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

Abstract

Method for determining a property of a maneuver of a carrier, computer, system and associated carrier The present invention relates to a method for determining at least one property of a maneuver of an object, 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, - of 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. 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 a maneuver of an object. The present invention also relates to a computer capable of implementing the determination method as well as to a system and a carrier comprising such a computer.

[0002] In the field of passive estimation of distance to an object, in particular a carrier, optronic equipment is used, in particular airborne, making it possible to determine the distance without active telemetry requiring laser or radar emission. Telemetry can in fact be limited by its range or by its lack of discretion, the emission being able to be detected by the object.

[0003] For this, it is known to use an estimator which is a Kalman filter applied to angular orientation measurements giving two angles under which the object is seen by a passive sensor. Such a technique is often referred to as a TPA technique, that is to say a passive trajectography technique by angle measurement.

[0004] Such a Kalman filter can be expressed in a Cartesian frame of reference (relative or absolute) or in a spherical frame of reference or in a hybrid form by alternating between the two types of frames of reference 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 the convergence of the Kalman filter is only possible for an assumed motion, which is most often a uniform rectilinear motion. In particular, a maneuver of the object causes the estimate of the Kalman filter assuming a uniform rectilinear motion to diverge.

[0006] There is a need for a method for determining a property of a maneuver of an object making it possible to maintain a relevant estimate of the position of the object, even in the presence of a maneuver of the latter.

[0007] For this purpose, the description describes a method for determining at least one property of a maneuver of an object, the determination method being implemented by a computer and comprising the steps of:

[0008] - obtaining measurements:

[0009] - of two angular orientations of the object relative 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 in isolation or in all technically possible combinations:

[0013] - an image of the object is provided comprising pixels, the radiometric signature being a quantity representative of the number of gray levels which are added to the pixels of the image due to the presence of the object.

[0014] - the 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 sub-step allowing to obtain an initial estimate of the position of the object, the estimator being applied to the measurements obtained and the initial estimate.

[0016] - the initialization sub-step is implemented by applying an estimator on angular orientations.

[0017] - the estimator used during the initialization sub-step 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 calculator capable of determining at least one property of a maneuver of an object, the calculator being capable of:

[0020] - obtain measurements:

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

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

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

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

[0025] - a first sensor capable of measuring two angular orientations of an object by report to the first sensor,

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

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

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

[0029] In the present description, the expression “suitable for” means indifferently “adapted for”, “adapted to” or “configured for”.

[0030] Characteristics and advantages of the invention will appear on reading the description which follows, given solely by way of non-limiting example, and made with reference to the appended drawings, in which:

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

[0032] - [Fig.2] [Fig.2] is a flowchart of an example implementation of a method of determining a property of a maneuver of an object, and

[0033] - [Fig.3] [Fig.3] illustrates an example of a maneuver that the determination method according to [Fig.2] allows to discriminate, and

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

[0035] A carrier 10 is shown schematically in [Fig.l].

[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 comprises a system 12 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, the determination system 12 seeks, for example, to obtain in real time the distance between the object and the determination system 12.

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

[0043] The observed carrier 14 is here represented 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.

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

[0045] This includes equipment with a steerable line of sight and a target tracking function such as a designation pod, an optronic ball or an infrared search and track device. This latter equipment is more often referred to as IRST equipment, the abbreviation IRST referring to the English term "InfraRed Seach and Track".

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

[0047] The sensor 16 is capable of measuring 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 reference frame, that is to say a reference frame centered on the sensor 16 with a first axis x corresponding to the north, a second y corresponding to the east and a third axis z corresponding to the bottom.

[0050] More specifically, the azimuth is the rotation around the third axis z which is positive in the north to east direction while the elevation is the rotation around a fourth axis y', the fourth axis y' is deduced from the second axis y by the rotation in azimuth. 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 gray levels which 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 relationship.

[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 in 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 • other terms are defined later after the introduction of specific benchmarks.

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

[0063] When the reference level is exceeded, it is considered that the difference comes 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 excesses of the reference level at each pixel.

