Method for determining a property of a maneuver of a carrier, computer, system and associated carrier

Abstract

Method for determining a property of a carrier's maneuver, computer, system, and associated carrier. The present invention relates to a method for determining at least one property of an object's maneuver, the determination method being implemented by a computer and comprising the steps of: - obtaining measurements of: - two angular orientations of the object relative to a sensor, - a radiometric signature of the object, - determining at least one property of the object's maneuver by applying an estimator to the measurements obtained. Figure for the abstract: Figure 3

Description

Title of the invention: Method for determining a property of a maneuver of a carrier, computer, system and associated carrier

[0001] The present invention relates to a method for determining at least one property of an object's movement. The present invention also relates to a computer for implementing the determination method, as well as to a system and a carrier comprising such a computer.

[0002] In the field of passive distance estimation to an object, particularly a carrier, optronic equipment, especially airborne equipment, is used to determine the distance without active telemetry requiring laser or radar emission. Telemetry can be limited by its range or its lack of discretion, as the emission can be detected by the object.

[0003] To achieve this, it is known to use an estimator which is a Kalman filter applied to angular orientation measurements, giving two angles at which the object is seen by a passive sensor. Such a technique is often referred to as a TPA technique, that is, a passive trajectory tracking technique using angle measurement.

[0004] Such a Kalman filter can be expressed in a Cartesian frame (relative or absolute) or in a spherical frame or in a hybrid form by alternating between the two types of frames according to the phases of the Kalman filter (typically a prediction phase in Cartesian and a correction phase in spherical).

[0005] However, it can be shown that convergence of the Kalman filter is only possible for an assumed motion, which is most often uniform rectilinear motion. In particular, a maneuver of the object causes the Kalman filter estimate assuming uniform rectilinear motion to diverge.

[0006] There is a need for a method of determining a property of a maneuver of an object that allows a relevant estimate of the object's position to be maintained, even in the presence of a maneuver of the object.

[0007] To this end, the description describes a method for determining at least one property of an object's movement, the determination method being implemented by a computer and comprising the steps of:

[0008] - obtaining measurements:

[0009] - of two angular orientations of the object with respect to a sensor, and

[0010] - of a radiometric signature of the object, and

[0011] - determination of at least one property of a maneuver of the object by application of an estimator on the measurements obtained.

[0012] According to particular embodiments, the determination method has one or more of the following characteristics, taken individually or in all technically possible combinations:

[0013] - an image of the object containing pixels is provided, the radiometric signature being a quantity representing the number of grey levels that are added to the pixels of the image due to the presence of the object.

[0014] - at least one property determined during the determination step is the presence of a maneuver of the object or the type of maneuver performed by the object.

[0015] - the determination step includes an initialization substep allowing to obtain an initial estimate of the object's position, the estimator being applied to the measurements obtained and the initial estimate.

[0016] - the initialization substep is implemented by applying an estimator to angular orientations.

[0017] - the estimator used during the initialization substep is a Kalman filter extended in modified spherical coordinates.

[0018] - the estimator applied to the measurements obtained is an extended Kalman filter invariant.

[0019] The description also describes a computer capable of determining at least one property of an object's maneuver, the computer being capable of:

[0020] - obtain measurements:

[0021] - of two angular orientations of the object with respect to a sensor, and

[0022] - of a radiometric signature of the object, and

[0023] - to determine at least one property of a maneuver of an object by applying a estimator based on the measurements obtained.

[0024] The description also proposes a system for determining at least one property of a maneuver of an object, the determination system comprising:

[0025] - a first sensor suitable for measuring two angular orientations of an object by in relation to the first sensor,

[0026] - a second sensor suitable for measuring a radiometric signature of the object, and

[0027] - a calculator as previously described, the calculator being suitable for obtaining the angular orientations and radiometric signature of the object by receiving measurements from each of the sensors.

[0028] The description also describes a carrier comprising a computer as previously described or a determination system as previously described.

[0029] In this description, the expression "specific to" means interchangeably "suitable for", "adapted to" or "configured for".

