Anti-projectile decoy adaptive tracking method and device based on measurement error multi-model

Abstract

This invention discloses an adaptive tracking method and device for anti-dropped decoys based on a multi-model approach to measurement errors, belonging to the field of radar target tracking technology. The method includes constructing motion and centroid interference models for passive radar dropped decoys to determine the impact of interference on radar measurements; constructing a set of passive radar measurement models characterizing the time-varying characteristics of measurement noise, and establishing a hybrid system with uncertain measurement noise by combining the target motion model; employing an interactive multi-model architecture combined with a capacitive Kalman filter algorithm to perform interactive and parallel filtering on each sub-model of the hybrid system; updating the posterior probability of the measurement noise in each sub-model at the current moment in real time based on the measurement residuals and information covariance; and performing weighted fusion of the state estimates of each sub-model to obtain the adaptive tracking result. This invention effectively solves the tracking divergence problem caused by weak observability and time-varying measurement errors in passive radar under dropped decoy interference, significantly improving the tracking accuracy and robustness of the system.

Description

Technical Field

[0001] This invention relates to radar measurement error adaptive target tracking technology, and in particular to an adaptive tracking method and device for anti-dropped decoys based on a multi-model measurement error. Background Technology

[0002] With the rapid development of modern electronic countermeasures technology, decoys have become a serious active jamming method that threatens radar detection effectiveness. These decoys simulate the electromagnetic characteristics of the target or induce radar beam deviation, resulting in a severe deterioration in the quality of target measurement data received by the radar. Specifically, the measurement error increases significantly and changes dynamically over time, greatly increasing the difficulty of stable target tracking.

[0003] While existing anti-jamming technologies attempt to suppress such interference at the signal processing level, they face significant challenges in practical engineering applications. On one hand, radar sensors are typically encapsulated as "black box" systems, outputting only processed point information (such as angle and distance) to higher layers, making it difficult to directly obtain the underlying raw signal characteristics (such as I / Q data and echo waveforms). On the other hand, even if the raw signal can be obtained, the computational complexity of designing anti-jamming algorithms at the signal processing layer is extremely high in the face of decoy interference with unknown mechanisms and dynamic variations, making it difficult to meet real-time requirements. Therefore, starting from the data processing layer (i.e., the target tracking layer) and directly utilizing contaminated measurement data for anti-jamming tracking has greater engineering versatility.

[0004] Among various radar systems, passive radar is favored for its good concealment and strong survivability, making it a typical application scenario for the aforementioned anti-jamming tracking technologies. However, passive radar typically only provides angular measurements of the target (such as azimuth and elevation angles). Limited by the geometric configuration of single-station passive positioning, the system inherently suffers from poor observability. When encountering decoy interference that causes unknown time-varying statistical characteristics of measurement errors (such as variance), this poor observability is further amplified: directly using conventional nonlinear filtering algorithms (such as extended Kalman filtering, capacitive Kalman filtering, etc.) for tracking is prone to filter gain mismatch, leading to a significant decrease in the accuracy of target position and velocity estimation, and even filter divergence and target loss, resulting in severely insufficient robustness of the system.

[0005] Therefore, there is an urgent need to study an adaptive tracking method that can effectively cope with the interference of thrown decoys under the condition that the underlying signal features cannot be obtained and the measurement error is unknown and time-varying, so as to solve the problems of low accuracy and easy divergence of existing methods in passive tracking weak observation scenarios. Summary of the Invention

[0006] The present invention aims to provide an adaptive tracking method and device for anti-dropped decoys based on a multi-model approach to measurement errors. This addresses the challenges of low tracking accuracy and easy divergence in passive radar under dropped decoy interference due to weak observability and time-varying measurement errors. The invention constructs a decoy interference mechanism model, establishes a set of measurement models characterizing the time-varying noise properties, and a hybrid system with uncertain measurement noise. A nonlinear filtering algorithm is used to process this hybrid system, and the target state is weighted and fused by real-time updates of the posterior probabilities of each noise model. This method achieves adaptive suppression of non-stationary interference noise without requiring the acquisition of the underlying raw signal, effectively improving the tracking accuracy and robustness of passive radar.

[0007] The present invention is achieved through the following technical solution.

[0008] In one aspect, this invention provides an adaptive tracking method for anti-thrown decoys based on a multi-model approach to measurement errors, comprising: A motion and centroid interference model of a passive radar-launched decoy is constructed to determine the decoy's motion in three-dimensional space and its interference with the radar system. Based on the aforementioned interference method, a set of passive radar measurement models characterizing the time-varying characteristics of measurement noise is constructed; Construct a target motion model to determine the target's motion in three-dimensional space; Based on the passive radar measurement model set and the target motion model, a hybrid system with measurement noise uncertainty is constructed, which includes multiple sub-models, wherein each sub-model is composed of a one-to-one combination of the target motion model and each measurement model in the passive radar measurement model set; Passive radar receives measurements from the target at the current moment; The interaction between the tracking results of the various sub-models of the hybrid system at the previous moment; Based on the interaction results and the sub-models of the hybrid system, capacitive Kalman filtering is performed on the interaction result sub-models to obtain the target state estimate, estimation error covariance, measurement residual and innovation covariance of each sub-model of the hybrid system at the current time. Based on the measurement residuals and the information covariance, update the probability that the measurement noise is in each sub-model of the hybrid system at the current moment; Based on the updated probability, the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment are weighted and fused to obtain the state estimates and estimation error covariance of the hybrid system for adaptive tracking of the target, thus realizing adaptive tracking against thrown decoys.