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

[0066] Preferably, the sensor 16 is a passive sensor 16, i.e. the sensor 16 does not emit any impulses to 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 16.

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

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

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

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

[0073] The determination method comprises an obtaining step E20 and a determining step E22.

[0074] During the obtaining step E20, the calculator 18 receives a plurality of pairs of measured angular orientations.

[0075] More precisely, the sensor 16 measures the two angular orientations at each instant.

[0076] The sensor 16 sends these measurements to the computer 18.

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

[0078] During the obtaining 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 gray 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 sub-step SE1 and an application sub-step SE2.

[0082] During the initialization sub-step SE1, the computer 18 applies a first estimator applied to the pairs of angular orientations 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 referred to as the MSC-EKF filter. The abbreviation MSC-EKF refers to the name English corresponding to “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 reference frame carried, as well as the associated covariance matrix.

[0085] The local geographic reference point carried designates a reference point 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 (ÿ>) downwards.

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

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

[0088] XMSC - Az The 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 linked to the carrier 10, and . XMSC denotes the i-th coordinate of the xMSC state vector.

[0090] During the application sub-step SE2, the calculator 18 applies a second estimator to the initial estimate and all of the measurements obtained.

[0091] The second estimator is thus applied to the initial estimate, the pairs of angular orientations 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 of “Invariant Extended Kalman Filter”.

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

[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 direct.

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

[0097] The application sub-step 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 Pq of the error fQ associated with the initial state^.

[0099] The observed carrier state 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. the translations, the rotations but not the symmetries) and which makes it possible to represent the position and the 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) relative to the ECEF frame, . pECEF csl a vector (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. The 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 (x1^') cos (x^) pk- cos (x™sc) sin (x¥sc) -^ësin«æ) = p 0) y0- o = 0 u Q =

[0104] Or: . cecef designates the vector giving the origin of the GLP reference frame in ECEF reference frame (corresponds to the position of carrier 10 assumed to be known), . pECEF-^RGLP denotes the rotation matrix giving the orientation of the GLP relative to the ECEF reference 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 from xMSC and t^GLP, and • euler_vers_rot_mat is a conversion function for obtaining a rotation matrix from Euler angles in intrinsic Tait-Bryan convention. • VqCEF is the velocity vector of the observed carrier 14 in ECEF frame which is written mathematically according to the following relation: TA1 AC1 X^E XMSC ' L0105J ^cos««-')cos(^) - ^ësüi(^)cos(xpc) - ^sêsin( Dri » j-MSC rl / .SC rMSC VECEF = ^CEF+ gECEF RGLP ^cos(x|fSC)sin(xJf.SC) -^Sin«SC)sin«SC) + COS «SC) XMS( XMSC ~ xmsc " COS ( Xj^SC )

[0106] The calculator 18 also obtains the coefficients of the covariance matrix Pq of the error £' associated with the initial state xo.

[0107] The covariance matrix P of the error f associated with a statex is classically defined as an element of p9x9 such that:

[0108] P = cov(D

[0109] Where: • cov ( A ) corresponds to the covariance of the quantity A.

[0110] To express the error £ associated with a statex, 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-

[0111] On the subspace p3, which represents the speed (in norm) of the observed carrier 14 as well as the curvature and the torsion characteristic of the trajectory followed by the observed carrier 14, the state error is defined here as an element of p3 such that:

[0112] } / z=ZZ=TT .ù-u.