[0030] Some features and advantages of the invention will become apparent from the following description, given solely by way of non-limiting example, and made with reference to the accompanying drawings, in which:

[0031] - [Fig. 1] [Fig. 1] is a schematic representation of a carrier equipped with a system for determining a property of an object's maneuver,

[0032] - [Fig.2] [Fig.2] is a flowchart of an example of the implementation of a method for determining a property of an object's operation, and

[0033] - [Fig.3] [Fig.3] illustrates an example of a maneuver that the determination method According to [Fig.2], it is possible to discriminate, and

[0034] - [Fig.4] [Fig.4] illustrates an example of a maneuver that can be discriminated using angular measurements only.

[0035] A carrier 10 is schematically represented in [Fig.1].

[0036] The carrier 10 shown is, for example, an airplane.

[0037] Alternatively, the carrier 10 is any type of aircraft such as a helicopter.

[0038] It is also possible to consider here a carrier which is a land or naval vehicle.

[0039] The carrier 10 includes a system for determining at least one property of a maneuver of an object.

[0040] A specific property may, depending on the case, be the presence of a maneuver and the type of maneuver.

[0041] For this purpose, the determination system 12 seeks, for example, to obtain in real time the distance between the object and the determination system 12.

[0042] Without being limiting, it is assumed in the following that the determination system 12 seeks to characterize the maneuver of another carrier 10, called the observed carrier 14.

[0043] The observed carrier 14 is represented here by a square to symbolize the fact that the observed carrier 14 is, in this context, generally very far from the carrier 10, typically several tens of kilometers away.

[0044] The determination system 12 can be seen as an optronic equipment of the carrier 10.

[0045] This includes equipment with a steerable line of sight and a target tracking function, such as a targeting pod, an optronic ball, or an infrared search and track device. The latter is more commonly referred to as IRST equipment, the abbreviation IRST standing for "Infrared Search and Track".

[0046] The determination system 12 comprises a sensor 16 and a computer 18.

[0047] The sensor 16 is adapted to measure two angular orientations of the observed carrier 14 compared to sensor 16.

[0048] Typically, the sensor 16 gives two angular values ​​which are V the azimuth and # the elevation.

[0049] The two orientations are defined in the local geographic coordinate system, that is to say a coordinate system centered on the sensor 16 with a first x-axis corresponding to north, a second y-axis corresponding to east and a third z-axis corresponding to bottom.

[0050] More specifically, the azimuth is the rotation about the third axis z, which is positive in the north-east direction, while the elevation is the rotation about a fourth axis y'. The fourth axis y' is derived from the second axis y by the azimuth rotation. The elevation is, moreover, chosen to be positive upwards.

[0051] The sensor 16 thus provides at each instant a pair of angular orientations of the observed carrier 14.

[0052] The sensor 16 also makes it possible to obtain a radiometric signature of the observed carrier 14.

[0053] According to the example described, the radiometric signature is the number of grey levels that are added to the pixels of the image due to the presence of the observed carrier 14.

[0054] In such a case, the signature is a representation of the energy of the observed carrier 14 which is deduced from the infrared signature according to the following relation.

[0055] The infrared signature SIR (a, P) can be decomposed as follows:

[0056] SIR(a,P) = SIR0 f(a, p)

[0057] Where: • SIR0; the total power radiated by the observed carrier 14 (the power radiated in all directions of space). The total power is written as follows: / r 577¾ = | 5 / 7? (a, due (as £)

[0058] where d£l(a, P) is the elementary solid angle, and • f(a, P) is the proportion of the total power radiated by the carrier observed 14 in the direction ( a, P ). This function can be obtained empirically, by averaging the corresponding power functions for different types of carrier, or theoretically, so as to reflect the high proportion of power radiated in the rear sector and the low proportion radiated in the front sector.

[0059] With these notations, the energy E of the observed carrier 14 measured in the image can be rewritten as follows:

[0060] rr • J? ç / » is a constant, and • the other terms are defined later after the introduction of specific benchmarks.

[0062] To obtain the value of the radiometric signature, an analysis of the grey levels without the observed carrier is carried out 14 to obtain a reference level.

[0063] When the reference level is exceeded, the difference is considered to originate from the observed carrier 14 and is therefore representative of the radiometric signature.

[0064] Here we will define the radiometric signature as the sum of the exceedances of the reference level in each pixel.

[0065] According to a particular example, sensor 16 is an optronic sensor 16.

