METHOD AND DEVICE FOR ESTIMATE THE CONDITION OF A MANEUVER OBJECTIVE USING A MOBILE RADAR

Description

Previous art

[0001] The invention relates generally to the field of surveillance systems and in particular to a method and device for estimation implemented in a mobile radar.

[0002] The use of radar has seen a major boom in recent years in various fields such as aeronautics, automotive, and metrology. Radar is an effective tool not only for detecting the presence of a distant target but also for monitoring the evolution of its state over time through an estimation process. Such a target state can be represented by a set of state parameters, classically including position, velocity, and acceleration.

[0003] Existing radars can be classified according to several criteria such as mobility, the frequency band of the signals handled, the mode of operation, etc. A radar can operate in an active mode in which the radar emits signals and analyzes the part backscattered by the target in question, or in a passive mode in which the role of the radar is limited to analyzing the signals that can be emitted by the target.

[0004] To estimate the state of a distant target using radar operating in active or passive mode, it is known to first develop a dynamic model, as accurate as possible, that represents the evolution of the target's state over time through a mathematical equation called the state equation. A filtering algorithm is then applied, using the developed state equation and taking into account experimental measurements taken by the radar, to estimate the target's state. Such a filtering algorithm is often implemented recursively, executing two steps at each iteration: a prediction step followed by a correction step, also called an update step. The first step consists of solving the state equation to provide a priori state.The second step of the filtering algorithm is triggered after receiving a measurement of the target's state and adjusts the target's a priori state, as already predicted, with the measurement to return a posteriori state of the target. The filtering algorithm can associate a covariance matrix with the posteriori state of the target to reflect the degree of reliability of the estimated posteriori state of the target.

[0005] The state of the target being tracked can evolve according to a linear dynamic model. In a discrete-time system, a linear dynamic model implies that each state parameter of the target at a given time k can be expressed by an equation comprising a linear combination of the state parameters of the target at the previous time (k-1). Similarly, a measurement of the state of the target at a given time k can comprise a linear combination of the state parameters of the target with respect to the same time k. Each calculated or measured state parameter of the target can be affected by noise, which can be additive Gaussian white noise whose parameters can differ from one state parameter of the target to another and from one measurement time to another. A linear dynamic model also preserves the law governing the noise that affects the state parameters of the target as it passes from one processing time to another.Suitable filters for tracking the linear evolution of a target have been proposed and implemented, such as the linear Kalman filter. A linear Kalman filter calculates the target's prior state at the prediction stage of each iteration by solving the state equation provided by the model and associates a covariance matrix, known as the prior covariance matrix, with the calculated prior state. The outputs of the prediction stage are used in the correction stage to calculate a gain for the Kalman filter, which is then used to weight the contributions of the target's prior state and the measurement when calculating the target's posterior state. A covariance matrix of the error, known as the posterior error covariance matrix, is calculated and associated with the target's posterior state. The outputs of the correction stage are then used as inputs in the next iteration of the linear Kalman filter.

[0006] Modern targets are increasingly maneuverable, so a linear evolution model is often unable to govern the evolution of their state. In a nonlinear evolution model, each target state parameter calculated at time k can comprise a nonlinear combination of the target's state parameters at the previous time (k-1). Similarly, each target state parameter measured at a given time k can comprise a nonlinear combination of the target's state parameters with respect to the same time k. A nonlinear state function linking two consecutive target states and a similarly nonlinear measurement function linking the target state to the measurement taken can be defined.The complexity of a nonlinear evolution model lies primarily in the fact that the law governing the noise affecting the target's state parameters at a given time (k-1) may not be the same at a later time k. For example, a random variable following a Gaussian probability distribution may lose its probability distribution by undergoing a nonlinear transformation. The Extended Kalman Filter (EKF) has been proposed to estimate the state of a target evolving according to a nonlinear model by linearizing, at each iteration, the state function governing the target's state evolution around the mean of the estimated state using the partial derivatives of the state function. Similarly, the measure function can be linearized around the estimated current state using the partial derivatives of the measure function.

