Distributed maneuvering target filtering method and device based on Gaussian filter

Abstract

The invention discloses a distributed maneuvering target filtering method and device based on a Gaussian filter. The method comprises the steps that radar sensor network parameters and a maneuvering model are initialized; determining a model interaction probability between each maneuvering model and other maneuvering models; calculating a state prediction value of the target in each maneuvering model after interaction and a corresponding state prediction covariance matrix; determining the measurement information of the target; iteratively calculating a state estimation value and a state estimation covariance matrix of the target in each maneuvering model after interaction, and iteratively calculating an estimation value of a hyper-parameter of each maneuvering model after interaction; carrying out fusion processing on calculation results; and determining a final state estimation value and a final state estimation covariance matrix of the target based on a result after fusion processing. According to the method, the stability and detection precision of low-altitude airspace high-maneuvering target tracking are greatly improved, and high anti-interference performance and robustness of the system are achieved.

Description

Technical Field

[0001] The present application belongs to the field of signal processing technology, and in particular, relates to a distributed maneuvering target filtering method and device based on a Gaussian filter. Background Art

[0002] With the rapid development of the low-altitude economy, low-altitude flying tools such as drones and low-altitude manned aircraft are increasingly used in logistics and transportation, agricultural management, security inspections, and emergency rescue. However, the increase in low-altitude flight activities has also brought many challenges such as airspace management and safety monitoring. Due to the characteristics of low-altitude aircraft such as high flight speed, small size, low flight altitude, and complex detection background, traditional airspace management systems are difficult to meet the monitoring and management needs of low-altitude flights. Therefore, effective monitoring and management methods for the low-altitude airspace environment have become one of the key supporting technologies for the development of the low-altitude economy.

[0003] Radar networking technology has important advantages in low-altitude aircraft monitoring. Through a network system composed of multiple radar sensor devices, it is possible to achieve all-round and multi-angle monitoring of low-altitude aircraft, improving the detection accuracy and coverage of the system. Compared with a single radar sensor, radar networking can provide more reliable aircraft detection and tracking in complex terrain environments, especially in terrain conditions such as densely populated urban areas, mountains, and forests. Radar networking can reduce monitoring blind spots and ensure accurate positioning and real-time tracking of low-altitude aircraft. In general, low-altitude airspace monitoring technology based on radar networking is not only an important means to ensure the safety of low-altitude aircraft, but also one of the core technologies to promote the healthy development of the low-altitude economy. In the future low-altitude economic ecology, radar networking and multi-sensor fusion will jointly constitute the key pillars of the intelligent low-altitude airspace management system.

[0004] In actual radar sensor detection and tracking tasks, due to the influence of low-altitude multipath effects, abnormal measurements of radar sensor position, angle, etc. may generate heavy-tailed non-Gaussian process noise and measurement noise. When the above situation occurs, traditional Gaussian nonlinear filters (extended Kalman filter, insensitive Kalman filter, etc.) may fail, and thus show extreme sensitivity to heavy-tailed non-Gaussian noise, resulting in a sharp deterioration in tracking accuracy. Summary of the invention

[0005] The present application provides a distributed maneuvering target filtering method and device based on a Gaussian filter, which are used to solve the above-mentioned problems or at least partially solve the above-mentioned problems.

[0006] In a first aspect, a distributed maneuvering target filtering method based on a Gaussian filter is disclosed, the method comprising:

[0007] Step S1: Initializing radar sensor network parameters, initializing multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initializing a measurement state transition model corresponding to each maneuver model;

[0008] Step S2: for each maneuvering model: determine the model interaction probability with other maneuvering models, and interact the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models;

[0009] Step S3: Calculate the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix;

[0010] Step S4: Determine the target measurement information;

[0011] Step S5: iteratively calculating the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculating the estimation value of the hyperparameter of each maneuvering model after the interaction;

[0012] Step S6: determining the probability update value of each maneuver model of the target after each interaction;

[0013] Step S7: fusing the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after the interaction;

[0014] Step S8: Determine the final state estimation value and the final state estimation covariance matrix of the target based on the result after the fusion processing.

[0015] Preferably, the step S1: initializing radar sensor network parameters, initializing multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initializing a measurement state transition model corresponding to each maneuver model, includes:

[0016] Step S11: Initializing radar sensor network parameters, including:

[0017] Defining a radar sensor network Among them, SS represents the node that receives and processes data, C represents the communication node, represents the communication link between communication nodes, and the set of adjacent nodes of the sth radar sensor is expressed as p represents the neighboring node that can communicate with the sth radar sensor;

[0018] Step S12: Initializing multiple maneuvering models of the target and the state transition models corresponding to each maneuvering model, including:

[0019] The maneuver model set of the target at time k is defined as Where M represents the number of target maneuver models, and the motion state vector of the target detected by the s-th radar sensor at time k is defined as Then the state transition model corresponding to each maneuver model is:

[0020]

[0021] in, Indicates that the maneuver model at the kth moment is i, f i (·) represents the state transfer function of the i-th maneuver model; is the motion state vector corresponding to the s-th radar sensor at time k-1 under maneuver model i, Indicates that the maneuver model at the k-1th moment is i, is the k-1 moment process noise vector;

[0022] Assume that the k-1 time process noise It obeys the tailed distribution, that is:

[0023]

[0024] where p(·) represents the probability density function, represents the process noise, The mean is 0 and the scale matrix is The degrees of freedom are Student's-t distribution; set the scale matrix The conjugate prior distribution of is the inverse-Wishart distribution, that is:

[0025]

[0026] in, express The degree of freedom is The inverse scaling matrix is The inverse wishart distribution of

[0027] Step S13: Initializing the measurement state transition model corresponding to each maneuvering model, including:

[0028]

[0029] in, represents the measurement value received by the sth radar sensor at time k, h s,i (·) represents the measurement transfer function corresponding to the i-th maneuver model in the s-th radar sensor, assuming that the measurement noise at time k is Follows a tailed distribution:

[0030]

[0031] Indicates the measurement noise The mean is 0 and the scale matrix is The degrees of freedom are Student's-t distribution.