[0066] Preferably, the sensor 16 is a passive sensor 16, that is to say that the sensor 16 emits no pulse towards the environment.

[0067] In such a case, the sensor 16 provides only a two-dimensional angular measurement.

[0068] A camera is an example of a passive optronic sensor.

[0069] The calculator 18 is an electronic circuit designed to manipulate and / or transform data represented by electronic or physical quantities in registers of the calculator and / or memories into other similar data corresponding to physical data in register memories or other types of display devices, transmission devices or storage devices.

[0070] As specific examples, the calculator 18 is implemented as a programmable logic component, such as an FPGA (Field Programmable Gate Array), or as an integrated circuit, such as an ASIC (Application-Specific Integrated Circuit).

[0071] The computer 18 is suitable for implementing a method for determining at least one property of a maneuver of the observed carrier 14.

[0072] An example of the operation of the computer 18 is now described with reference to [Fig.2] which illustrates a flowchart of the implementation of a method for determining at least one property of a maneuver of the observed carrier 14.

[0073] The determination process comprises a production step E20 and a determination step E22.

[0074] During the E20 acquisition step, the computer 18 receives a plurality of measured angular orientation pairs.

[0075] More specifically, the sensor 16 measures the two angular orientations at every instant.

[0076] Sensor 16 sends these measurements to computer 18.

[0077] The calculator 18 thus has, for each measurement instant, a pair of angular orientations.

[0078] During the acquisition step E20, the sensor 16 measures a radiometric signature of the observed carrier 14.

[0079] Here, the radiometric signature is obtained by an analysis of the grey levels in the image.

[0080] During the determination step E22, the computer 18 determines at least one property of a maneuver of the object.

[0081] The determination step E22 comprises an initialization substep SE1 and an application substep SE2.

[0082] During the initialization substep SE1, the computer 18 applies a first estimator to the angular orientation pairs to obtain an initial estimate of the position of the observed carrier 14. According to the example described, the first estimator is an extended Kalman filter in modified spherical coordinates. Other estimators could nevertheless be used here, such as a Kalman filter in Cartesian coordinates.

[0083] The extended Kalman filter in modified spherical coordinates is more often called the MSC-EKF filter. The abbreviation MSC-EKF refers to the designation English equivalent of "Modified Spherical Coordinates Extended Kalman Filter".

[0084] The MSC-EKF filter provides the position and velocity of the observed carrier 14 in modified spherical coordinates in the local geographic frame carried, as well as the associated covariance matrix.

[0085] The local geographic reference frame designated is a reference frame whose origin is the position of the sensor 16, the first axis Qv) is directed towards geographic North, the second axis ( E) towards the East and the last axis ( o) downwards.

[0086] In the following, this reference mark will be referred to as the GLP reference mark.

[0087] More precisely, the xMSC state vector estimated by the MSC-EKF filter is written under the shape :

[0088] XMSC - Az El 7r Âzco^EÏ) . El .A, | YMSC •4^9 yMSC yMSC •*4 rMSC

[0089] Where: • Az; azimuth angle of the observed carrier 14 in the GLP frame linked to the carrier 10, • El; elevation angle of the observed carrier 14 in the GLP frame linked to the carrier 10, • r: distance to the observed carrier 14, • Àz: angular velocity of the observed carrier 14 in azimuth in the GLP frame linked to the carrier 10, • El: angular velocity of the observed carrier 14 in elevation in the GLP frame linked to the carrier 10, • r: radial velocity of the observed carrier 14 in the GLP frame attached to the carrier 10, and . XMSC denotes the i-th coordinate of the state vector xMSC.

[0090] During the application substep SE2, the calculator 18 applies a second estimator to the initial estimate and the set of measurements obtained.

[0091] The second estimator is thus applied to the initial estimate, the angular orientation pairs and the radiometric signatures.

[0092] The second estimator is an invariant extended Kalman filter.

[0093] An invariant extended Kalman filter is more often referred to as an IEKF filter, the abbreviation IEKF referring to the corresponding English name "Invariant Extended Kalman Filter".

[0094] Before detailing operations 01, 02 and 03 implemented by the IEKF filter, several reference frames are introduced, namely the Serret-Frenet frame and the ECEF frame.