[0009] The present invention further prefers the following solutions to the above technical solutions: Preferably, a motion and centroid interference model of a passive radar-launched decoy is constructed to determine the decoy's motion in three-dimensional space and its interference with the radar system, including: Considering the combined effects of air resistance and gravity, the nonlinear motion trajectory of the decoy in complex environments is determined, and a motion model of the passive radar-launched decoy is constructed. Based on the fact that the decoy and the target are spatially close and cannot be distinguished by radar beams due to their high radiation power, a centroid state is synthesized by weighted averaging of the target state and the decoy state based on the power coefficient, and a centroid interference model for passive radar measurement model of the thrown decoy is constructed.

[0010] Preferably, the tracking results of each sub-model of the hybrid system at the previous moment include: Based on the probability that the measurement noise was in each sub-model of the hybrid system at the previous time step, and the prior probability that the measurement noise would transfer between sub-models, calculate the probability that the measurement noise was in each sub-model at the current time step after the interaction, and the conditional probability that the measurement noise would transfer between sub-models at the current time step. Based on the probabilities solved in the previous step, the tracking results of each sub-model of the hybrid system at the previous moment are interacted to obtain the target state estimates of each sub-model after interaction, as well as the estimation error covariance.

[0011] Preferably, capacitive Kalman filtering is applied to the interaction result sub-model to obtain the target state estimate, estimation error covariance, measurement residual, and innovation covariance of each sub-model of the hybrid system at the current time, including: Based on the target state estimates and estimation error covariance matrices given by each sub-model of the hybrid system after interaction, calculate the target state volume point and the innovation covariance. Based on the target motion model contained in each sub-model, the target state volume point is transformed to obtain the one-step prediction value of the target state volume point; Based on the one-step predicted value of the target state volume point, calculate the one-step predicted value of the target state and the prediction error covariance under each sub-model; Based on the one-step predicted value of the target state and the prediction error covariance under each sub-model, recalculate the one-step predicted value of the target state volume point and the one-step predicted value of the innovation covariance. Based on the passive radar measurement model contained in each sub-model, the one-step prediction value of the target state volume point is transformed to obtain the one-step prediction value of the measurement volume point. Based on the one-step predicted value of the measurement volume point and the one-step predicted value of the target state volume point, calculate the one-step predicted value of the measurement, the information covariance, the filter gain and the measurement residual. Based on the measured one-step prediction value, the information covariance, and the filtering gain, the target state estimate and estimation error covariance given by each sub-model at the current time are obtained.

[0012] Preferably, updating the probability that the measurement noise is in each sub-model of the hybrid system at the current time based on the measurement residual and the innovation covariance includes: Based on the measurement residuals and the information covariance, calculate the likelihood function values ​​of the measurement noise at the current moment for each sub-model of the hybrid system; Based on the likelihood function values ​​of the measured noise in each sub-model of the hybrid system at the current time, and the probability of the measured noise in each sub-model at the current time after the interaction, update the probability of the measured noise in each sub-model at the current time.

[0013] In another aspect, the present invention provides an adaptive tracking device for anti-throwing decoys based on a multi-model measurement error, comprising: The module is used to construct motion and centroid interference models for passive radar-launched decoys; construct a set of passive radar measurement models to characterize the time-varying characteristics of measurement noise; and construct a target motion model to determine the target's motion in three-dimensional space. Construct a hybrid system with measurement noise uncertainty that includes multiple sub-models; The interaction module is used to interact with the tracking results of the various sub-models of the hybrid system at the previous moment; The filtering module is used to perform capacitive Kalman filtering on the interaction result sub-model to obtain the target state estimate, estimation error covariance, measurement residual and innovation covariance of each sub-model of the hybrid system at the current time. The update module is used to update the probability that the measurement noise is in each sub-model of the hybrid system at the current moment; The weighted fusion module is used to perform weighted fusion of the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment, so as to obtain the state estimates and estimation error covariance of the hybrid system for adaptive tracking of the target, and realize adaptive tracking against thrown decoys.

[0014] The present invention, by adopting the above technical solution, has the following beneficial effects: 1. This invention constructs a passive radar decoy jamming model and establishes a passive radar measurement model set to characterize the time-varying characteristics of measurement noise. It achieves the discretization characterization and coverage of the continuous and unknown time-varying characteristics of measurement noise under jamming conditions, effectively overcoming the defect that it is difficult to describe the statistical characteristics of non-stationary interference noise when there is a lack of original echo data.

[0015] 2. This invention further constructs a hybrid system with uncertain measurement noise. By updating the posterior probabilities of each noise model in real time and performing weighted fusion estimation of the target state, it achieves adaptive matching of the tracking filter to time-varying measurement noise. This approach effectively compensates for the weakness of observability caused by the single-station passive positioning geometry of passive radar, and solves the problems of filter divergence and target loss caused by gain mismatch when directly using conventional nonlinear filtering algorithms for tracking. It significantly improves the system's survivability and combat effectiveness in complex electronic warfare environments.