[0007] An extended Kalman filter, however, presents numerous drawbacks. In particular, it does not guarantee convergence and does not respect the invariances that the system being estimated may possess. An extended Kalman filter can exhibit divergences that may be initiated by small errors in state estimation. Furthermore, the linearization of the state and / or measurement functions required at each iteration of such a filter necessitates significant computing power that is often unavailable on board, for example, in the case of an airborne radar.

[0008] To overcome such limitations of the extended Kalman filter, a variant of this filter, called the invariant extended Kalman filter (also referred to by the acronym 'IEKF'), is known to be used, as described, for example, in Marion Pilté, Silvère Bonnabel, and Frédéric Barbaresco, Invariant Extended Kalman Filter for Target Tracking, URSI France 2018. An IEKF filter takes advantage of the invariances that the system to be estimated may exhibit. Transformations such as rotation and translation can leave a system to be estimated invariant. An IEKF filter consists of defining the stochastic processes of the noise and modifying the gains of the extended Kalman filter so that they respect the invariances of the system to be estimated. The IEKF has the advantage of considering the noise affecting the system to be estimated as independent of the predicted state of the maneuvering target.This approach significantly reduces computational complexity compared to a conventional extended Kalman filter. An IEKF filter is typically used for tracking maneuvering targets with a radar (also called an 'observer') fixed relative to the ground.

[0009] There is therefore a need for an improved method and device for estimating the state of a maneuvering target implemented in a mobile radar relative to the ground. General definition of the invention

[0010] The invention improves the situation. To this end, a method for estimating the state of a target is proposed, implemented in a mobile radar operating in a given space. The radar receives a plurality of estimation signals relating to the target. The method comprises one or more iterations, each iteration being associated with a given instant and including a step of applying an invariant extended Kalman filter. Each iteration provides an estimate of the target's state represented by state data comprising a set of state parameters and an associated covariance matrix. The state data is defined with respect to a reference frame associated with the position of the mobile radar. Each current iteration comprises the steps of: Apply a transformation operation to the frame, which provides a transformed frame, the transformed frame being associated with the position of the moving radar at the time associated with the current iteration, Update in the transformed frame the state data determined at the previous iteration, Apply the invariant extended Kalman filter.

[0011] The step of applying the invariant extended Kalman filter advantageously includes the steps of: Determine an estimated a priori state of the target defined in the transformed frame from the data including the state data determined in the previous iteration updated in the transformed frame, Determine an a posteriori state of the target defined in the transformed frame from the data including the data of the estimated a priori state of the target and the data from at least one of the estimation signals.

[0012] According to the invention, the target state parameters include an orientation matrix, a curvature parameter defining the curvature of the target trajectory, a torsion parameter, the magnitude of a velocity vector representing the velocity of the target, and target position data defined by Cartesian coordinates.

[0013] The radar can operate in active and passive modes. The estimation signals can then include one or more passive estimation signals sequentially emitted by the maneuvering target and one or more active estimation signals backscattered by the maneuvering target in response to at least one active signal emitted by the mobile radar.

[0014] In one embodiment, the number of active estimation signals is less than the number of passive estimation signals.

[0015] The a posterior state of the target can also be determined from the noise covariance matrix associated with each tracking signal, the noise covariance matrix associated with an active estimation signal being different from the noise covariance matrix associated with a passive estimation signal.

[0016] The target can evolve in a fixed two-dimensional plane of motion over time.

[0017] In one embodiment, the state parameters may include an angle defining the heading of the target, a two-dimensional Cartesian position of the target, a curvature parameter defining the curvature of the target's trajectory, and a magnitude of a velocity vector representing the velocity of the maneuvering target in the plane of motion.

[0018] In one embodiment, the state parameters of the target may further include the magnitude of the velocity vector representing the velocity of the maneuvering target defined with respect to a fixed and time-invariant measurement frame.

[0019] Only one active estimation signal among the estimation signals can be used to estimate the state of the maneuvering target.