[0095] The Serret-Frenet frame is denoted (f, N, B) and is defined by the following three vectors: • a tangent vector T, this vector being defined as tangent to the trajectory (oriented in the direction of movement of the observed carrier 14), • a normal vector N, this vector being defined as normal to the trajectory (in the osculating plane, oriented towards the center of the osculating circle), and • a binomial vector g, this vector being defined so that the trihedron ( T, N, B ) is right-handed.

[0096] The ECEF frame designates a reference frame whose origin is the center of the Earth and whose axes are fixed to the Earth. The acronym ECEF refers to the corresponding English term "Earth-Centered Earth-Fixed".

[0097] The application substep SE2 comprises three operations 01, 02 and 03 implemented successively, an initialization operation 01, a prediction operation 02 and an estimation operation 03.

[0098] During the initialization operation 01, the computer 18 obtains the initial state xo of the observed carrier 14 and the covariance matrix Po of the error ^ associated with the initial state x0.

[0099] The state of the observed carrier 14 is defined as follows:

[0100] { / ,z} = H]

[0101]

[0102] Or: • x E SE(3\ SE(3) being the special Euclidean group which contains all the direct isometries of p3 (i.e. translations, rotations but not symmetries) and which allows us to represent the position and orientation of the observed carrier 14, • zeP3 . gECEF-SF csl |a rotation matrix (of size 3x3) giving the orientation of the Serret-Frenet frame (and therefore of the observed carrier 14) with respect to the ECEF frame, . pECEF csl un veC(eur (of size 3x1) giving the position of the observed carrier 14 in the ECEF frame, • is a zero matrix (of size 1x3), • y is the curvature (in the plane of the osculating circle), • r is the torsion (measures how the observed carrier 14 moves out of the plane osculator), and • u is the speed of the observed carrier 14. Calculator 18 calculates the initial state xo of the IEKF filter from the state vector xMSC according to the equations of the following system:

[0103] pECEF - CECEF + pECEF^RGLP cos ( x 1 ^' ) cos ( x^ ) pk- cos ( x™ sc ) sin ( x¥ sc ) -^ësin« æ ) = p 0 ) y0- o = 0 uQ =

[0104] Or: . cecef denotes the vector giving the origin of the GLP frame in the ECEF frame (corresponds to the position of the carrier 10 assumed to be known), pECEF-^RGLP denotes the rotation matrix giving the orientation of the GLP with respect to the ECEF frame (depends only on the position of the carrier 10 assumed to be known), represent the route and the slope of the observed carrier 14. They are expressed in terms of xMSC and t^GLP, and euler_vers_rot_mat is a conversion function that allows obtaining a rotation matrix from Euler angles in intrinsic Tait-Bryan convention. yECEF CS( |c velocity vector of the observed carrier 14 in ECEF frame which mathematically, it can be written according to the following relationship:

[0105] pECEF - gECEF + ^ECEF^RGLP x»fSC xMSC cos (^^)005(^^) - sin(cos(x^50) - -^sinlx^^) rwsc XMSC ^■coslx^jsinO^c) -^sin(x^sc)sin(xfsc) + -^fcosC^c) yMSC _ ±( ymsc \ XMSC X-MSC VVb (A 3 I

[0106]

[0107]

[0108]

[0109]

[0110] [YES]

[0112] Calculator 18 also obtains the coefficients of the covariance matrix Po of the error £() associated with the initial state xo. The covariance matrix P of the error f associated with a state x is defined classically as a p9x9 element such as: P = cov(f) Or: • cov( A) corresponds to the covariance of the quantity A. To express the error £ associated with a state x, it is useful to define more precisely the notion of error in the state space which is partitioned into two subspaces, namely the special Euclidean group SE(3) and P3- On the subspace p3, which represents the velocity (in magnitude) of the observed carrier 14 as well as the characteristic curvature and torsion of the trajectory followed by the observed carrier 14, the state error is defined here as an element of p3 such that: nz =zz = u-ui

[0113] Where: • y, t and ù are the estimated values ​​of curvature, torsion and velocity of the observed carrier 14, and y, T and H: the true values ​​of the curvature, torsion and velocity of the carrier observed 14.