[0016] 3. The present invention provides an adaptive tracking method for anti-dropped decoys based on multiple measurement error models. This method effectively solves the technical problem of low target tracking accuracy and insufficient robustness of passive radar under the condition that the original signal characteristics of the radar cannot be obtained and the measurement error is unknown and time-varying due to the interference of dropped decoys.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, do not constitute an undue limitation of the invention. In the drawings: Figure 1 The implementation process of an adaptive tracking method for anti-thrown decoys based on multiple measurement error models is described. Figures 2(a), 2(b), and 2(c) show the root mean square errors of the target's position estimation in the three directions of northeast, south, and north. Figures 3(a), 3(b), and 3(c) show the root mean square error of the velocity estimation of the target in the three directions of northeast, south, and north. Figure 4 The posterior probabilities of each model calculated by the algorithm proposed in this invention are given. Figure 5 A schematic diagram of the anti-throwing decoy adaptive tracking device based on a multi-model measurement error according to the present invention is shown. Detailed Implementation

[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0020] This invention provides an adaptive tracking method for anti-thrown decoys based on a multi-model approach to measurement errors, the implementation process of which is as follows: Figure 1 As shown, it includes the following steps: S101: Construct a motion and centroid interference model for a passive radar-launched decoy to determine the decoy's motion in three-dimensional space and its interference with the radar system.

[0021] In this embodiment, a motion and centroid interference model of a passive radar-launched decoy is constructed. On the one hand, this model is used to reveal the motion law of the launcher in three-dimensional space and the interference mechanism that causes the centroid to shift in radar measurement data. On the other hand, it can provide a physical model basis for the subsequent construction of a passive radar measurement model set that characterizes the time-varying characteristics of measurement noise.

[0022] 11) Construct a motion model for a passive radar-launched decoy: Once a throwable decoy is released, its motion in three-dimensional space is not simply inertial motion, but is primarily influenced by both air resistance (aerodynamic drag) and its own gravity. Air resistance hinders the motion; its direction is opposite to the velocity vector, and its magnitude is related to the square of the decoy's flight velocity, air density, drag coefficient, and the decoy's frontal area. Gravitational acceleration, on the other hand, always acts on the vertical axis. This physical force analysis is specifically reflected in the construction of the model's acceleration input vector, thus accurately describing the nonlinear trajectory of the decoy in complex environments. The model formula is as follows:

[0023] In the formula, Indicates that the bait is in The state vector at any given time contains position and velocity components; Represents the state transition matrix of the decoy; The gain matrix representing the decoy's acceleration; express The acceleration of the decoy at any given moment; express Noise during the movement of the decoy at any given moment; This represents the noise covariance matrix of the decoy's motion process as assumed by the motion model.

[0024] State transition matrix Gain matrix and decoy acceleration The definition is as follows:

[0025] In the formula, Indicates the sampling interval; Indicates the drag coefficient; Indicates air density; Indicates the windward area of ​​the decoy; This indicates the mass of the decoy at the current moment; Represents gravitational acceleration; , , express The components of the decoy's velocity along each axis of the coordinate system at any given moment; Represents a symbolic function.

[0026] 12) Construct a centroid interference model for passive radar-dropped decoys: Passive radar detects targets by receiving signals from radiation sources. When a high-powered decoy and a target are spatially close and indistinguishable by the radar beam, the "target" detected by the radar is actually the centroid of the combined radiated energy of both. This model quantitatively describes this physical process: the combined centroid state is a weighted average of the target state and the decoy state based on a power coefficient. The power coefficient is determined by the ratio of the decoy's radiated power to the target's radiated power. As the proportion of decoy power increases, the centroid measured by the radar will shift significantly towards the decoy, causing the radar tracking trajectory to deviate from the true target, introducing a measurement bias that is difficult to eliminate by conventional means. The model formula is as follows:

[0027] In the formula, Indicates the center of mass of the disturbance is at The state vector at any given time; Indicates that the bait is in The state vector at any given time; Indicates the target is The state vector at any given time; , These represent the radiated power of the decoy and the target, respectively. This represents the power coefficient.

[0028] S102: Based on the interference method, construct a set of passive radar measurement models that characterize the time-varying properties of measurement noise.

[0029] In this embodiment, a set of passive radar measurement models characterizing the time-varying properties of measurement noise is constructed. On the one hand, different noise covariance matrices are set to discretize the phenomenon of unknown time-varying statistical characteristics of measurement error under the interference of dropped decoys. On the other hand, it can provide a model basis for the subsequent construction of hybrid systems with uncertain measurement noise and the implementation of interactive multi-model filtering.

[0030] The passive radar measurement model set characterizing the time-varying properties of measurement noise is constructed as follows:

[0031] In the formula, for The set of passive radar measurement information at any given moment; for The azimuth angle of the target relative to the sensor as measured by the passive radar at any given time. for The elevation angle of the target relative to the sensor, measured by the passive radar at any given moment; , , Indicate target The position coordinates of the object in the three directions in the northeast-northeast coordinate system at any given moment; for The first moment Measurement noise in a measurement model assumption; For the first The measurement noise covariance matrix of the measurement model assumption.

