d ) . X in the absence of measurement error. The initial approximation X can therefore be obtained by minimizing the root mean square deviation criterion of the following linear residuals: f d − A d . X where the vector f and the matrix A are constructed from all the angular deviations ADOA and the positions of the landmarks.

[0058] The value X̂ 0 minimum is given by the following expression: X ^ 0 = A d + f d where the matrix A ( d ) +< is the pseudo-inverse matrix of the matrix A ( d ) , determined by the following expression: A d + = A d t A d − 1 A d t .

[0059] In the next step 150, the calculation module 22 implements an optimization algorithm and determines a next approximation of the position of the mobile device 12 from a previous approximation, using an iterative relationship. During the first implementation of step 150, the previous approximation is equal to the initial approximation determined in step 140. Then, step 150 is for example repeated several times to obtain a desired precision of the position of the mobile device 12.

[0060] In step 150, each subsequent approximation is for example obtained by applying a maximum likelihood estimator consisting of minimizing a least squares criterion. For example, with a Gauss-Newton type algorithm, the following approximation u i+1 can be found from the previous approximation you ( u0 corresponding to the initial approximation determined during step 140) using the following expression: u i + 1 = u i + H t D t D . B AOA . D t − 1 DH − 1 . H t D t . D . B AOA D t − 1 D AOA − h AOA u i Or AOA is the vector of deposit measurements; AOA is the covariance matrix of the vector AOA ; h AOA is the observation function of the deposits, such that: h AOA X = α ref − atan y i − y x i − x with ( xi, yi ) corresponding to the position of the landmark i ; ( x, y ) coordinates of X ; α ref the angular reference of the bearing measurements atan the arctangent function; H is the Jacobian matrix associated with h AOA : H = ∂ AOA ∂ X .

[0061] Finally, with this maximum likelihood estimator, the precision of the estimation is optimal and can be determined according to the following expression of the Cramer-Rao Bound: BCR = H t B − 1 H − 1 .

[0062] It is then understood that the present invention has a certain number of advantages. First of all, the invention makes it possible to determine or specify the position of a mobile device by fully utilizing any number of bearing measurements on landmarks of imprecise positions and by initially verifying the observability of this position.

[0063] This determination is made using an optimal global statistical approach taking into account both inaccuracies in the position of landmarks and inaccuracies in direction measurements, while remaining efficient and unbiased.

[0064] Finally, thanks to the invention, it is possible to estimate the precision of the solution obtained.

Claims

1. A reorienting method based on a plurality of landmarks (14-1, ..., 14-N) when geolocating a mobile device (12), comprising the following steps: - acquiring (110) M sighting measurements of the landmarks (14-1, ..., 14-N) with respect to a reference landmark, positions of the landmarks (14-1, ..., 14-N) and precisions associated with these positions, said sighting measurements forming a sighting measurement vector; - transforming (120) the sighting measurement vector into an angular error vector using a transition matrix such that each component of the angular error vector corresponds to an angular error between a pair of landmarks (14-1, ..., 14-N); - determining (140) an initial approximation of the position of the mobile device (12) using a linear observation model, said initial approximation being determined as a representative point of the points of intersection of a plurality of iso-curves, each iso-curve representing an circular arc comprised between a pair of landmarks (14-1, ..., 14-N) and with an angle at the center of the circle equal to twice the angular error between said pair of landmarks (14-1, ..., 14-N); - determining (150) a following approximation of the position of the mobile device (12) and the associated precision from a preceding approximation, by using an iterative relationship, the preceding approximation initially being equal to the initial approximation and further comprising a step of verifying (130) an observability criterion comprising determining a regression circle from the position of each landmark and a known position of the mobile device (12), the regression circle being obtained by minimizing a mean squared error criterion, the steps (140, 150) for determining the initial approximation and the following approximation being implemented when the observability criterion is met, wherein the observability criterion is met when at least one of said positions is moved away from the regression circle by a predetermined distance.

2. The method according to any one of the preceding claims, wherein the determining step (140) for determining the initial approximation comprises, for a pair of landmarks (14-1, ... , 14-N), determining a center and a radius of the circle forming the arc of circle corresponding to this pair.

3. The method according to claim 2, wherein the determining step (140) for determining the initial approximation comprises determining the initial approximation by minimizing the mean squared error criterion of the residues of the linear observation model, the linear observation model being built on all of said centers and radii.

4. The method according to claim 3, wherein the point representative of the points of intersection of the plurality of iso-curves is the result of said minimization.

5. The method according to any one of the preceding claims, wherein the transition matrix is selected so that each pair of landmarks (14-1, ..., 14-N) comprises two adjacent landmarks (14-1, ..., 14-N) according to an order defined by the geographical positions of these landmarks (14-1, ..., 14-N).

6. The method according to any one of the preceding claims, wherein each following approximation is obtained by applying a maximum likelihood estimator, preferably with a Gauss-Newton algorithm.

7. The method according to any one of the preceding claims, wherein the number M is strictly greater than 3.

8. A computer program product including software instructions which, when implemented by computer equipment, implement the method according to any one of the preceding claims.

9. A reorienting device (10) on a plurality of landmarks (14-1, ..., 14-N) when geolocating a mobile device (12), comprising technical means (21, 22, 23) suitable for implementing the method according to any one of claims 1 to 7.