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

[0114] On the subspace of the special Euclidean group ££(3), which represents the position and orientation of the observed carrier 14 in the ECEF frame, the state error ^x is defined as an element of SE^3) such that:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] tECEF^SF to ecef-sf ,T R We tECEF^SF / ^ECEF R {p Or: . jÆCEF cj ^ECEF-^SF denote respectively the estimated values ​​of the position and orientation of the observed carrier 14, and . pECEF cl rECEF-*sf denote respectively 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^CEF-^SF CS( a rotation matrix (i.e. belonging to the group SO(3))- 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 A ecef-^sf RR Or: * ( ) is an antisymmetric matrix (i.e. belonging to the Lie algebra of SO(3))- As a result, the error associated with statex is finally defined as an element of p9 and can be expressed mathematically as follows: ^R tECEF^SF / ^ECEF ) yy T-7 U~U To obtain the covariance matrix Pq of the error £0 associated with the initial state xo, the calculator 18 first calculates the coefficients of the covariance matrix This pSF covariance matrix is ​​calculated in a new space within which the state vector is expressed mathematically: XSF = Or : 'PT' Pn Pb U h , P , Pt, P^ and P b 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 the representation of the state of the observed carrier 14 but allows, as described below, to calculate the covariance of the error on the position of the observed carrier 14 in the Serret-Frenet frame, and • H, h and P are the spherical coordinates of the velocity vector of the observed carrier 14 in the Serret-Frenet frame.

[0127] The function allowing to calculate the vector xSF from the vector xMSC is noted j-si^wsc cl verifies by definition the following mathematical relation:

[0128] xSF - fSF"MSC {XMSC)

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

[0130] nSF _ rSF~*MSC nMSC rSF^MSCT

[0131] Where: jSF^MSC denotes the Jacobian matrix associated with the function j-SF^MSC

[0132] • pMSC denotes the covariance matrix associated with the vector xMSC, and • M1 denotes the transpose of the matrix M. The calculator 18 then obtains the covariance matrix Pç\ of the error associated with the initial state xo from the coefficients of the covariance matrix pSF as follows:

[0133] 0 0 0 0 0 0 0 0 1 0 pSF *6.6 pSF *3.6 pSF *1.6 *2.6 »SF *3.6 0 0 nSF' *4.6 0 pSF *5.6 pSF *5.5 pSF ^1.5 pSF *3.5 0 0 pSF * 4.5 0 nSF *1.6 pSF * 1.5 pSF * ht «SF * 1.2 pSF *1.3 0 0 pSF *1.4 0 pSF *2.6 p^F *2.5 mSF *1.2 nSF * 2.2 p^F “2.3 0 0 pSF *2.4 0 pSF r 3.6 pSF *3.5 pSF *1.3 PZ pSF *3.3 0 0 pSF *3.4 0 0 0 0 0 0 qp 0 0 0 0 0 0 0 0 0 0 1 o pSF *4.6 pSF *4.5 pSF r 1.4 pSF *2.4 pSF *3.4 0 0 P^F 1 * 4.41

[0134] During the prediction operation 02, the calculator 18 predicts the state and the associated covariance Pk+iik at the instant ^+i of the next measurement, from the estimated state and the associated covariance Pkik at the instant of the last measurement.

[0135] In the previous notation, denotes the predicted value for quantity A at time h knowing the value for quantity A at time tj.

[0136] The calculator 18 deduces the predicted state xk+ük at time ^+1 from the last estimated state xkik at date using the following system:

[0137] Or: (j^SF — [ r 0 y ] T denotes the instantaneous rotational velocity vector of the carrier

[0138]

[0139]

[0140]

[0141] observed 14 in the Serret-Frenet reference frame, ( represents the matrix associated with the vector product (noted “x”) with the vector , such that V ae p3 ( c^F)x ■ a = (^FX a, • ^ = ^+r^, and • ^F = [u 0 0]r denotes the velocity vector of the observed carrier 14 in the Serret-Frenet frame, As a remark, it can be noted 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: '^cef^sf = recef^sf^ pECEF^CE^SF^ ü = q Ji<

[0142] Where: * a = F aT aT aaa ]rest the random vector (of size 9x1) modeling ["w " / > “y “wJ the model noise (assumed to be Gaussian with zero mean and covariance matrix ô).

[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+uk at the instant from the last associated covariance P^ using the following relation:

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

[0146] iO -y 0 0 0 0 0 -1 0 | y 0 -r 0 0 0 0 0 0 0 T 0 0 0 0 -1 0 0 0 0 0 0 -y 0 0 0-1 A- 0 0 -uy 0 -t 0 0 0 0 U 0 0 T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 !o 0 0 0 0 0 0 0 o 1

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

[0148] ^A^ + q

[0149] Integrating this equation over the time interval Ai allows us to obtain according to the following equation:

[0150] The previous formulation is thus obtained by noting that = MW)'

[0151] At the end of the prediction operation 02, the computer 18 thus has the state xk+iik as well as the associated covariance Pk+iik at the instant ^+f.