[0032] Preferably, the step S2: for each maneuvering model: determining the model interaction probability with other maneuvering models, interacting the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models, includes:

[0033] Step S21: Calculate the model prediction probability of maneuver model j corresponding to the s-th radar sensor at time k and model interaction probability

[0034]

[0035] in, Indicates any represents the probability update value of model i at time k-1, represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value, represents the probability of transferring from the i-th maneuvering model to the j-th maneuvering model from time k-1 to time k; Indicates that the maneuver model at time k is j, Represents the probability update value of model i at time k-1;

[0036] Step S22: Determine the state vector of the maneuver model i after interaction at time k-1 State covariance matrix after interaction And the distribution hyperparameter mixture parameters after interaction:

[0037]

[0038] in, and They represent the state estimation value and state estimation covariance matrix of maneuver model j at time k-1 respectively;

[0039] Determine the distribution hyperparameter mixing parameters after interaction of maneuver model i at time k-1:

[0040]

[0041] in, is the degree of freedom mixing parameter of maneuver model i at time k-1, is the scale matrix mixing parameter of maneuver model i at time k-1, is the estimated value of the degrees of freedom of the maneuver model j at time k-1, is the estimated value of the scale matrix of maneuver model j at time k-1.

[0042] Preferably, the step S3: calculating the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix, wherein:

[0043]

[0044] F i represents the state transfer function f of the i-th maneuver model i The Jacobian matrix of (·), represents the process noise covariance matrix of the i-th maneuver model at time k, (·) T represents the transpose operation. represents the state prediction value of the target after the interaction with the i-th maneuver model, represents the state prediction covariance matrix of the target in the i-th maneuver model after interaction.

[0045] Preferably, the step S4: determining the target measurement information include:

[0046]

[0047] in, Indicates the measurement information of the target, represents the measurement value of the target obtained by the s-th radar sensor at time k, represents the measurement noise covariance matrix of the s-th radar sensor at time k.

[0048] Preferably, the step S5: iteratively calculating the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculating the estimated value of the hyperparameter of each maneuvering model after the interaction, comprises:

[0049] Step S51: Initialize the number of iterations n to 0;

[0050] Step S52: Determine whether the iteration termination condition is met. If so, proceed to step S6; otherwise, assign the current iteration number n to n plus 1, and update With the current measurement covariance matrix Enter step S53, wherein:

[0051]

[0052] is the state covariance distribution scale matrix of the n-1th iteration output at the kth moment, is the state covariance distribution degree of freedom of the n-1th iteration output at the kth time, is the degrees of freedom of the measurement covariance distribution output at the n-1th iteration at the kth time, and E(·) represents the expectation operation;

[0053] Step S53: Update the state estimation value and state estimation covariance matrix of the target in the maneuver model after the interaction, where:

[0054]

[0055] H s,i Denotes the measurement transfer function h s,i The Jacobian matrix of (·) is represents the new information covariance of the nth iteration at time k, represents the filter gain of the nth iteration at time k, represents the n-1th iteration result of the state estimation value at time k, represents the state estimation covariance matrix of the n-1th iteration at time k, represents the iteration result of the state estimation value at the nth iteration at time k, represents the state prediction value, represents the state estimation covariance matrix of the nth iteration at time k, and T represents the transpose operation;

[0056] Step S54: Determine the estimated values ​​of the hyperparameters of the interactive maneuver model, where:

[0057]

[0058] tr(·) represents the trace operation, (·) -1 represents the inverse operation, and are the estimated values ​​of the hyperparameters for the nth iteration, v 1 is the state covariance distribution freedom update factor, v 2 is the update factor for the degrees of freedom of the measurement covariance distribution, is the state vector dimension; is the intermediate calculation amount, expressed as:

[0059]

[0060] Step S55: Update the state covariance distribution scale matrix output at the k-th time and the n-th iteration in:

[0061]

[0062] is the updated value of the n-th iteration degree of freedom at the k-th moment, is the initialization value of the 0th iteration degree of freedom at time k, is the update value of the scale matrix at the kth moment and the nth iteration, Initialize the scale matrix for the 0th iteration at time k.

[0063] Preferably, the step S6: determining the probability update value of each maneuver model of the target after each interaction includes:

[0064] Step S61: Calculate the likelihood probability of the target in each interactive maneuver model

[0065] Where N represents the preset number of iterations, is the likelihood probability of maneuver model i, are all the measured values ​​of radar sensor s from time 1 to time k-1, is the conditional probability, is the new information covariance matrix of the Nth iteration, Measure the degrees of freedom of the covariance matrix distribution for the Nth iteration;

[0066] Step S62: Calculate the probability update value of the target in each interactive maneuver model

[0067]

[0068] in, represents the model probability prediction value at time k, It is the probability update value of the maneuver model after the interaction at the kth moment.