[0032] S103: Construct a target motion model to determine the target's motion in three-dimensional space.

[0033] In this embodiment, a target motion model is constructed to describe the evolution of the target's motion state in three-dimensional space over time. On the other hand, it provides a mathematical model basis for the subsequent construction of a hybrid system with uncertain measurement noise and the implementation of the state prediction step of capacitive Kalman filtering.

[0034] The target motion model is constructed as follows:

[0035] In the formula, Indicates the target is The state vector at any given time; The state transition matrix represents the objective. Indicates the target is The state vector at any given time; Represents the noise gain matrix of the target; express Noise during the target motion process at any given time; This represents the noise covariance matrix of the target motion process assumed in the model.

[0036] The above formula needs to be set according to the actual motion of the target. If the target is undergoing three-dimensional coordinated turn (3D-CT), the specific target motion model is as follows:

[0037] The relevant parameters are calculated as follows:

[0038] matrix and Specifically:

[0039] In the formula, Indicates the sampling interval; the target state vector is ; , , represent The components of the target position on the three axes in a three-dimensional Cartesian coordinate system at any given time; , , represent The components of the target velocity on the three axes in a three-dimensional Cartesian coordinate system at any given moment; , , represent The components of the target's angular velocity on the three axes in a three-dimensional rectangular coordinate system at any given moment; Represents a diagonal matrix; Represents Kronecker.

[0040] S104: Based on the passive radar measurement model set and target motion model, construct a hybrid system with measurement noise uncertainty, including multiple sub-models.

[0041] In this embodiment, a hybrid system with uncertain measurement noise is constructed. On the one hand, it is used to uniformly describe the continuous motion process of the target in three-dimensional space and the discrete switching process of the statistical characteristics of measurement noise of passive radar under interference conditions. On the other hand, it can provide a complete system model foundation for subsequent parallel filtering and state estimation fusion using interactive multi-model algorithms.

[0042] Construct a hybrid system with measurement noise uncertainty comprising multiple sub-models, where each sub-model... The formula is as follows:

[0043] In the formula, for The set of passive radar measurement information at any given moment; for The azimuth angle of the target relative to the sensor as measured by the passive radar at any given time. for The elevation angle of the target relative to the sensor, measured by the passive radar at any given moment; for The first moment Measurement noise in a measurement model assumption; For the first The measurement noise covariance matrix of the measurement model assumption.

[0044] S105: Passive radar receives measurements from the target at the current moment.

[0045] S106: The tracking results of each sub-model of the hybrid system at the previous moment.

[0046] In this embodiment, the state estimates and covariances of each sub-model of the hybrid system at the previous time step are weighted and mixed (i.e., input interaction) using the Markov transition probability matrix and the model probabilities from the previous time step. This step aims to introduce prior information about the possible switching between different measurement noise modes and motion modes of the hybrid system before filtering by using probability weighting, thereby smoothing the abrupt model transition caused by changes in interference states, effectively avoiding tracking divergence caused by hard model switching, and providing the optimal initial state input that incorporates historical prior information for the filters of each sub-model at the current time step.

[0047] The tracking results of the various sub-models of the hybrid system at the previous moment are analyzed using the following method: 61) Based on the probability that the measurement noise was in each sub-model of the hybrid system at the previous time step, and the prior probability that the measurement noise would transfer between sub-models, calculate the probability that the measurement noise was in each sub-model at the current time step after the interaction, and the conditional probability that the measurement noise would transfer between sub-models at the current time step, as shown in the following formula:

[0048]

[0049] In the formula, Measurement noise after input interaction is in the sub-model The probability of; The number of models in the model set; The measurement noise is represented by the sub-model. Transfer to sub-model The prior probability; To measure noise Always in the sub-model The probability of; for Time-based noise measurement from sub-model Transfer to sub-model The conditional probability.

[0050] 62) Based on the probabilities solved in the previous step, the tracking results of each sub-model of the hybrid system at the previous time step are interacted to obtain the target state estimates of each sub-model after interaction, as well as the estimation error covariance, as shown in the following formula:

[0051]

[0052] In the formula, For the measurement noise after interaction, it is in the sub-model State estimate; The number of models in the model set; for Time-sub model The target state estimate; for Time-based noise measurement from sub-model Transfer to sub-model The conditional probability; For the measurement noise after interaction, it is in the sub-model The estimation error covariance matrix; for Time-sub model The estimated error covariance matrix.

[0053] S107: Based on the interaction results and the sub-models of the hybrid system, perform capacitive Kalman filtering on the interaction result sub-models to obtain the target state estimate, estimation error covariance, measurement residual, and innovation covariance of each sub-model of the hybrid system at the current time.

[0054] In this embodiment, capacitive Kalman filtering is applied to the interaction results based on each sub-model of the hybrid system. On the one hand, the nonlinear statistical characteristics of the capacitive point transfer are utilized to achieve accurate estimation of the target state under the specific noise assumptions of each sub-model. On the other hand, the calculated measurement residuals and information covariance can provide a computational basis for subsequent evaluation of model credibility (i.e., calculation of the likelihood function) and updating the model probability.