[0020] In one embodiment, the method may further include determining the elevation angle and azimuth angle defining the direction in which the maneuvering target lies relative to the mobile radar from a passive estimation signal received by the mobile radar.

[0021] In some embodiments, the method may further include determining at least one of the following parameters from an active estimation signal received by the mobile radar: the elevation angle and the azimuth angle defining the direction in which the maneuvering target is located relative to the mobile radar, the relative distance separating the mobile radar from the target, the radial velocity of the target relative to the mobile radar.

[0022] In various forms of implementation, mobile radar can be airborne or space-based.

[0023] The state data received by the first iteration can be initialization state data.

[0024] It is further proposed a mobile radar comprising a device for estimating the state of a target evolving in a given space, the radar receiving a plurality of estimation signals relating to the target, executing one or more iterations, each of the iterations associated with a given instant comprising an application of an invariant extended Kalman filter and providing an estimate of the state of the target represented by state data comprising a set of state parameters and an associated covariance matrix, the state data being defined with respect to a frame associated with the position of the mobile radar at said instant, fixed throughout an iteration, and the target state parameters (101) comprising an orientation matrix, a curvature parameter defining the curvature of the target's trajectory, a torsion parameter, the magnitude of a velocity vector representing the velocity of said target,and target position data defined by Cartesian coordinates. The state estimation device is configured to execute at each iteration: , A coordinate transformation function capable of applying a transformation operation to the coordinate system, which provides a transformed coordinate system, the transformed coordinate system being associated with the position of the mobile radar at the time associated with the current iteration, An update function capable of updating in the transformed coordinate system the state data determined at the previous iteration, An invariant extended Kalman filter.

[0025] The invariant extended Kalman filter includes: A prediction function capable of determining an estimated a priori state of the target defined in the transformed frame from data including the state data determined in the previous iteration updated in the transformed frame, A correction function capable of determining an a posteriori state of the target defined in the transformed frame from data including the data of the estimated a priori state of the target and the data from at least one of the tracking signals. Brief description of the figures

[0026] Other features and advantages of the invention will become apparent from the following description and the accompanying figures, in which: [ Fig.1 ] represents an example of a system in which a target estimation device is implemented, according to embodiments of the invention, [ Fig. 2] represents another example of a system in which a target estimation device is implemented, according to other embodiments of the invention, [ Fig. 3 ] represents the evolution of the trajectory of a maneuvering target in a three-dimensional space equipped with a reference frame defined by a moving radar over time, according to one embodiment, and [ Fig. 4 ] represents a target estimation method, according to embodiments of the invention. Detailed description

[0027] There figure 1This represents an example of a system for tracking the state of a target 100, comprising a mobile radar 102 equipped with a device for estimating the state of a maneuvering target, according to embodiments of the invention. The estimating device is configured to track the evolution over time of the state of a maneuvering target 101. The maneuvering target 101 can be any object moving in three-dimensional (3D) space, such as an aircraft, a drone, or a rocket. The mobile radar 102 can be used by a second object, such as an aircraft, moving in the same 3D space. The movement of the maneuvering target can be independent of the movement of the mobile radar. The maneuvering target can move along one or more geometric shapes with a speed that can vary over time. Such geometric shapes can include helices, straight line segments, etc.

[0028] The mobile radar 102 can be configured to alternate between active and passive modes, in a manner that may not be periodic. In active mode, the mobile radar 102 emits electromagnetic signals toward the maneuvering target 101. These electromagnetic signals may strike the maneuvering target 101 and be reflected back in the direction from which they originated, according to a principle of backscattering. Backscattered electromagnetic signals from the maneuvering target 101 can then be received by the mobile radar 102 for analysis. The mobile radar 102 can be configured to determine a plurality of parameters about the position of the maneuvering target from these backscattered electromagnetic signals.Such parameters may include the azimuth and elevation angles defining the direction in which the maneuvering target 101 is located, the distance separating the mobile radar 102 from the maneuvering target 101, and the relative radial velocity of the maneuvering target 101 with respect to the mobile radar 102.