[0069] In a second aspect, a distributed maneuvering target filtering device based on a Gaussian filter is disclosed, the device comprising:

[0070] Initialization module: configured to initialize radar sensor network parameters, initialize multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initialize a measurement state transition model corresponding to each maneuver model;

[0071] Interaction module: configured to: for each maneuvering model: determine the model interaction probability with other maneuvering models, and interact the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models;

[0072] A first calculation module: configured to calculate the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix;

[0073] A second computing module: configured to determine measurement information of a target;

[0074] A third calculation module: configured to iteratively calculate the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculate the estimated value of the hyperparameter of each maneuvering model after the interaction;

[0075] A fourth calculation module: configured to determine probability update values ​​of each maneuver model of the target after each interaction;

[0076] A fusion module: configured to fuse the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after each interaction;

[0077] The fifth computing module is configured to determine the final state estimation value and the final state estimation covariance matrix of the target based on the result after the fusion processing.

[0078] In a third aspect, an electronic device is disclosed, the electronic device comprising:

[0079] at least one processor; and

[0080] a memory communicatively connected to the at least one processor; wherein,

[0081] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method described above.

[0082] In a fourth aspect, a non-transitory computer-readable storage medium storing computer instructions is disclosed, wherein the computer instructions are used to cause the computer to execute the method as described above.

[0083] This application proposes a distributed maneuvering target filtering method and device based on Gaussian filter, which solves the tailing problem by modeling the one-step prediction probability distribution and the likelihood probability distribution as Student's t distribution respectively, and iteratively updates the hyperparameters of each distribution based on the variational Bayesian method to obtain the optimal distribution parameters, and fuses the data of multiple radar sensors based on the consistency fusion algorithm, which can effectively overcome the limitations of a single radar sensor in a low-altitude complex environment, enhance the tracking stability, detection accuracy and anti-interference ability of high-maneuvering targets under the background of tailing noise, and ensure accurate monitoring in complex flight scenarios. This application has important theoretical value and practical application potential. It not only provides a more efficient and reliable technical means for the safety management of low-altitude airspace and the monitoring of aircraft, but also lays the foundation for the intelligent management of emerging fields such as drones in the low-altitude economy. By improving the accuracy and efficiency of airspace management, promoting the sustainable development of the low-altitude economy, and ensuring flight safety, it has broad market application prospects.

[0084] This application has the following technical effects:

[0085] This application is a distributed robust Student's-t maneuvering target filtering method of Gaussian approximate filter. By introducing Student's t distribution modeling and variational Bayesian hyperparameter update strategy, it effectively solves the problems of trailing noise interference and target motion uncertainty in low-altitude flight environment. With the support of multi-sensor consistency fusion algorithm, this application greatly improves the stability and detection accuracy of high-maneuvering target tracking in low-altitude airspace, and achieves high anti-interference and robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is a flowchart of a distributed maneuvering target filtering method based on a Gaussian filter;

[0087] Figure 2 is another flow chart of a distributed maneuvering target filtering method based on a Gaussian filter;

[0088] Figure 3 This is a schematic diagram of radar sensor layout and target trajectory distribution;

[0089] Figure 4 A schematic diagram showing the comparison of target distance and velocity estimation accuracy under a single radar sensor background;

[0090] Figure 5 A schematic diagram showing the comparison of target distance and velocity estimation accuracy in the context of distributed radar sensors;

[0091] Figure 6 A schematic diagram showing a comprehensive comparison of target distance estimation accuracy between a single radar sensor and a distributed radar sensor;

[0092] Figure 7 A schematic diagram showing a comprehensive comparison of target velocity estimation accuracy between a single radar sensor and a distributed radar sensor;

[0093] Figure 8 A schematic diagram showing the comparison of model probability estimation in the context of distributed radar sensors;

[0094] Fig. 9 It is a structural schematic diagram of a distributed maneuvering target filtering device based on Gaussian filter. DETAILED DESCRIPTION

[0095] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0096] like Figure 1 As shown, the present application provides a distributed maneuvering target filtering method based on a Gaussian filter, the method comprising:

[0097] Step S1: Initializing radar sensor network parameters, initializing multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initializing a measurement state transition model corresponding to each maneuver model;

[0098] Step S2: for each maneuvering model: determine the model interaction probability with other maneuvering models, and interact the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models;

[0099] Step S3: Calculate the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix;

[0100] Step S4: Determine the target measurement information;

[0101] Step S5: iteratively calculating the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculating the estimation value of the hyperparameter of each maneuvering model after the interaction;

[0102] Step S6: determining the probability update value of each maneuver model of the target after each interaction;

[0103] Step S7: fusing the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after the interaction;

[0104] Step S8: Determine the final state estimation value and the final state estimation covariance matrix of the target based on the result after the fusion processing.