[0055] Based on the sub-models of the hybrid system, capacitive Kalman filtering is applied to the interaction result sub-model. The specific method is as follows: 71) Based on the interaction sub-model Given the target state estimate and the estimation error covariance matrix, the covariance between the target state volume point and the innovation is calculated using the following formula:

[0056]

[0057] In the formula, express Time-sub model The new information covariance; express Measurement noise after time-interaction is in the sub-model The estimation error covariance matrix; express Time-sub model The One target state volume point; express Measurement noise after time-interaction is in the sub-model State estimate; This represents the basic volume point set.

[0058] in, and The definition is as follows:

[0059]

[0060] in, Let be the dimension of the target state space. express A set of points in 3D space, i.e.

[0061] 72) Based on the sub-model The included target motion model transforms the target state volume point to obtain a one-step prediction value of the target state volume point, as shown in the following formula:

[0062] In the formula, express Time-sub model The One-step prediction value for each target state volume point.

[0063] 73) Calculate the sub-model based on the one-step predicted value of the target state volume point. The formulas for the one-step prediction of the target state and the prediction error covariance are as follows:

[0064]

[0065] In the formula, Submodel The next step prediction value of the target state; Submodel The prediction error covariance.

[0066] 74) Based on the sub-model Given the target state one-step prediction value and prediction error covariance, recalculate the target state volume point one-step prediction value and the innovation covariance one-step prediction value, as follows:

[0067]

[0068] In the formula, Submodel The one-step prediction of the new information covariance.

[0069] 75) Based on the sub-model The passive radar measurement model transforms the one-step predicted value of the target state volume point to obtain the one-step predicted value of the measurement volume point, as shown in the following formula:

[0070] In the formula, Submodel The One-step prediction value for each volume measurement point; , , Submodel The The first three components of the one-step prediction value of the target state volume point.

[0071] 76) Based on the one-step predicted value of the measurement volume point and the one-step predicted value of the target state volume point, calculate the one-step predicted value of the measurement, the innovation covariance, the filter gain, and the measurement residual, as shown in the following formula:

[0072]

[0073]

[0074]

[0075]

[0076] In the formula, Submodel The measurement of the predicted value in one step; express Time-sub model The new information covariance; For the first The measurement noise covariance matrix of the measurement model assumptions; express Time-sub model The cross-covariance matrix; express Time-sub model Volumetric Kalman gain; express Time-sub model Measurement residuals.

[0077] 77) Based on the measured one-step prediction value, the new information covariance, and the filter gain, obtain the sub-model at the current time step. The given target state estimate and estimation error covariance are given by the following formulas:

[0078]

[0079] In the formula, express Time-sub model The given target state estimate; express Time-sub model The given estimation error covariance matrix.

[0080] S108: Based on the measurement residuals and the information covariance, update the probability that the measurement noise is in each sub-model of the hybrid system at the current moment.

[0081] In this embodiment, the probability of the measurement noise being in each sub-model of the hybrid system at the current moment is updated based on the measurement residual and the information covariance. On the one hand, by calculating the likelihood function, the matching degree between the preset measurement noise parameters of each sub-model and the current actual radar measurement data (i.e., model credibility) is evaluated in real time. On the other hand, the updated probability of each sub-model is used as an adaptive weight to provide a calculation basis for the subsequent weighted fusion of the state estimates of each sub-model to obtain the final adaptive tracking result.

[0082] The probability of the measurement noise being in each sub-model of the hybrid system at the current time is updated as follows: 81) Based on the measurement residuals and the innovation covariance, calculate the measurement noise at the current moment within the sub-model. The likelihood function value is given by the following formula:

[0083] In the formula, express Time-sub model The likelihood function value; This represents the dimension of the passive radar measurement model.

[0084] 82) Based on the noise measured at the current moment, it is in the sub-model. The likelihood function value, and the measurement noise at the current time after the interaction within the submodel. The probability of updating the measurement noise at the current time step within the sub-model. The probability of is given by the following formula:

[0085] In the formula, To measure noise Always in the sub-model The probability of; For the measurement noise after interaction, it is in the sub-model The probability of; for The likelihood-weighted sum of probabilities after each interaction time.

[0086] Among them, the likelihood weighted sum of the probabilities after the interaction The definition is as follows:

[0087] In the formula, This represents the number of models in the passive radar measurement model set.

[0088] S109: Based on the updated probability, the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment are weighted and fused to obtain the state estimates and estimation error covariance of the hybrid system for adaptive tracking of the target, thereby realizing adaptive tracking against thrown decoys.

[0089] In this embodiment, the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment are weighted and fused. On the one hand, the updated probabilities of each sub-model are used as adaptive weights to integrate the estimation results of multiple local filters based on different noise assumptions into a global optimal estimate. On the other hand, by outputting an overall state estimate that matches the statistical characteristics of the current measurement noise, the measurement deviation caused by the thrown decoy is effectively suppressed, and finally, anti-interference adaptive tracking of the target is achieved.

[0090] The target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment are weighted and fused to achieve adaptive tracking against thrown decoys, as shown in the following formula:

[0091]

[0092] In the formula, for State estimates of a time-mixed system for adaptive target tracking; for Time-sub model The target state estimate; for The estimation error covariance matrix of a time-mixed system for adaptive target tracking.