[0029] In a passive operating mode, the mobile radar 102 does not emit electromagnetic signals in the direction of the maneuvering target 101 and directly analyzes any signals that may be deliberately emitted by the maneuvering target 101. The mobile radar 102 can determine the direction of the maneuvering target 101, defined by its azimuth and elevation angles relative to its position, by analyzing a signal emitted by the maneuvering target 101. A passive operating mode of the mobile radar 102 has the advantage of allowing discreet tracking of the maneuvering target 101. In such an operating mode, the mobile radar 102 determines fewer parameters about the position of the maneuvering target 101 than in an active operating mode.

[0030] Embodiments of the invention can implement both operating modes of the mobile radar 102 so as to frequently obtain passive measurements and occasionally active measurements. For example, a passive measurement can be acquired every one or two seconds, while an active measurement can be performed every minute. When an active estimation signal and a passive estimation signal are received simultaneously to estimate the target's state, the radar can be configured to process only the active signal, which allows for the determination of more parameters about the target's position than a passive estimation signal. The radar can receive estimation signals irregularly over time.In the absence of passive estimation signals deliberately emitted by the target to be tracked, the radar can be configured to use the active estimation signals it generates to maintain tracking of the target's state.

[0031] In other embodiments of the invention, the mobile radar 102 can be configured to operate in an active-only mode. Such an operating mode is advantageous when the maneuvering target does not emit electromagnetic signals or when the attenuation of the signals emitted by the maneuvering target prevents their detection and exploitation by the mobile radar. The attenuation of the electromagnetic signal power is proportional to their frequency and to the distance separating the maneuvering target 101 from the mobile radar 102.

[0032] Alternatively, the mobile radar can be configured to operate in a purely passive mode. This mode offers the advantage of enabling discreet tracking.

[0033] There figure 2 represents another example of a system 100 in which a device for estimating the state of a moving target 101 can be implemented, according to embodiments of the invention. In the example of the figure 2The maneuvering target 101 can move in a two-dimensional (2D) plane. This target can be terrestrial, such as a car or a surface vessel (ship or other). Alternatively, it can be an airborne target reduced to a 2D model when its movement is consistently in a two-dimensional plane. The movement of the maneuvering target 101 in a two-dimensional plane can, for example, follow a straight or sinusoidal trajectory. The maneuvering target 101 can change the characteristics of its trajectory at any time. These characteristics can include the geometric shape of the trajectory and the speed of movement.

[0034] There figure 3is a diagram representing state parameters of the maneuvering target 101 when the target evolves in a three-dimensional space associated with a measurement frame (301) whose center corresponds to the position of the mobile radar 102, according to certain embodiments of the invention.

[0035] The state of target 101 is represented by state data comprising a set of state parameters and a covariance matrix associated with those parameters. The state data can all be defined with respect to the same measurement frame. Alternatively, some state data can be defined in a different measurement frame relative to other state data.

[0036] According to the invention, the target state parameters include an orientation matrix R twhich can define a frame of reference whose basis vectors constitute a Frenet-Serret trihedron linked to the maneuvering target 101. The origin of such a trihedron can be defined by the position of the target 101, the basis vectors of the trihedron being unit vectors, orthogonal in pairs, and comprising: A tangent vector T to the trajectory and collinear with the target's velocity vector (assuming no slippage), a normal vector N oriented towards the local center of curvature of the trajectory, and a binomial vector B complete the trihedron to obtain an orthonormal basis. The target's state parameters include a trajectory curvature parameter. γ t and a torsion parameter τ t .The trajectory curvature parameter represents the tendency of the maneuvering target 101 to deviate from the osculating plane. The two parameters of curvature and torsion govern the evolution of the orientation matrix according to the following relationships: d T → dt = γ t N → ; d N → dt = − γ t T → + τ t B → ; d B → dt = − τ t N →

[0037] The state parameters of the maneuvering target 101 further include the target's position in Cartesian coordinates xt defined in measurement reference frame 301 and standard ut of the target's velocity vector.