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] On the subspace of the Euclidean special group SE(3)> which represents the position and orientation of the observed carrier 14 in the ECEF frame, the state error is defined as an element of SE(3) such that: tECEF^SF * ECEF^SF R 1 R 0[3 TECEF^SF{ ^ecef R ( P Or: • ^ecef cj ^ECEF^SF respectively denote the estimated values ​​of the position and orientation of the observed carrier 14, and . pECEF cl rEcef-sf respectively denote the true values ​​of the position and orientation of the observed carrier 14. In the previous equation, the error on the orientation of the observed carrier 14 rTECEF-*SF^ECEF-^SF eS{ a rotation matrix (i.e., belonging to the SOi^- group When the rotation error is small, this rotation matrix can be approximated. by linearization on the Lie algebra of the group SO(3) as follows: tECEF-^SF * ECEF^SF R t R Or: * ( ) is an antisymmetric matrix (i.e., belonging to the Lie algebra of SOÏ^)- It follows that the error associated with state x is finally defined as an element of p9 and can be expressed mathematically as follows: F ï *R rTECEF -SF ^ECEF _ pECEF ') TT UU To obtain the covariance matrix Pn of the error associated with the initial state, calculator 18 first calculates the coefficients of the covariance matrix pSI\ This covariance matrix p^ is calculated in a new space within which the state vector is expressed mathematically:

[0125] r / y Pn XSF - PB U h . P,

[0126] where: • Pt, Pn, and Pb denote the coordinates of the vector giving the position of the observed carrier 14 in the Serret-Frenet frame. Note that, by definition of the Serret-Frenet frame, these three coordinates are zero. This space is not of interest for representing the state of the observed carrier 14 but allows, as described later, the calculation of the covariance of the error on the position of the observed carrier 14 in the Serret-Frenet frame, and • u, h and P are the spherical coordinates of the velocity vector of the observed carrier 14 in the Serret-Frenet frame.

[0127] The function for calculating the vector xSF from the vector xMSC is denoted j-sf-^msc cl, which by definition satisfies the following mathematical relationship:

[0128] XSF= fF^CÇxMSC)

[0129] The pSF covariance matrix is ​​then calculated according to the following formula:

[0130] pSF _ jSF-^MSC pMSC jSF-^MSCT

[0131] Where: * jSF^msc denotes the Jacobian matrix associated with the function ^f^msc • pMSC denotes the covariance matrix associated with the vector xMSC, and • mt denotes the transpose of the matrix M.

[0132] The calculator 18 then obtains the covariance matrix of the error associated with the initial state xo from the coefficients of the covariance matrix pSF as follows:

[0133] 1 zr2 l amil 0 0 0 0 0 0 0 0 i 0 pSF r^F *5.6 pSF *1.6 pSF *2.6 pSF *3.6 0 0 pSF' *4.6 0 nSF 1>S'F *5.5 pSF P 1.5 pSF *2.5 0 0 pSF *4.5 0 nSF *1.6 p^F *1.5 *1.1 pSF *1.2 0 0 p^F * 1.4 Po- 0 pSF *2.6 p^F *2.5 pSF *1.2 pSF r 2.2 pSF *2.3 0 0 pSF *2.4 0 p$F r 3.6 pSF *3.5 pSF *1.3 p^F *3.3 0 0 pSF *3.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CT? 0 0 nSF *4.6 pSF *4.5 p^F *1.4 p^F *2.4 pSF *3.4 0 0 »SF *4.4!

[0134]

[0135]

[0136] During the prediction operation 02, the computer 18 predicts the state and associated covariance Pk+ük at the time ^+i of the next measurement, from the estimated state and associated covariance Pkik at the time of the last measurement. In the previous notation, denotes the predicted value for the quantity A at time tj given the value for the quantity A at time tj. Calculator 18 deduces the predicted state xk+ük at time ^+1 from the last estimated state xkik at date using the following system:

[0137]

[0138]

[0139]