[0093] The present invention will be further illustrated below through specific embodiments.

[0094] S101: Construct a motion and centroid interference model for passive radar-dropped decoys.

[0095] Motion model is Its state transition matrix Gain matrix and decoy acceleration As shown below:

[0096] In the above formula, the sampling period The initial mass of the chaff / flare The burning speed of the chaff is drag coefficient air density ; Frontal area of ​​the chaff / flare gravitational acceleration .

[0097] The centroid disturbance model is shown below:

[0098] In the above formula, the power coefficient ; S102: Construct a set of passive radar measurement models to characterize the time-varying properties of measurement noise:

[0099] In the above formula, the measurement noise covariance matrix under interference-free conditions is:

[0100] Assumed measurement noise covariance matrix under interference conditions:

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] S103: The target motion model is constructed as follows:

[0107] The relevant parameters are calculated as follows:

[0108] matrix and Specifically:

[0109] In the above formula, the sampling period ; S104: Based on the passive radar measurement model and the target motion model, a hybrid system with measurement noise uncertainty is constructed, which includes multiple sub-models.

[0110] The number of models it contains is determined to be 7 according to the specific embodiment S102, and the number of sub-models is 7. The formula is as follows:

[0111] S105: Passive radar receives the current moment, i.e. Moment, measurement from the target .

[0112] S106: Interact with the previous moment, i.e. At any given moment, the tracking results of each sub-model of the hybrid system.

[0113] First, calculate the interaction after The probability of measurement noise being present in each sub-model at each time step, and the conditional probability of measurement noise transitioning between sub-models. The prior probabilities of measurement noise transitioning between models used in the calculation are as follows:

[0114] Then, to The tracking results of each sub-model of the time-varying hybrid system, namely the target state estimate and the estimation error covariance matrix given by each sub-model, are interacted to obtain the tracking results of each sub-model after interaction.

[0115] S107: Perform capacitive Kalman filtering on the interaction result sub-model based on each sub-model of the hybrid system.

[0116] Regarding the seven models determined in specific embodiment S102, the following will be described using sub-models. Let's take an example to illustrate.

[0117] The first step is to analyze the sub-models after the interaction. Given and , computational sub-model The target state volume point and new information covariance .

[0118] The second step is based on the sub-model. Includes target motion model, pair model The target state volume point Transformation is performed to obtain the sub-model. The target state volumetric point one-step prediction value .

[0119] The third step is based on the sub-model. The target state volumetric point one-step prediction value , computational sub-model The next step prediction value of the target state and prediction error covariance And recalculate to obtain the sub-model The target state volumetric point one-step prediction value One-step prediction of the covariance of the new information .

[0120] Fourth step, based on the sub-model Includes passive radar measurement models and sub-models. The target state volume point Transformation is performed to obtain the sub-model. One-step prediction value of the measured volume point .

[0121] Fifth step, based on the sub-model The target state volumetric point one-step prediction value One-step prediction value of the measured volume point , computational sub-model The next step of measurement prediction value New information covariance Filter gain and measurement residuals .

[0122] Step 6, based on the sub-model The next step of measurement prediction value New information covariance and filter gain ,get Time-sub model The given target state estimate Estimation error covariance ,Right now Time-sub model The tracking results.

[0123] S108: Update based on the measurement residuals and new information covariance obtained in S107. The probability of noise being present in each sub-model is measured at each time step. The following section focuses on the sub-model. Let's take an example to illustrate.

[0124] First, according to Time-sub model Measurement residuals With new information covariance ,calculate Time measurement noise is in the sub-model likelihood function value Secondly, according to Time measurement noise is in the sub-model likelihood function value and after interaction Time measurement noise is in the sub-model probability ,renew Time measurement noise is in the sub-model probability .

[0125] S109: According to The probability of noise being present in each sub-model at any given time is measured. The target state estimates and estimation error covariance of each sub-model at the current time are weighted and fused to obtain the state estimate and estimation error covariance of the hybrid system for adaptive target tracking, thus achieving adaptive tracking against thrown decoys. The specific calculation is shown below:

[0126]

[0127] In the formula, for State estimates of a time-mixed system for adaptive target tracking; for The estimation error covariance matrix of a time-mixed system for adaptive target tracking.

[0128] Figures 2(a), 2(b), and 2(c) show the root mean square errors of the target's position estimation in the three directions of northeast and sky, respectively; Figures 3(a), 3(b), and 3(c) show the root mean square errors of the target's velocity estimation in the three directions of northeast and sky, respectively.

[0129] As shown in the figure, when interference occurs, directly using CKF cannot effectively track the target. The root mean square errors of the target's position and velocity estimation in the three directions of northeast, zenith, and celestial are all diverging, indicating that the target is lost. However, when using the method proposed in this invention to track the target, the root mean square errors of the target's position and velocity estimation in the three directions of northeast, zenith, and celestial are all subject to brief fluctuations, but eventually converge. This indicates that the method proposed in this invention effectively reduces the impact of measurement noise uncertainty, solves the problem of low accuracy and easy divergence of existing methods in passive tracking weak observable scenarios, and enhances the target tracking capability of passive radar.