[0038] The target's state parameters defined at time t can thus be represented by the vector X t following : X t = R t x t γ t τ t u t

[0039] The evolution over time of the state parameters of the maneuvering target 101 can be determined from the evolution of the axes of the orientation matrix given by relation (1), considering that the target obeys piecewise constant commands. Such commands are represented by the curvature parameters. γ t and torsion τ t and the magnitude of the velocity vector ut .

[0040] The variations in the state parameters of the maneuvering target 101 can be represented by the following derivatives: dx t dt = R t v t + w t x ; d R t dt = R t w t + w t ω × ; dγ t dt = 0 + w t γ ; dτ t dt = 0 + w t τ ; du t dt = 0 + w t u In equation (3): (a) × of R 3×3< denotes the antisymmetric matrix associated with a vector a of R 3< such that for a vector b of ℝ 3 : a × b = a ∧ b , v t = u t 0 0 , ω t = τ t 0 u t , and Each of the elements w t x , w t ω , w t γ , w t τ , w t u represents an additive Gaussian white noise.

[0041] The state parameters of the maneuvering target 101 comprise two groups of state parameters. The first group of state parameters includes the orientation matrix R t and the position of the target x t The first group of state parameters can be represented by a square matrix χ t , depending on the orientation matrix R t and the position of the target x t , such as : χ t = R t x t 0 1 , 3 1

[0042] The second group of state parameters includes the curvature parameter γ t , the torsion parameter τ t and the magnitude of the velocity vector ut of the target. The second group of state parameters can be represented by a matrix ζ t dependent on the curvature parameter γ t , of the torsion parameter τ t and the magnitude of the velocity vector ut of the target, such as: ζ t = γ t τ t u t

[0043] According to other embodiments of the invention, the maneuvering target 101 can evolve in a two-dimensional (2D) plane. In such embodiments, the state of the target can be described by state parameters comprising the Cartesian coordinates x t of the target in 2D, the curvature of the trajectory γ t , the heading of the target θ, speed change of course γ = dθ dt and the magnitude of the velocity vector u. The state parameters of the target can be represented by a state vector having the following components: x t , γ t , 0, y, u .

[0044] There figure 4is a flowchart representing the steps implemented in the method for estimating the state of a maneuvering target 101, according to certain embodiments of the invention. The method for estimating the state of a maneuvering target 101 can advantageously be implemented in a ground-mobile radar 102 configured to receive passive and / or active measurements of the position of the maneuvering target 101. Such a method is recursive and may comprise one or more iterations of a set of steps.

[0045] The method for estimating the state of a target is based on an invariant extended Kalman filter and further includes a transformation step 401 of the measurement frame 301 and an update step 402 of the state of the moving target 101 already estimated in a previous iteration of the estimation process in the transformed measurement frame 301. The transformation of the measurement frame 301 at each iteration allows manipulation of the estimated a priori and a posteriori states of the target 101 and a measured position defined with respect to the same measurement frame 301. Such a transformation of the frame significantly reduces the computational complexity. The estimation process may further include a step for redefining certain parameters of the state of the moving target 101 in an absolute measurement frame (a step not shown in the diagram). figure 4). Such a step of redefining certain parameters can be performed after the correction step of the invariant extended Kalman filter 404. The operation of the estimation method as described with reference to the figure 4 can be performed using a discrete-time system that associates a time instant tk with each iteration of the process. The time interval between two successive instants, tk-1 and tk, may not be constant. The iteration associated with an instant tk may receive the state estimated during the previous iteration. Furthermore, the first iteration of the estimation process represented by the figure 4 can receive a target initialization state. Such an initialization state can be configured to ensure the convergence of the target state estimation process.