[0105] The step S1: initializing radar sensor network parameters, initializing multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initializing a measurement state transition model corresponding to each maneuver model, includes:

[0106] Step S11: Initializing radar sensor network parameters, including:

[0107] Defining a radar sensor network Among them, SS represents the node that receives and processes data, C represents the communication node, represents the communication link between communication nodes, and the set of adjacent nodes of the sth radar sensor is expressed as p represents the neighboring node that can communicate with the sth radar sensor;

[0108] Step S12: Initializing multiple maneuvering models of the target and the state transition models corresponding to each maneuvering model, including:

[0109] The maneuver model set of the target at time k is defined as Where M represents the number of target maneuver models, and the motion state vector of the target detected by the s-th radar sensor at time k is defined as Then the state transition model corresponding to each maneuver model is:

[0110]

[0111] in, Indicates that the maneuver model at the kth moment is i, f i (·) represents the state transfer function of the i-th maneuver model; is the motion state vector corresponding to the s-th radar sensor at time k-1 under maneuver model i, Indicates that the maneuver model at the k-1th moment is i, is the k-1 moment process noise vector;

[0112] Assume that the k-1 time process noise It obeys the tailed distribution, that is:

[0113]

[0114] where p(·) represents the probability density function, represents the process noise, The mean is 0 and the scale matrix is The degrees of freedom are Student's-t distribution; set the scale matrix The conjugate prior distribution of is the inverse-Wishart distribution, that is:

[0115]

[0116] in, express The degree of freedom is The inverse scaling matrix is The inverse wishart distribution of

[0117] Step S13: Initializing the measurement state transition model corresponding to each maneuvering model, including:

[0118]

[0119] in, represents the measurement value received by the sth radar sensor at time k, h s,i (·) represents the measurement transfer function corresponding to the i-th maneuver model in the s-th radar sensor, assuming that the measurement noise at time k is Follows a tailed distribution:

[0120]

[0121] Indicates the measurement noise The mean is 0 and the scale matrix is The degrees of freedom are Student's-t distribution;

[0122] The step S2: for each maneuvering model: determining the model interaction probability with other maneuvering models, interacting the motion state of the target in the maneuvering model, the model parameters and hyper parameters of the maneuvering model with other maneuvering models, including:

[0123] Step S21: Calculate the model prediction probability of maneuver model j corresponding to the s-th radar sensor at time k and model interaction probability

[0124]

[0125] in, Indicates any represents the probability update value of model i at time k-1, represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value, represents the probability of transferring from the i-th maneuvering model to the j-th maneuvering model from time k-1 to time k; Indicates that the maneuver model at time k is j, Represents the probability update value of model i at time k-1;

[0126] Step S22: Determine the state vector of the maneuver model i after interaction at time k-1 State covariance matrix after interaction And the distribution hyperparameter mixture parameters after interaction:

[0127]

[0128] in, and They represent the state estimation value and state estimation covariance matrix of maneuver model j at time k-1 respectively;

[0129] Determine the distribution hyperparameter mixing parameters after interaction of maneuver model i at time k-1:

[0130]

[0131] in, is the degree of freedom mixing parameter of maneuver model i at time k-1, is the scale matrix mixing parameter of maneuver model i at time k-1, is the estimated value of the degrees of freedom of the maneuver model j at time k-1, is the estimated value of the scale matrix of maneuver model j at time k-1.

[0132] The step S3: calculating the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix, wherein:

[0133]

[0134] F i represents the state transfer function f of the i-th maneuver model i The Jacobian matrix of (·), represents the process noise covariance matrix of the i-th maneuver model at time k, (·) T represents the transpose operation. represents the state prediction value of the target after the interaction with the i-th maneuver model, represents the state prediction covariance matrix of the target in the i-th maneuver model after interaction.

[0135] Step S4: Determine the target measurement information include:

[0136]

[0137] in, Indicates the measurement information of the target, represents the measurement value of the target obtained by the s-th radar sensor at time k, represents the measurement noise covariance matrix of the s-th radar sensor at time k.

[0138] The step S5: iteratively calculating the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculating the estimated value of the hyperparameter of each maneuvering model after the interaction, includes:

[0139] Step S51: Initialize the number of iterations n to 0;

[0140] Step S52: Determine whether the iteration termination condition is met. If so, proceed to step S6; otherwise, assign the current iteration number n to n plus 1, and update With the current measurement covariance matrix Enter step S53, wherein:

[0141]

[0142] is the state covariance distribution scale matrix of the n-1th iteration output at the kth moment, is the state covariance distribution degree of freedom of the n-1th iteration output at the kth time, is the degrees of freedom of the measurement covariance distribution output at the n-1th iteration at the kth time, and E(·) represents the expectation operation;

[0143] Step S53: Update the state estimation value and state estimation covariance matrix of the target in the maneuver model after the interaction, where:

[0144]

[0145] H s,i Denotes the measurement transfer function h s,i The Jacobian matrix of (·) is represents the new information covariance of the nth iteration at time k, represents the filter gain of the nth iteration at time k, represents the n-1th iteration result of the state estimation value at time k, represents the state estimation covariance matrix of the n-1th iteration at time k, represents the iteration result of the state estimation value at the nth iteration at time k, represents the state prediction value, represents the state estimation covariance matrix of the nth iteration at time k, and T represents the transpose operation;

[0146] Step S54: Determine the estimated values ​​of the hyperparameters of the interactive maneuver model, where:

[0147]

[0148] tr(·) represents the trace operation, (·) -1 represents the inverse operation, and are the estimated values ​​of the hyperparameters for the nth iteration, v 1 is the state covariance distribution freedom update factor, v 2 is the update factor for the degrees of freedom of the measurement covariance distribution, is the state vector dimension; is the intermediate calculation amount, expressed as:

[0149]

[0150] Step S55: Update the state covariance distribution scale matrix output at the k-th time and the n-th iteration in:

[0151]

[0152] is the updated value of the n-th iteration degree of freedom at the k-th moment, is the initialization value of the 0th iteration degree of freedom at time k, is the update value of the scale matrix at the kth moment and the nth iteration, Initialize the scale matrix for the 0th iteration at time k.