[0140] Or: * (j$SF — [ t 0 y ] ! denotes the instantaneous rotation velocity vector of the observed carrier 14 in the Serret-Frenet frame, ( represents the matrix associated with the cross product (denoted "x") with the vector , such that G P3 ( "SF)X ' " "SF X a, • ^ = ^+r^, and • vSF = [u 0 0]r denotes the velocity vector of the observed carrier 14 in the Serret-Frenet frame, As a point of note, it can be observed that this system comes from a time integration over the time interval A? of the system corresponding to the evolution model describing the kinematics of the observed carrier 14. This model assumes that the curvature y, the torsion T, and the velocity u are constant. Under this assumption, the evolution model is governed by the following equations:

[0141]

[0142] pECEP^gECEF-SF^ Jr Y = «y * = 0T ü = q ~U Or: * a — [ al ai aaa 1rest 'c random vector (of size 9x1) modeling ["w “p "y "mJ model noise (assumed to be Gaussian with zero mean and covariance matrix θ).

[0143] With the assumptions used and without deviation from the evolution model, the speed, curvature and torsion are constant, so that the observed carrier 14 describes a circular helix.

[0144] During the prediction operation 02, the calculator 18 also calculates the associated covariance Pk+iik at time tk+[ from the last associated covariance Pj^ using the following relation: P

[0145] Where: • B- exp(A At), 2 4 being a matrix such that:

[0146] iO -y 0 0 0 0 0 -1 0 ( y 0 -T 0 0 0 0 0 0 0 T 0 0 0 0-100 0 0 0 0 -y 0 0 0 -1 A = 0 0 -uy 0 -r 0 0 0 0 U 0 0 T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 P 0 0 0 0 0 0 0 0 0 '0 0 0 0 0 0 0 0 0 '

[0147] As a remark, this formulation comes from the fact that it can be shown that the evolution of the error £ associated with the state x is governed by the following equation:

[0148] ^A^ + q

[0149] Integrating this equation over the time interval At gives £ according to the following equation:

[0150] The preceding formulation is thus obtained by noting that

[0151] At the end of the prediction operation 02, the computer 18 thus has the state xk+ük as well as the associated covariance Pk+nk at time ^+1-

[0152] During the estimation operation 03, the computer 18 estimates the state xk+iik+iet the associated covariance Pk+uk+ i with the measurement J^+i realized at time ^+1 by the sensor 16.

[0153] In this sense, the estimation operation 03 can be interpreted as an update operation.

[0154] During this estimation operation 03, the computer 18 estimates the estimated state xk+iik+i and the associated covariance Pk+iik+i using the following system:

[0155] Where: * [ Ô 7 Ô T 8 Ô ô ]T “ K s denotes the correction vector applied to the predicted state xk+iik, and • is a function defined by:

[0156] l-cos(j|ôJt) ^rsinjjlôj 2 G(ô^ = h+

[0157] where ^3 is the 3rd order identity matrix and ( &M)X denotes the matrix associated with the cross product with the 5W matrix. • / 9 is the identity matrix of order 9, • H is a matrix such that:

[0158] Or: • is the first coordinate of the vector p^^ giving the position of the carrier observed 14 in the GLP frame, • hAz is an observation function of the azimuth angle of the observed carrier 14 in the GLP frame, a function that depends non-linearly on the position P of the observed carrier 14, this function satisfying:

[0159] h Az = atan2 ( p^ p N ) • PN is the first coordinate of the vector p^^ giving the position of the observed carrier 14 in the GLP frame, • Pe is the second coordinate of the vector p' giving the position of the observed carrier 14 in the GLP frame, • âà is the derivative of a quantity A with respect to the position P of the carrier âp observed 14, • hE> is an observation function of the elevation angle of the observed carrier 14 in the GLP frame, a function that depends non-linearly on the position P of the observed carrier 14, this function hEl satisfying: [° 16 °1 -atan[-J— \ \pI+Pe J • Pj) is the third coordinate of the vector p^^ giving the position of the carrier observed 14 in the GLP frame, • hE is an observation function of the energy of the observed carrier 14 in the image, a function that depends non-linearly on the position P and the orientation R of the observed carrier 14, this function hE satisfying: C° 16 U = • vec(.) is the vectorization operator for a matrix by concatenating its columns, • C is the matrix such that: »3^ »3.3 \ € = I $3.3

[0162] , and D is the matrix such that:

[0163] 0 0 0 | 0 0-1 0 1 0 0 0 1 D = 0 0 0 -10 0 0-10 1 0 0 'ooo! • sk+\ is the innovation that is defined by: =11 «mw** j,£ / -£ŒF । „ • & is the Kalman gain, this gain being obtained by the following formula: k = n«| fc ( +^r 1

[0164] Where: • M'1 denotes the inverse matrix of matrix A, • N is the covariance matrix of the noise vector n - [ nEt nE ]T which is a random vector modeling the measurement noise (assumed here to be Gaussian with zero mean).