[0046] According to the transformation step of measurement frame 401, a new measurement frame 301 (also called the transformed frame) can be defined between times tk-1 and tk. The transformed frame 301 can have as its origin the position where the radar will be located at time tk associated with the current iteration of the target state estimation process. Such a position can be known precisely in advance. The three axes of the transformed frame 301 can be oriented in the respective directions East, North, and Up. The change of measurement frame 301 can therefore involve a rotation relative to the previous measurement frame 301. The transformed frame 301 is defined by its origin and its axis system. (O k , ek , nk , uk ) can be defined from the previous measurement frame 301 (O k-1 , e k-1 , n k-1 , u k-1 ) according to the following relations: O k − 1 O k → = o x e → k − 1 + o y n → k − 1 + o z u → k − 1 e → k − 1 = e x e → k + e y n → k + e z u → k n ¯ k − 1 = n x e → k + n y n → k + n z u → k n ¯ k − 1 = n x e → k + n y n → k + n z u → k

[0047] The elements ox, oy, oz, ex, ey, ez, nx, ny, nz, ux, uy and uz can be real numbers, the value of these numbers being able to change from one iteration to another.

[0048] The measurement frame change step 401 can be followed by a target state update step 402 as estimated in the previous iteration t k-1 in the transformed frame 301. In one embodiment, the state parameters of the maneuvering target 101 evolving in a 3-dimensional space that can be redefined in the transformed frame 301 may include the orientation matrix R t and the position of the target defined by its Cartesian coordinates xt. In the 402 update step, the target state can be redefined using a coordinate change matrix. M k − 1 k defined by the following elements: M k − 1 k = e x n x u x e y n y u y e z n z u z

[0049] The orientation matrix estimated at iteration t k-1 of the estimation process can be updated in the transformed frame 301, according to the following relationship: R ^ k − 1 k − 1 repère à t k = M k − 1 k R ^ k − 1 k − 1 repère à t k − 1

[0050] Similarly, the position of the maneuvering target 101 estimated at iteration t k-1 of the estimation process can be redefined in the transformed frame 301, according to the following relationship: x ^ k − 1 k − 1 repère à t k = M k − 1 k x ^ k − 1 k − 1 repère à t k − 1 − o x o y o z

[0051] State parameters of the maneuvering target 101 can be associated with the transformed frame 301 without undergoing any transformation. Such parameters can include the curvature parameters γ t and torsion τ t and the magnitude of the velocity vector ut of the target.

[0052] The state of the target thus updated in the transformed frame 301 can then be used to apply an extended Kalman filter invariant according to steps 403 and 404.

[0053] Applying a Kalman filter comprises a prediction step 403 and a correction step 404. In the prediction step 403, a prediction of the target state is made using the target state estimated at the previous iteration tk-1, as redefined in the transformed frame 301, and a state equation governing the evolution of the target trajectory, taking into account the invariances that characterize such evolution. The prediction step 403 provides a prior state of the target and an associated covariance matrix. The predicted target state, comprising a set of state parameters and an associated covariance matrix, can be defined with respect to the transformed measurement frame 301.

[0054] In step 403 of predicting the state of the maneuvering target 101 evolving in three-dimensional space, the following equations are solved to go from estimates made at time t k-1 to the estimates made just now TK : d χ t ^ dt = χ t ^ v t ^ , d ζ t ^ dt = 0

[0055] In equation (10), vt denotes a square matrix of order four defined by the state parameters of the target ζ t according to the following relationship: v t = 0 − γ t 0 u t γ t 0 − τ t 0 0 τ t 0 0 0 0 0 0

[0056] The covariance matrix associated with the estimated state parameters can be determined by solving the Riccati equation given by the following relationship: dP t dt = A t P t + P t A t T + Q t

[0057] In equation (12), Q t denotes a covariance matrix of state noise and A t denotes a given evolution matrix defined by the following relationship: A t = − τ ^ t 0 γ ^ t × 0 3 , 3 0 1 0 0 0 0 1 0 0 − u ^ t 0 0 × − τ ^ t 0 γ ^ t × 0 0 1 0 0 0 0 0 0 0 3 , 3 0 3 , 3 0 3 , 3

[0058] In correction step 404, the pre-estimated target state data, including the set of state parameters and the associated covariance matrix, as determined in step 403, are used. The correction step may also use a target state measurement determined in step 405, which may be incomplete and / or noisy, along with a covariance matrix associated with the measurement noise.