[0152] During the estimation operation 03, the computer 18 estimates the state xi<+iik+i and the associated covariance Pk+uk+i with the measurement J^+i carried out at the instant tk+i 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 calculator 18 estimates the estimated state xk+iik+i as well as the associated covariance Pk+iik+i using the following system: Fr p» F r FF > «JOT-Sf^e \ «- Pis + 3|k + v Pk4.qk '-^l + lH Ykn[& Y ~ *9m|& As

[0155] Where: * ï a T fi TRX x 1T — ir „ denotes the correction vector applied to [ 0« Op Oy Ox Ou ] — A ■ $£+| the predicted state xk+iik , and • G{ ôu) is a function defined by:

[0156] l-cos(]|ô(J|) ô(!!-sin[]|ô'(j|) 2

[0157] where / 3 is the identity matrix of order 3 and ( denotes the matrix associated with the vector product with the matrix 5^. • I9 is ​​the identity matrix of order 9, • H is a matrix such that:

[0158] Where: • Py is the first coordinate of the vector p^GLP giving the position of the observed carrier 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 which depends non-linearly on the position P of the observed carrier 14, this function ^Az verifying:

[0159] L _ atan2 ( p^ p) • 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 dp observed 14, • hEI is an observation function of the elevation angle of the observed carrier 14 in the GLP frame, a function which depends non-linearly on the position P of the observed carrier 14, this function h11 verifying: t°16°l A^-atanf-rM • Pp is the third coordinate of the vector p^^giving the position of the observed carrier 14 in the GLP frame, • hE is an observation function of the energy of the observed carrier 14 in the image, a function which depends non-linearly on the position P and the orientation R of the observed carrier 14, this function hE verifying: 101611 • vec(.) is the vectorization operator of a matrix by concatenation of its columns, • It is the matrix such that: $33 $33 \ £= : \ $33 $3.,3

[0162]

[0163] , And D is the matrix such that: 0 0 -1 -1 0 1 -1 0 ^+i is the innovation which is defined by: • “B W'*') - + «« K is the Kalman gain, this gain being obtained by the following formula: K = (H Aff1

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172] Or: • denotes the inverse matrix of matrix A, • N is the covariance matrix of the noise vector n = [nEl nE]T which is a random vector modeling the measurement noise (assumed here to be Gaussian with zero mean). As a side note, it may be noted that these expressions derive from the observation model as now described. For sensor 16, the measurement vector associated with the observed carrier 14 is defined as follows: El E]t Or: • 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 bound to the carrier 10, and • E is the energy of the observed carrier 14. The observation model, which allows the statex to be linked to the measurement vector, is written mathematically according to the following system: Az = atan2 ( p^ pN ) + / P \ El= -atanl -:---...... 4- nE1 \ ! E = 0) + nE 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 a flow of incident photons in gray level in the image, • $ is the size of the entrance pupil area of ​​the sensor 16, • SIR(a, p) is the power radiated by the observed carrier 14 per unit of solid angle in the direction (a, fl), • (V'» 0) corresponds to the angular direction under which the sensor 16 is seen from the observed carrier 14, and • nE is the third component of the noise vector”. The angles V and 7 correspond to the yaw and pitch angles associated with the rotation matrix giving the orientation of the LDV reference frame of the sensor 16 relative to the Serret-Frenet reference point of the observed carrier 14.