[0165] As a remark, it may be noted that these expressions are derived from the observation model as is now described.

[0166] For the sensor 16, the measurement vector associated with the observed carrier 14 is defined as follows:

[0167] El E]T

[0168] Where: • Az is the azimuth angle of the observed carrier 14 in the GLP frame linked to the carrier 10, • El is the elevation angle of the observed carrier 14 in the GLP linked to the carrier 10, and • E is the energy of the observed carrier 14.

[0169] The observation model, which allows the state x to be linked to the measurement vector θ, is mathematically written according to the following system:

[0170] Az = aten2(PgP N )+ El = - atan / > - j + Hfi El E=^^^^ 3) +n E

[0171]

[0172]

[0173]

[0174]

[0175]

[0176]

[0177]

[0178] Or: • nAz is the first component of the noise vector”, • nEi is the second component of the noise vector”, • 7 is a constant, specific to sensor 16, allowing the conversion of a flux of photons incident in greyscale in the image, • $ is the size of the surface area of ​​the sensor's entrance pupil 16, SER(a, fi) is the power radiated by the observed carrier per unit solid angle in the direction (a, fi), • (tp, 6) corresponds to the angular direction under which sensor 16 is viewed since the observed carrier 14, and • nE is the third component of the noise vector Angles V and 9 correspond to the yaw and pitch angles associated with the rotation matrix giving the orientation of the LDV frame of sensor 16 relative to the Serret-Frenet reference point of the observed carrier 14. Yaw and pitch angles correspond respectively to the first two rotations Z and Y' in intrinsic Tait-Bryan convention (convention commonly used in aeronautics). The LDV reference frame corresponds to the line-of-sight reference frame. The LDV reference frame is defined as follows: its origin corresponds to the optical center of the sensor 16 (coinciding in a first approximation with the center of mass of the carrier 10), the first axis is oriented in the direction of sight of the sensor 16, the second axis is parallel to the lines of the image (oriented from left to right) and the last axis is parallel to the columns of the image (oriented from top to bottom). In practice, / ^^^^st is calculated using the following formula: rSF-LDV _ [ rECEF-*SF ] TrECEF~*RGLPrRGLP~*LDV Or: . jjRGLP-*LDV is |a rotation matrix giving the orientation of the LDV frame relative to the GLP frame (matrix calculated by composition of the attitudes of the LDV frame in the carrier frame 10 and of the attitudes of the carrier 10 in the GLP frame). Using the observation functions hEl and hE, the previous expressions can be reformulated according to the following system:

[0179] Az-h M (p) +

[0180]

[0181]

[0182] El = h El (p) + n El E = h E (p, R) +n E The innovation A4+i corresponding to the measure ^+t thus becomes: kg Or: • pfiCEF is ja pOSj(jon true of the observed carrier 14 in the ECEF frame at KA 1 the instant ^+1, and * gECEF^SF^signs the true orientation of the observed carrier 14 in the ECEF frame at time ^+i. Furthermore, the true position and orientation of the observed carrier 14 can expressing itself according to the predicted position and orientation and the state error according to the following relationships: |W - «K#S!r + «»)J

[0183] Where: • is the state error on the position of the observed carrier 14, an error expressed in the Lie algebra of SE(3), and • is the state error on the attitude of the observed carrier 14, error expressed in the Lie algebra of SE(3)

[0184] Combining the preceding equations, after first-order linearization, yields the following relationship:

[0185] sk+l = HÇ + n

[0186] It follows that the covariance Sk+1 of the innovation $k+l can be written as:

[0187] It follows that Kalman's gain can be written as: * =

[0188] With finally the relation rx TT ? s- s ]^_ f <, 31 comes: [Ow Op OyOTOu] — AS^+] 1^'41 = IA ~

[0189] The process just described therefore makes it possible to exploit the radiometric information of the observed carrier 14 measured in an image in order to resolve the ambiguities that may exist for certain maneuvers.