[0059] In correction step 404, an error parameter and a Kalman gain are first calculated. The posterior state of the target can then be estimated by taking into account the target state measure determined in step 405. A covariance matrix associated with the posterior state of the target is then estimated.

[0060] The error parameter can be defined as the difference between the measured state of the target and its predicted state. The calculation of the error parameter can use one of the state parameters of the maneuvering target. In embodiments of the invention, the calculation of the error parameter can use the estimated position of xt and the measured position Y k of the state of the target according to the following relationship: z k = R t k ^ Y k − x t k ^

[0061] The estimated position and the measured position are defined relative to the same measurement frame, which may be the transformed frame 301. When the current iteration of the target state estimation process is associated with an active estimation signal, the measured position can be determined from one or more position parameters provided by the active estimation signal. Such position parameters include, in this embodiment, the distance between the moving radar and the maneuvering target. Alternatively, when the current iteration is associated with a passive estimation signal, the measured position can be determined from at least the elevation and azimuth angles provided by the passive estimation signal. Such a passive mode of operation may use one or more localization techniques to determine the position of the maneuvering target.Such localization techniques may include analysis of the angle of arrival and analysis of the strength of the received signal.

[0062] The Kalman gain can be determined using the following relationship: L k = P t k H T HP t k H T + R t k ^ N R t k ^ T − 1

[0063] In equation (15), the matrix H is defined by H = (0 3.3 I 3 0 3.3 ).

[0064] The state of the maneuvering target 101 estimated a posteriori can then be calculated according to equation (16): χ t k + ^ = χ t k ^ exp L k z k 1 : 6 , ζ t k + ^ = ζ t k ^ + L k z k 7 : 9

[0065] The covariance matrix associated with the estimated a posteriori state can then be obtained by calculating: P t k + ^ = I 9 − L k H P t k

[0066] According to embodiments of the invention, the state parameters of the maneuvering target may include the magnitude of the target's velocity vector defined with respect to an absolute reference frame, which may be the Earth's reference frame. Such a magnitude of the velocity vector can be obtained from the velocity vector of the mobile radar relative to the ground and the velocity vector of the maneuvering target relative to the mobile radar. The velocity vector of the mobile radar relative to the ground can be accurately determined by the mobile radar itself.

[0067] Those skilled in the art will understand that the target state estimation and estimation method, according to the embodiments, can be implemented in various ways by hardware, software, or a combination of hardware and software, including in the form of program code that can be distributed as a program product in various forms. In particular, the program code can be distributed using computer-readable media, which may include computer-readable storage media and communication media. The methods described herein can, in particular, be implemented in the form of computer program instructions executable by one or more processors in a computer system. These computer program instructions can also be stored in computer-readable media.

Claims

1. Method for estimating the status of a target (101) implemented in a mobile radar (102) moving in a given space, said radar receiving a plurality of estimation signals relating to said target (101), the method comprising one or more iterations, each of said iterations being associated with a given moment and comprising a step of applying an invariant extended Kalman filter, each iteration providing an estimation of the status of the target represented by status data comprising a set of status parameters and an associated covariance matrix, said status data being defined in relation to a reference point associated with the position of said mobile radar at said moment, fixed throughout an iteration, and the target status parameters (101) comprising an orientation matrix, a curvature parameter defining the curvature of the trajectory of the target, a torsion parameter, the norm of a speed vector representing the speed of said target, and position data of the target defined by Cartesian coordinates, the method being characterised in that each current iteration comprising the steps consisting in: - Applying a transformation operation to the reference point (401), which provides a transformed reference point, the transformed reference point being associated with the position of the mobile radar at the moment associated with the current iteration, - Updating (402) in the transformed reference point, the determined status data at the preceding iteration, - Applying the invariant extended Kalman filter (403, 404), said step of applying the invariant extended Kalman filter comprising the steps consisting in: - Determining an a priori estimated status (403) of the target defined in the transformed reference point from the data comprising the determined status data at the preceding iteration updated in the transformed reference point, - Determining an a posteriori status of the target (404) defined in the transformed reference point from the data comprising the data of the a priori estimated status and the data coming from at least one of the estimation signals.