[0153] The iteration termination condition is that the number of iterations n reaches a preset number of iterations or the accuracy value is less than a first preset threshold, that is,

[0154]

[0155] Among them, T d is the precision, ||·|| 2 It means to find the second norm, is the estimated value of the nth iteration state, is the estimated value of the state at the n-1th iteration.

[0156] The step S6: determining the probability update value of each maneuver model of the target after each interaction, comprises:

[0157] Step S61: Calculate the likelihood probability of the target in each interactive maneuver model

[0158] Where N represents the preset number of iterations, is the likelihood probability of maneuver model i, are all the measured values ​​of radar sensor s from time 1 to time k-1, is the conditional probability, is the new information covariance matrix of the Nth iteration, Measure the degrees of freedom of the covariance matrix distribution for the Nth iteration;

[0159] Step S62: Calculate the probability update value of the target in each interactive maneuver model

[0160]

[0161] in, represents the model probability prediction value at time k, It is the probability update value of the maneuver model after the interaction at the kth moment.

[0162] The step S7: fusing the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after each interaction, includes:

[0163] Step S71: Calculate the information vector for the state estimation covariance matrix Information Matrix in:

[0164]

[0165] is the state estimate of the target in the maneuver model after the interaction;

[0166] Step S72: Information vector Information Matrix Perform consistent fusion processing.

[0167]

[0168] Where l represents the index of the number of consistent fusions, (l) represents the result of the lth fusion, and the maximum value of l is L, which represents the Lth fusion; δ s,p is the consistency fusion weight coefficient;

[0169] Step S73: performing consistency fusion processing on the estimated values ​​of the hyperparameters of each maneuvering model of the target after the interaction and the probability update values ​​of each maneuvering model of the target after each interaction.

[0170]

[0171] in, is the updated value of the degrees of freedom obtained at the Nth iteration.

[0172] Step S8: Determine the final state estimation value and the final state estimation covariance matrix of the target based on the result of the fusion processing, including:

[0173] Step S81: Calculate the final state estimate and the final state estimate covariance matrix

[0174] in, represents the information matrix after the Lth fusion, Represents the information vector after the Lth fusion;

[0175] Step S82: Calculate the state estimation value multi-model interaction result Results of multi-model interaction with state estimation covariance

[0176]

[0177] in, Represents the model probability update value after the Lth fusion, represents the state estimate of maneuver model i of radar sensor s at time k.

[0178] like Figure 2-Figure 8 As shown, the present application provides a specific embodiment of a distributed maneuvering target filtering method based on a Gaussian filter.

[0179] Step 1: Initialize system parameters.

[0180] 1.1 Initialize radar sensor network parameters: define radar sensor network S represents the node that receives and processes data, C represents the communication node, represents the communication link between communication nodes. Assume that the neighboring node set ratio of the sth radar sensor is expressed as Where p represents the adjacent node that can communicate with the radar sensor s;

[0181] The specific radar sensor location and communication relationship are as follows: Figure 2 shown.

[0182] 1.2 Initialize the motion state transfer model: Define the target maneuver model set at time k as Where M represents the number of target maneuver models, and the motion state of the target detected by the s-th radar sensor at time k is defined as Then we have:

[0183]

[0184] in Indicates that the maneuver model at the kth moment is i, f i (·) represents the state transfer function of the i-th maneuvering model; assuming that the process noise at time k-1 It obeys the tailed distribution, that is:

[0185]

[0186] Where p(·) represents the probability density function, St(·; μ, Σ, v) represents the Student's-t distribution with mean μ, scale matrix Σ, and degrees of freedom σ; based on this, we set The conjugate prior distribution of is:

[0187]

[0188] where IW(·; t,T) represents the inverse Wishart distribution with t degrees of freedom and T inverse scaling matrix.

[0189] This example selects but is not limited to the number of target maneuver models M=3, which are uniform motion, left and right turning models with known turning rates of ±0.1rad / s. Model 1 indicates that the target is in uniform motion, and its state transfer matrix is ​​expressed as:

[0190]

[0191] T represents the sampling time interval. This example selects but is not limited to T = 1s. Models 2 and 3 represent turning models with known turning rates, and their state transfer matrices are expressed as:

[0192]

[0193] This example uses but is not limited to F 2 =F(w 1 ),w 1 =0.1rad / s, F 3 =F(w 2 ),w 2 =-0.1rad / sw;

[0194] This example selects but is not limited to three motion models corresponding to the motion state vectors: Where x and y represent the distance of the target on the x-axis and y-axis respectively. and Represent the speed of the target on the x-axis and y-axis respectively. The process noise variance of the three motion states is 1m / s 2 ;

[0195] 1.3 Initialize the measurement state transfer model:

[0196]

[0197] in represents the measured value corresponding to the sth model at time k, h s,i(·) represents the measurement transfer function corresponding to the i-th motion model in the s-th radar sensor, assuming that the measurement noise at time k is Follows a tailed distribution:

[0198]

[0199] represents the measurement noise scale matrix of radar sensor s at time k.

[0200] This example uses but is not limited to the measurement vectors under three motion models: [R,θ] T , where R represents the target distance, θ represents the target azimuth, and the measurement noise of each radar sensor under the three models is initialized to σ R =10m,σ θ =0.2°.