[0173]

[0174]

[0175]

[0176]

[0177]

[0178] The yaw and pitch angles correspond respectively to the first two rotations Z and Y' in the 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 (confused in first approximation with the center of mass of the wearer 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, Jf^^^is calculated using the following formula: gSF-LDV _ [ rECEF~*SF ] TrECEF-RGLPrRGLP-LDV Or: • rRGLP-*ldv csl |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 carrier frame 10 and the carrier 10 attitudes in GLP frame). Using the observation functions hEl and hE, the previous expressions can be reformulated according to the following system:

[0179] [Az = hAz(p)+nAz ■ El = hEl(p) + nEl E = hE(p, R} + nE

[0180] The innovation ^+1 corresponding to the measurement thus becomes:

[0181]

[0182] Or: * is 'a Pos^0°n true of the observed carrier 14 in the ECEF frame at the instant ^+i, and * ™ECEF-*SF denotes the true orientation of the observed carrier 14 in the frame “fc+1 ECEF at time ^+1- Furthermore, the true position and orientation of the observed carrier 14 can be expressed as a function of the predicted position and orientation and the state error according to the following relationships: | P&'H P4' * l14' ^¢¢41 S p ' %p. A r -» iT } aâ'ŒF^SF I «OT?--+57^ »£ŒF-»SF| »EC£F^jXFr* i / js iT ~ ^4i|üf 1¾ * (Wxl

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

[0184] The combination of the preceding equations makes it possible to obtain, after first-order linearization, the following relation:

[0185] sk+] = HÇ+n

[0186] We deduce that the covariance S^+i of the innovation is written:

[0187] It follows that the Kalman gain is written:

[0188] With finally the relation rx T x T xsxv „ , it comes: [A, Op 5y<\OuJ = Ksk+1 ~ — KH)

[0189] The method which has just been described therefore makes it possible to exploit the radiometric information of the observed carrier 14 measured in an image in order to remove the ambiguities which 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 moves from the cross 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 No. 2, the observed carrier 14 moves from the cross 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 added to the maneuvers that can already be detected from angular observations.

[0193] [Fig.4] shows two examples of maneuvers that can be discriminated from angular observations alone.

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

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

[0196] Other embodiments making it possible to obtain the same advantages are also conceivable.

[0197] Any technique other than an MSC-EKF filter allowing the SE1 initialization sub-step to be carried out can be considered here.

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

[0199] In the case of an ambiguity between two types of maneuvers (one leading the observed carrier 14 to go in one direction and the second to go in the opposite direction), the predictions for an increasing distance and a decreasing distance can be calculated simultaneously. One of the two hypotheses may be abandoned when the infrared signature is more or less flagrantly 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 pulses to the environment.

[0202] Thus, in a general case, the determination system 10 comprises a first sensor capable of measuring two angular orientations of an object relative to the first sensor, a second sensor capable of measuring a radiometric signature of the object, and a calculator 18 capable of obtaining the angular orientations and the radiometric signature of the object by receiving the measurements from each of the sensors.

Claims

Claims

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 relative to a sensor (16), - of 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.

2. A determination method 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 gray levels which are added to the pixels of the image due to the presence of the object.

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

4. Determination method according to any one of claims 1 to 3, in which the determination step comprises an initialization sub-step making it possible to obtain an initial estimate of the position of the object, the estimator being applied to the measurements obtained and the initial estimate.

5. A determination method according to claim 4, wherein the initialization sub-step is implemented by applying an estimator to the angular orientations.

6. A determination method according to any one of claims 1 to 5, wherein the estimator used during the initialization sub-step is an extended Kalman filter in modified spherical coordinates.

7. Determination method according to any one of claims 1 to 6, in which the estimator applied to the measurements obtained is an invariant extended Kalman filter.

8. Calculator (18) capable of determining at least one property of a maneuver of an object, the calculator (18) being capable of: - obtaining measurements: - of two angular orientations of the object relative to a sensor (16), and - of a radiometric signature of the object, and - determining at least one property of a maneuver of an object by applying an estimator to the measurements obtained.

9. System for determining (12) at least one property of a maneuver of an object, the determination system (12) comprising: - a first sensor capable of measuring two angular orientations of an object relative to the first sensor, - a second sensor capable of measuring a radiometric signature of the object, and - a calculator (18) according to claim 8, the calculator (18) being capable of obtaining the angular orientations and the radiometric signature of the object by receiving the measurements from each of the sensors.

10. Carrier (10) comprising a calculator (18) according to claim 8 or a determination system (12) according to claim 9.

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