2. Method for estimating the status of a target according to claim 1, characterised in that the radar operates in active mode and in passive mode, and in that said estimation signals comprise one or more passive estimation signals, sequentially emitted by said manoeuvring target (101) and one or more active estimation signals backscattered by said manoeuvring target in response to at least one active signal emitted by the mobile radar (102).

3. Method for estimating the status of a target according to claim 2, characterised in that the number of active estimation signals is less than the number of passive estimation signals.

4. Method for estimating the status of a target according to claim 3, characterised in that the a posteriori status of said target is further determined from the noise covariance matrix associated with each monitoring signal, the noise covariance matrix associated with an active estimation signal being different from the noise covariance matrix associated with a passive estimation signal.

5. Method for estimating the status of a target according to any one of preceding claims 2 to 4, characterised in that said torsion parameter is maintained substantially equal to zero.

6. Method for estimating the status of a target according to claim 5, characterised in that the status parameters comprise an angle defining the course of the target, a Cartesian position of the two-dimensional target, a curvature parameter defining the curvature of the trajectory of the target and a norm of a speed vector representing the movement speed of the maneuvering target (101) in said movement plane.

7. Method for estimating the status of a target according to any one of the preceding claims, characterised in that the status parameters of the target further comprise the norm of the speed vector representing the speed of the manoeuvring target (101) defined in relation to a measuring reference point, fixed and invariant over time.

8. Method for estimating the status of a target according to any one of claims 2 to 7, characterised in that one single active estimation signal from among said estimation signals is used to estimate the status of the maneuvering target (101).

9. Method for estimating the status of a target according to any one of the preceding claims, characterised in that it further comprises the determination of the elevation angle and of the azimuth angle defining the direction in which the maneuvering target (101) is located in relation to said mobile radar (102) from a passive estimation signal received by the mobile radar (102).

10. Method for estimating the status of a target according to any one of the preceding claims, characterised in that it further comprises the determination of at least one of the following parameters from an active estimation signal received by the mobile radar (102): - the elevation angle and the azimuth angle defining the direction in which the maneuvering target (101) is located in relation to said mobile radar (102), - the relative distance separating the mobile radar (102) from the target (101), - the radial speed of the target (101) in relation to said mobile radar (102).

11. Method for estimating the status of a target according to any one of the preceding claims, characterised in that the mobile radar (102) is airborne or spatial.

12. Method for estimating the status of a target according to any one of the preceding claims, characterised in that the status data received by the first iteration are initialisation status data.

13. Mobile radar (102) comprising a device for estimating the status of a target (101) moving in a given space, said radar receiving a plurality of estimation signals relating to said target (101), executing one or more iterations, each of said iterations associated with a given moment comprising an application of an invariant extended Kalman filter and providing an estimation of the status of the target represented by status data comprising a set of status parameters and an associated covariance matrix, said status data being defined in relation to a reference point associated with the position of said mobile radar at said moment, fixed throughout an iteration, and the target status parameters (101) comprising an orientation matrix, a curvature parameter defining the curvature of the trajectory of the target, a torsion parameter, the norm of a speed vector representing the speed of said target, and position data of the target defined by Cartesian coordinates, the radar being characterised in that said status estimation device is configured to execute, at each iteration: - A reference point transformation function, capable of applying a transformation operation to the reference point, which provides a transformed reference point, the transformed reference point being associated with the position of the mobile radar at the moment associated with the current iteration, - An updating function, capable of updating in the transformed reference point, the determined status data at the preceding iteration, - An invariant extended Kalman filter, said invariant extended Kalman filter comprising: - A prediction function capable of determining an a priori estimated status of the target defined in the transformed reference point from the data comprising the determined status data at the preceding iteration updated in the transformed reference point, - A correction function, capable of determining an a posteriori status of the target defined in the transformed reference point from the data comprising the data of the a priori estimated status and the data coming from at least one of the monitoring signals.