[0130] Figure 4 The posterior probability of the model calculated by the algorithm proposed in this invention is given. This represents the measurement noise covariance matrix of a passive radar in the absence of decoy interference. , , , , , The increasing diagonal elements represent the increased uncertainty in measurement noise when decoy interference is present. Comparing the results in the figure, when the target releases passive radar decoy interference at 15 seconds... The model posterior probability represented by the noise matrix decreases rapidly from probability 1, while the model posterior probabilities represented by the other measurement noise matrices all increase to varying degrees; as the interference from the thrown decoys disappears, The posterior probabilities of the models represented by the noise matrix gradually increase back to probability 1, while the posterior probabilities of the models represented by the other measurement noise matrices gradually decrease to probability 0. This demonstrates that the changes in the posterior probabilities of each measurement model calculated by the method proposed in this invention can match the changes in the actual measurement noise in time, indirectly proving that the algorithm has a good tracking effect on the target.

[0131] As can be seen from the above experiments and embodiments, the present invention can reduce the impact of interference on passive radar tracking when the magnitude of radar measurement error is unknown and time-varying, realize the passive radar's adaptive tracking of target measurement error, and effectively improve the tracking accuracy and robustness of passive radar.

[0132] like Figure 5 As shown, according to an exemplary embodiment of the present invention, an anti-throwing decoy adaptive tracking device 100 based on a multi-model measurement error is provided to implement the method, comprising: Module 110 is used to build a motion and centroid interference model for a passive radar-launched decoy. Construct a set of passive radar measurement models to characterize the time-varying properties of measurement noise; Construct a target motion model to determine the target's motion in three-dimensional space; Construct a hybrid system with measurement noise uncertainty that includes multiple sub-models; Interaction module 120 is used to interact with the tracking results of each sub-model of the hybrid system at the previous moment; The filtering module 130 is used to perform volumetric Kalman filtering on the interaction result sub-model to obtain the target state estimate, estimation error covariance, measurement residual and innovation covariance of each sub-model of the hybrid system at the current time. Update module 140 is used to update the probability that the measurement noise is in each sub-model of the hybrid system at the current time. The weighted fusion module 150 is used to perform weighted fusion of the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current time to obtain the state estimates and estimation error covariance of the hybrid system for adaptive tracking of the target, so as to realize adaptive tracking against thrown decoys.

[0133] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. An adaptive tracking method for anti-thrown decoys based on a multi-model approach to measurement errors, characterized in that, include: A motion and centroid interference model of a passive radar-launched decoy is constructed to determine the decoy's motion in three-dimensional space and its interference with the radar system. Based on the aforementioned interference method, a set of passive radar measurement models characterizing the time-varying characteristics of measurement noise is constructed; Construct a target motion model to determine the target's motion in three-dimensional space; Based on the passive radar measurement model set and the target motion model, a hybrid system with measurement noise uncertainty is constructed, which includes multiple sub-models, wherein each sub-model is composed of a one-to-one combination of the target motion model and each measurement model in the passive radar measurement model set; Passive radar receives measurements from the target at the current moment; The interaction between the tracking results of the various sub-models of the hybrid system at the previous moment; Based on the interaction results and the sub-models of the hybrid system, capacitive Kalman filtering is performed on the interaction result sub-models to obtain the target state estimate, estimation error covariance, measurement residual and innovation covariance of each sub-model of the hybrid system at the current time. Based on the measurement residuals and the information covariance, update the probability that the measurement noise is in each sub-model of the hybrid system at the current moment; Based on the updated probability, the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment are weighted and fused to obtain the state estimates and estimation error covariance of the hybrid system for adaptive tracking of the target, thus realizing adaptive tracking against thrown decoys.

2. The adaptive tracking method for anti-thrown decoys based on a multi-model measurement error according to claim 1, characterized in that, A motion and centroid interference model of a passive radar-launched decoy is constructed to determine the decoy's motion in three-dimensional space and its interference with the radar system, including: Considering the combined effects of air resistance and gravity, the nonlinear motion trajectory of the decoy in complex environments is determined, and a motion model of the passive radar-launched decoy is constructed. Based on the fact that high-radiated-power decoys and targets are spatially close and cannot be distinguished by radar beams, a centroid state is synthesized by a weighted average of the target state and decoy state based on the power coefficient, thus constructing a centroid interference model for passive radar measurement of thrown decoys: In the formula, Indicates the center of mass of the disturbance is at The state vector at any given time; Indicates that the bait is in The state vector at any given time; Indicates the target is The state vector at any given time; , These represent the radiated power of the decoy and the target, respectively. This represents the power coefficient.

3. The anti-toss decoy adaptive tracking method based on measurement error multi-model according to claim 1, characterized in that, Based on the aforementioned interference method, a set of passive radar measurement models characterizing the time-varying properties of measurement noise is constructed, as shown in the following formula: In the formula, for The set of passive radar measurement information at any given moment; for The azimuth angle of the target relative to the sensor as measured by the passive radar at any given time. for The elevation angle of the target relative to the sensor, measured by the passive radar at any given moment; , , Indicate target The position coordinates of the object in the three directions in the northeast-northeast coordinate system at any given moment; for The first moment Measurement noise in a measurement model assumption; For the first The measurement noise covariance matrix of the measurement model assumption.