[0190] This is particularly the case for maneuvers shown in [Fig.3].

[0191] In the case of maneuver 1, the observed carrier 14 evolves from the transverse sector to the rear sector, which results in a significant increase in the energy measured in the image at the level of the observed carrier 14, due to the unmasking of its nozzle, whereas in the case of maneuver 2, the observed carrier 14 evolves from the transverse sector to the front sector, which results in a more or less marked decrease in the energy measured in the image at the level of the observed carrier 14.

[0192] These detected maneuvers are in addition to the maneuvers that can already be detected from angular observations.

[0193] Figure 4 presents two examples of maneuvers that can be discriminated from of angular observations only.

[0194] The process thus makes it possible to better characterize the maneuvers carried out by the observed carrier 14.

[0195] The combined use of angular and radiometric measurements thus makes it possible to maintain good accuracy of estimation on the distance of the observed carrier 14 during and after the maneuver of the observed carrier 14, in a greater number of scenarios.

[0196] Other embodiments that provide the same advantages are also conceivable.

[0197] Any technique other than an MSC-EKF filter enabling the initialization substep SE1 to be carried out may be considered here.

[0198] It is also possible to use a different approach to adding energy in the measurement vector presented previously.

[0199] In the case of ambiguity between two types of maneuvers (one leading the observed carrier 14 to move in one direction and the other to move in the opposite direction), predictions for an increasing distance and a decreasing distance can be calculated simultaneously. One of the two hypotheses can be abandoned when the infrared signature is more or less blatantly incompatible with the estimated distance.

[0200] From a hardware point of view, it is possible to use one sensor for angular observations and a different sensor to obtain the radiometric signature.

[0201] Preferably, each of these sensors is a passive sensor, that is to say that the sensor does not emit any pulse towards the environment.

[0202] Thus, in a general case, the determination system 10 comprises a first sensor suitable for measuring two angular orientations of an object with respect to the first sensor, a second sensor specifically designed to measure a radiometric signature of the object, and a computer 18 specifically designed to obtain the angular orientations and the radiometric signature of the object by receiving the measurements from each of the sensors.

Claims

Demands

1. Method for determining at least one property of a maneuver of an object, the determination method being implemented by a computer (18) and comprising the steps of: - obtaining measurements of: - two angular orientations of the object with respect to a sensor (16), - a radiometric signature of the object, - determining at least one property of a maneuver of the object by applying an estimator to the measurements obtained and an initial estimate of the position of the object, the determination step comprising an initialization substep enabling the initial estimate of the position of the object to be obtained, the initialization substep being implemented by applying an estimator to the angular orientations.

2. A method of determination according to claim 1, wherein an image of the object comprising pixels is provided, the radiometric signature being a quantity representative of the number of grey levels that are added to the pixels of the image due to the presence of the object.

3. A method of determination according to claim 1 or 2, wherein at least one property determined during the determination step is the presence of a maneuver of the object or the type of maneuver performed by the object.

4. A method of determination according to any one of claims 1 to 3, wherein the estimator used during the initialization substep is an extended Kalman filter in modified spherical coordinates.

5. A method of determination according to any one of claims 1 to 4, wherein the estimator applied to the measurements obtained is an invariant extended Kalman filter.

6. A computer (18) capable of determining at least one property of a maneuver of an object, the computer (18) being capable of: - obtaining measurements of: - two angular orientations of the object with respect to a sensor (16), and - a radiometric signature of the object, and - determine at least one property of a maneuver of an object by applying an estimator to the measurements obtained and an initial estimate of the position of the object, the calculator step proper to obtain the initial estimate of the position of the object by applying an estimator to the angular orientations.

7. A system for determining (12) at least one property of a maneuver of an object, the system for determining (12) comprising: - a first sensor adapted to measure two angular orientations of an object with respect to the first sensor, - a second sensor adapted to measure a radiometric signature of the object, and - a computer (18) according to claim 6, the computer (18) being adapted to obtain the angular orientations and the radiometric signature of the object by receiving the measurements from each of the sensors.

8. Carrier (10) comprising a calculator (18) according to claim 6 or a determination system (12) according to claim 7.

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