[0201] Step 2: Model interaction of the motion state, model parameters, and hyperparameters of each target model.

[0202] 2.1. Calculate the model prediction probability of the sth radar sensor target model j at time k Probability of interacting with the model

[0203]

[0204] in represents the probability update value of model i at time k-1, represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value, represents the probability of transferring from maneuver model i to maneuver model j from time k-1 to time k;

[0205] In this example, the model probability is initialized as The Markov transition probability matrix (TPM) is initialized to the following values:

[0206]

[0207] 2.2. Calculate the interaction state of the target i-th model Covariance value with interaction state and the mixing parameters of each distribution,

[0208] 1. Calculate the interaction state of the target i-th model Covariance value with interaction state

[0209]

[0210] in, and They represent the state estimation value and the state estimation covariance matrix (obtained from the previous moment) of the maneuvering model j at moment k-1 respectively, and ∑· represents the summation operation.

[0211] This example uses but is not limited to the following initialization method, where the initial state value Initialize according to the real state, the state covariance at the initial moment Initialize in the following way,

[0212]

[0213] Where T = 1s represents the radar sensor data rate, and r takes the following form,

[0214]

[0215] 2.3. Calculate the mixed parameters of each distribution hyperparameter

[0216]

[0217] This example uses but is not limited to the following initialization methods: Where n x =4 represents the dimension of the target motion state vector, τ=5 represents the iteration factor;

[0218] Step 3: Calculate the state prediction value of each maneuver model State prediction covariance matrix

[0219] 1. Calculate the state prediction value of each maneuver model State prediction covariance matrix

[0220] i=1,...,M represents the target maneuver model index, F i represents the state transfer function f of the i-th maneuver model i The Jacobian matrix of (·), represents the process noise covariance matrix of model i at time k, (·) T Represents a transpose operation.

[0221] Step 4: Calculate target measurement information

[0222]

[0223] in represents the target measurement value obtained by the s-th radar sensor at time k, represents the measurement noise covariance matrix of radar sensor s at time k.

[0224] Step 5: Calculate the state estimate based on variational iteration State Estimation Covariance Matrix With the estimated values ​​of each hyperparameter,

[0225] For the convenience of representation, the variables carrying the superscript of the number of variational iterations [n] in the following steps are temporarily omitted from the radar sensor number s and the maneuver model number i.

[0226] Initialize the first variational iterative inverse wishart distribution parameters:

[0227]

[0228] The superscript [0] indicates the first variational iteration.

[0229] Update the nth variational iteration state estimation covariance matrix and the measurement covariance matrix

[0230] This example selects but is not limited to the following parameter initialization:

[0231] Update the state estimate x k|k and the state estimation covariance matrix P k|k

[0232]

[0233] where H represents the Jacobian matrix of the measurement transfer function h(·), S k|k-1 represents the innovation covariance, K k represents the gain at time k, represents the n-1th iteration result of the state estimation value at time k, Represents the n-1th iteration result of the state estimation covariance matrix at time k.

[0234] Update the hyperparameters of the nth variational iteration and

[0235]

[0236] in

[0237] γ x =tr(D x E(Σ k ))

[0238]

[0239] D x =P k|k +(x k|k -x k|k-1 )(x k|k -x k|k-1 ) T

[0240] D z =HP k|k H T +(z k -Hx k|k )(z k -Hx k|k ) T

[0241] Where tr(·) represents the trace operation, D x With D z represents the intermediate variable, v 1 ,v 2 They represent constants related to the degrees of freedom. In this example, we use but are not limited to v 1 =v 2 =5.

[0242] renew The result of the nth variational iteration

[0243]

[0244] Determine the iteration termination condition

[0245]

[0246] ||·|| 2 Indicates the second norm. The above expression means that when T d ≤ε, where ε represents the minimum value. In this example, the iteration termination threshold ε=10 is selected but not limited to -8 , set the number of iterations at the end of the iteration to N. If the above iteration conditions are met, go to step 6, otherwise repeat the iteration operation of step 5.

[0247] Step 6: Calculate the model probability update value corresponding to each model;

[0248] 1. Calculate the likelihood value of each maneuver model,

[0249]

[0250] Where N represents the total number of variational iterations.

[0251] 2. Calculate the model probability estimate,

[0252]

[0253] Step 7: Estimate the state in step 5 State Estimation Covariance Matrix Hyperparameters Perform consistent multi-radar sensor fusion processing (Consensus),

[0254] 1. Calculate the information vector for the state estimate and the state estimate covariance Information Matrix

[0255] 2. Information vector Information Matrix Conduct Consensus processing,

[0256]

[0257] Where δ represents the fusion weight coefficient, l = 1, 2, ..., L, and L represents the number of consistent fusions; this example selects but is not limited to L = 5.

[0258] 3. Hyperparameters Model Probability Conduct Consensus processing,

[0259]

[0260] Step 8: Calculate the state update value and the state estimation covariance matrix

[0261] 1. Calculate the state estimate and the state estimate covariance matrix,

[0262]

[0263] in represents the information matrix after the Lth fusion, Represents the information vector after the Lth fusion;

[0264] 2. Calculate the state estimate value and the multi-model interaction results Results of multi-model interaction with state estimation covariance

[0265]

[0266] in It represents the updated model probability value after the Lth fusion. In summary, the status update is completed.