4. The adaptive tracking method for anti-thrown decoys based on a multi-model measurement error according to claim 1, characterized in that, The target motion model is constructed as follows: In the formula, Indicates the target is The state vector at any given time; The state transition matrix represents the objective. Indicates the target is The state vector at any given time; Represents the noise gain matrix of the target; express Noise during the target motion process at any given time; This represents the noise covariance matrix of the target motion process assumed by the model.

5. The adaptive tracking method for anti-thrown decoys based on a multi-model measurement error according to claim 4, characterized in that, Based on the passive radar measurement model set and target motion model, a hybrid system with measurement noise uncertainty is constructed, comprising multiple sub-models. The formula is as follows: In the formula, for The set of passive radar measurement information at any given moment; for The azimuth angle of the target relative to the sensor as measured by the passive radar at any given time. for The elevation angle of the target relative to the sensor, measured by the passive radar at any given moment; for The first moment Measurement noise in a measurement model assumption; For the first The measurement noise covariance matrix of the measurement model assumption.

6. The adaptive tracking method for anti-thrown decoys based on a multi-model measurement error according to claim 1, characterized in that, The tracking results of the various sub-models of the hybrid system at the previous moment are interactive, including: Based on the probability that the measurement noise was in each sub-model of the hybrid system at the previous time step, and the prior probability that the measurement noise would transfer between sub-models, calculate the probability that the measurement noise was in each sub-model at the current time step after the interaction, and the conditional probability that the measurement noise would transfer between sub-models at the current time step. Based on the probabilities solved in the previous step, the tracking results of each sub-model of the hybrid system at the previous moment are interacted to obtain the target state estimates of each sub-model after interaction, as well as the estimation error covariance.

7. The anti-raining decoy adaptive tracking method based on measurement error multi-model according to claim 1, characterized in that, Based on the interaction results and the sub-models of the hybrid system, capacitive Kalman filtering is performed on the interaction result sub-models to obtain the target state estimates, estimation error covariance, measurement residuals, and innovation covariance of each sub-model of the hybrid system at the current time, including: Based on the target state estimates and estimation error covariance matrices given by each sub-model of the hybrid system after interaction, calculate the target state volume point and the innovation covariance. Based on the target motion model contained in each sub-model, the target state volume point is transformed to obtain the one-step prediction value of the target state volume point; Based on the one-step predicted value of the target state volume point, calculate the one-step predicted value of the target state and the prediction error covariance under each sub-model; Based on the one-step predicted value of the target state and the prediction error covariance under each sub-model, recalculate the one-step predicted value of the target state volume point and the one-step predicted value of the innovation covariance. Based on the passive radar measurement model contained in each sub-model, the one-step prediction value of the target state volume point is transformed to obtain the one-step prediction value of the measurement volume point. Based on the one-step predicted value of the measurement volume point and the one-step predicted value of the target state volume point, calculate the one-step predicted value of the measurement, the information covariance, the filter gain and the measurement residual. Based on the measured one-step prediction value, the information covariance, and the filtering gain, the target state estimate and estimation error covariance given by each sub-model at the current time are obtained.

8. The adaptive tracking method for anti-thrown decoys based on a multi-model measurement error according to claim 1, characterized in that, Based on the measurement residuals and the innovation covariance, update the probability that the measurement noise is in each sub-model of the hybrid system at the current time, including: Based on the measurement residuals and the information covariance, calculate the likelihood function values ​​of the measurement noise at the current moment for each sub-model of the hybrid system; Based on the likelihood function values ​​of the measured noise in each sub-model of the hybrid system at the current time, and the probability of the measured noise in each sub-model at the current time after the interaction, update the probability of the measured noise in each sub-model at the current time.

9. The anti-raining decoy adaptive tracking method based on measurement error multi-model according to claim 1, characterized in that, We perform weighted fusion of the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment to obtain the state estimates and estimation error covariance of the hybrid system for adaptive target tracking: In the formula, for State estimates of a time-mixed system for adaptive target tracking; for Time-sub model The target state estimate; The number of models in the model set; To measure noise Always in the sub-model The probability of; for The estimation error covariance matrix of a time-mixed system for adaptive target tracking; for Time-sub model The estimated error covariance matrix.

10. An adaptive tracking device for anti-throwing decoys based on a multi-model measurement error according to any one of claims 1-9, characterized in that, include: The module is used to build motion and centroid interference models for passive radar-launched decoys. Construct a set of passive radar measurement models to characterize the time-varying properties of measurement noise; construct a target motion model to determine the target's motion in three-dimensional space; Construct a hybrid system with measurement noise uncertainty that includes multiple sub-models; The interaction module is used to interact with the tracking results of the various sub-models of the hybrid system at the previous moment; The filtering module is used to perform capacitive Kalman filtering on the interaction result sub-model to obtain the target state estimate, estimation error covariance, measurement residual and innovation covariance of each sub-model of the hybrid system at the current time. The update module is used to update the probability that the measurement noise is in each sub-model of the hybrid system at the current moment; The weighted fusion module is used to perform weighted fusion of the target state estimates and estimation error covariance of each sub-model of the hybrid system at the current moment, so as to obtain the state estimates and estimation error covariance of the hybrid system for adaptive tracking of the target, and realize adaptive tracking against thrown decoys.

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