[0267] The practicability of the present invention is demonstrated by the following simulation examples:

[0268] Simulation conditions and parameters

[0269] The simulation scenario is set as single target tracking, and the radar sensor network is deployed as follows: Figure 2 As shown, the number of radar sensors is 12. The switching sequence of the models marked with model numbers 1, 2, and 3 is:

[0270] {1,2,3,2,1,3,1}, each model duration is 1→30s, 2→40s, 3→40s. The process noise variance is q=1, and the measurement noise variance is [σ R ,σ θ ]=[10m,0.2°], the total simulation time is 250s, the process noise outlier ratio is 10%, and the corresponding process noise variance is 100; the measurement noise outlier ratio is 10%, and the corresponding measurement noise variance is 40×[σ R ,σ θ ], number of fusions L = 5.

[0271] like Fig. 9 As shown, the present application provides a distributed maneuvering target filtering device based on a Gaussian filter, the device comprising:

[0272] Initialization module: configured to initialize radar sensor network parameters, initialize multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initialize a measurement state transition model corresponding to each maneuver model;

[0273] Interaction module: configured to: for each maneuvering model: determine the model interaction probability with other maneuvering models, and interact the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models;

[0274] A first calculation module: configured to calculate the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix;

[0275] A second computing module: configured to determine measurement information of a target;

[0276] A third calculation module: configured to iteratively calculate the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculate the estimated value of the hyperparameter of each maneuvering model after the interaction;

[0277] A fourth calculation module: configured to determine probability update values ​​of each maneuver model of the target after each interaction;

[0278] A fusion module: configured to fuse the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after each interaction;

[0279] The fifth computing module is configured to determine the final state estimation value and the final state estimation covariance matrix of the target based on the result after the fusion processing.

[0280] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application is described in detail with reference to the above embodiments, a person skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some or all of the technical features can be replaced by equivalents, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A distributed maneuvering target filtering method based on Gaussian filter, characterized in that: The method comprises the following steps: Step S1: Initializing radar sensor network parameters, initializing multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initializing a measurement state transition model corresponding to each maneuver model; Step S2: for each maneuvering model: determine the model interaction probability with other maneuvering models, and interact the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models; Step S3: Calculate the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix; Step S4: Determine the target measurement information; Step S5: iteratively calculating the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculating the estimated value of the hyperparameter of each maneuvering model after the interaction; Step S6: determining the probability update value of each maneuver model of the target after each interaction; Step S7: fusing the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after each interaction; Step S8: Determine the final state estimation value and the final state estimation covariance matrix of the target based on the result after the fusion processing.

2. The method according to claim 1, characterized in that The step S1: initializing radar sensor network parameters, initializing multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initializing a measurement state transition model corresponding to each maneuver model, includes: Step S11: Initializing radar sensor network parameters, including: Defining a radar sensor network Among them, SS represents the node that receives and processes data, C represents the communication node, represents the communication link between communication nodes, and the set of adjacent nodes of the sth radar sensor is expressed as p represents the neighboring node that can communicate with the sth radar sensor; Step S12: Initializing multiple maneuvering models of the target and the state transition models corresponding to each maneuvering model, including: The maneuver model set of the target at time k is defined as Where M represents the number of target maneuver models, and the motion state vector of the target detected by the s-th radar sensor at time k is defined as Then the state transition model corresponding to each maneuver model is: in, Indicates that the maneuver model at the kth moment is i, f i (·) represents the state transfer function of the i-th maneuver model; is the motion state vector corresponding to the s-th radar sensor at time k-1 under maneuver model i, Indicates that the maneuver model at the k-1th moment is i, is the k-1 moment process noise vector; Assume that the k-1 time process noise It obeys the tailing distribution, that is: where p(·) represents the probability density function, represents the process noise, The mean is 0 and the scale matrix is The degrees of freedom are Student's-t distribution; set the scale matrix The conjugate prior distribution of is the inverse-Wishart distribution, that is: in, express The degree of freedom is The inverse scaling matrix is The inverse wishart distribution of Step S13: Initializing the measurement state transition model corresponding to each maneuvering model, including: in, represents the measurement value received by the sth radar sensor at time k, h s,i (·) represents the measurement transfer function corresponding to the i-th maneuver model in the s-th radar sensor, assuming that the measurement noise at time k is Follows a tailed distribution: Indicates the measurement noise The mean is 0 and the scale matrix is The degrees of freedom are Student's-t distribution.

3. The method according to claim 2, characterized in that The step S2: for each maneuvering model: determining the model interaction probability with other maneuvering models, interacting the motion state of the target in the maneuvering model, the model parameters and hyper parameters of the maneuvering model with other maneuvering models, including: Step S21: Calculate the model prediction probability of maneuver model j corresponding to the s-th radar sensor at time k and model interaction probability in, Indicates any represents the probability update value of model i at time k-1, represents the Markov transition probability matrix at time k, where Pr(·) represents the probability value, represents the probability of transferring from the i-th maneuvering model to the j-th maneuvering model from time k-1 to time k; Indicates that the maneuver model at time k is j, Represents the probability update value of model i at time k-1; Step S22: Determine the state vector of the maneuver model i after interaction at time k-1 State covariance matrix after interaction And the distribution hyperparameter mixture parameters after interaction: in, and They represent the state estimation value and state estimation covariance matrix of maneuver model j at time k-1 respectively; Determine the distribution hyperparameter mixing parameters after interaction of maneuver model i at time k-1: in, is the degree of freedom mixing parameter of maneuver model i at time k-1, is the scale matrix mixing parameter of maneuver model i at time k-1, is the estimated value of the degrees of freedom of the maneuver model j at time k-1, is the estimated value of the scale matrix of maneuver model j at time k-1.

4. The method according to claim 3, characterized in that The step S3: calculating the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix, wherein: F i represents the state transfer function f of the i-th maneuver model i The Jacobian matrix of (·), represents the process noise covariance matrix of the i-th maneuver model at time k, (·) T represents the transpose operation, represents the state prediction value of the target after the interaction with the i-th maneuver model, represents the state prediction covariance matrix of the target in the i-th maneuver model after interaction.

5. The method according to claim 4, characterized in that Step S4: Determine the target measurement information include: in, Indicates the measurement information of the target, represents the measurement value of the target obtained by the s-th radar sensor at time k, represents the measurement noise covariance matrix of the s-th radar sensor at time k.

6. The method according to claim 5, characterized in that The step S5: iteratively calculating the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculating the estimated value of the hyperparameter of each maneuvering model after the interaction, includes: Step S51: Initialize the number of iterations n to 0; Step S52: Determine whether the iteration termination condition is met. If so, proceed to step S6; otherwise, assign the current iteration number n to n plus 1, and update With the current measurement covariance matrix Enter step S53, wherein: is the state covariance distribution scale matrix of the n-1th iteration output at the kth moment, is the state covariance distribution degree of freedom of the n-1th iteration output at the kth time, is the degrees of freedom of the measurement covariance distribution output at the n-1th iteration at the kth time, and E(·) represents the expectation operation; Step S53: Update the state estimation value and state estimation covariance matrix of the target in the maneuver model after the interaction, where: H s,i The Jacobian matrix representing the measurement transfer function hs,i(·) is represents the new information covariance of the nth iteration at time k, represents the filter gain of the nth iteration at time k, represents the n-1th iteration result of the state estimation value at time k, represents the state estimation covariance matrix of the n-1th iteration at time k, represents the iteration result of the state estimation value at the nth iteration at time k, represents the state prediction value, represents the state estimation covariance matrix of the nth iteration at time k, and T represents the transpose operation; Step S54: Determine the estimated values ​​of the hyperparameters of the interactive maneuver model, where: tr(·) represents the trace operation, (·) -1 represents the inverse operation, and are the estimated values ​​of the hyperparameters for the nth iteration, v1 is the update factor for the state covariance distribution degrees of freedom, v2 is the update factor for the measurement covariance distribution degrees of freedom, is the state vector dimension; is the intermediate calculation amount, expressed as: Step S55: Update the state covariance distribution scale matrix output at the k-th time and the n-th iteration in: is the updated value of the n-th iteration degree of freedom at the k-th moment, is the initialization value of the 0th iteration degree of freedom at time k, is the update value of the scale matrix at the kth moment and the nth iteration, Initialize the scale matrix for the 0th iteration at time k.

7. The method according to claim 6, characterized in that The step S6: determining the probability update value of each maneuver model of the target after each interaction, comprises: Step S61: Calculate the likelihood probability of the target in each interactive maneuver model Where N represents the preset number of iterations, is the likelihood probability of maneuver model i, are all the measured values ​​of radar sensor s from time 1 to time k-1, is the conditional probability, is the new information covariance matrix of the Nth iteration, Measure the degrees of freedom of the covariance matrix distribution for the Nth iteration; Step S62: Calculate the probability update value of the target in each interactive maneuver model in, represents the model probability prediction value at time k, It is the probability update value of the maneuver model after the interaction at the kth moment.

8. A distributed maneuvering target filtering device based on Gaussian filter, characterized in that: The device comprises: Initialization module: configured to initialize radar sensor network parameters, initialize multiple maneuver models of the target, a state transition model corresponding to each maneuver model, and initialize a measurement state transition model corresponding to each maneuver model; Interaction module: configured to: for each maneuvering model: determine the model interaction probability with other maneuvering models, and interact the motion state of the target in the maneuvering model, the model parameters and hyperparameters of the maneuvering model with other maneuvering models; A first calculation module: configured to calculate the state prediction value of the target in each maneuver model after the interaction and the corresponding state prediction covariance matrix; A second computing module: configured to determine measurement information of a target; A third calculation module: configured to iteratively calculate the state estimation value and the state estimation covariance matrix of the target in each maneuvering model after the interaction based on the measurement information of the target, and iteratively calculate the estimated value of the hyperparameter of each maneuvering model after the interaction; A fourth calculation module: configured to determine probability update values ​​of each maneuver model of the target after each interaction; A fusion module: configured to fuse the state estimation value of the target in each maneuvering model after the interaction, the state estimation covariance matrix, the estimated value of the hyperparameter of each maneuvering model after the interaction, and the probability update value of the target in each maneuvering model after each interaction; The fifth computing module is configured to determine the final state estimation value and the final state estimation covariance matrix of the target based on the result after the fusion processing.

9. A computer-readable storage medium, wherein a plurality of instructions are stored in the storage medium; the plurality of instructions are used for a processor to load and execute the method as claimed in any one of claims 1 to 7.

10. An electronic device, characterized in that: The electronic device comprises: A processor, which is used to execute multiple instructions; A memory for storing a plurality of instructions; The plurality of instructions are used to be stored in the memory and loaded and executed by the processor according to any one of claims 1 to 7.

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