Self-adaptive tracking method and system for maneuvering magnetic target

Abstract

The invention relates to a self-adaptive tracking method and system for a maneuvering magnetic target, and belongs to the technical field of target tracking and magnetic detection. The method comprises the following steps: establishing a target physical model and a motion model, and determining a state variable of a tracked magnetic target according to the models; constructing a state space model, and obtaining a motion state equation and a nonlinear observation equation of the magnetic target according to the determined state variable; constructing an IMM-AKKF-FNN model, comprising the following steps: a maneuvering decision-making layer adopts an IMM framework, runs a plurality of filters for different motion modes in parallel, and performs probability weighting according to the likelihood of each model so as to adaptively cope with macroscopic motion mode switching of a target; the nonlinear filtering layer adopts AKKF as a core state estimator in each model of the IMM framework; the noise sensing layer is provided with a pre-trained FNN for each AKKF. According to the invention, the tracking precision and robustness can be improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of target tracking and magnetic detection, and relates to a moving magnetic target tracking method and system using an interactive multiple model (IMM) framework and adaptive kernel Kalman filtering (AKKF). BACKGROUND

[0002] Magnetic target tracking technology estimates the position, velocity and other motion states of a target by detecting local magnetic field anomaly changes caused by a ferromagnetic object, and has important application value in military defense (such as submarine and mine detection), civil security (such as vehicle monitoring), geophysical exploration and other fields. However, in actual applications, a magnetic target often has a maneuvering behavior, and its motion mode may change suddenly. At the same time, the measurement of a magnetic field signal and a target dynamics model usually present significant nonlinear characteristics, which bring challenges to accurate and robust magnetic target tracking.

[0003] Currently commonly used target tracking filtering algorithms include extended Kalman filtering (EKF), unscented Kalman filtering (UKF) and particle filtering (PF). EKF realizes linearization by first-order Taylor expansion of a nonlinear function, but has limited accuracy in a strong nonlinear case. UKF uses unscented transformation to approximate the mean and covariance of a state distribution, and has better processing capability for nonlinearity than EKF, but it is still based on Gaussian assumption. PF approximates a posterior probability density by a large number of weighted random particles, and can theoretically handle any nonlinear and non-Gaussian problem, but has large computation and is prone to particle degeneracy and impoverishment problems.

[0004] For target maneuvering problems, an interactive multiple model (IMM) algorithm is widely used. The IMM algorithm runs a group of filters for different motion modes in parallel, and performs probability weighted fusion according to the matching degree of each filter with the current observation, so as to adaptively track a maneuvering target. In existing literature, there are studies on combining IMM with UKF or its variants for magnetic target tracking, which to some extent improves the tracking performance of a maneuvering target.

[0005] In recent years, adaptive kernel Kalman filter (AKKF) has attracted attention as a new nonlinear Bayesian filtering method. AKKF embeds the probability density function (pdf) of the state into the reproducing kernel Hilbert space (RKHS) by using kernel mean embedding (KME) for representation and realizes linear prediction and update in the high-dimensional feature space. AKKF can approximate any pdf without Gaussian assumption, and in some cases, it can achieve comparable or even better performance than PF with fewer particles, while avoiding the resampling problem of PF. Existing researches have applied AKKF to metal target tracking based on magnetic anomaly detection (MAD), verifying its potential in dealing with magnetic tracking nonlinear problems and estimating magnetic parameters.

[0006] However, whether AKKF is used alone or combined with existing IMM-UKF / SRUKF, the system process noise covariance matrix Q and the observation noise covariance matrix R are usually assumed to be fixed constants in application. However, in actual magnetic target tracking scenarios, this assumption is often not true. For example, when the target suddenly maneuvers, the deviation of its motion model from the actual trajectory will increase, which is equivalent to an increase in process noise Q; when the electromagnetic environment around the sensor deteriorates, the observation noise R will increase. Fixed Q and R cannot adapt to such dynamic changes, which will lead to decreased filter performance, slow response, and even divergence, which constitutes a technical problem that needs to be solved in the prior art. SUMMARY

[0007] Therefore, the purpose of the present application is to provide an adaptive tracking method and system for maneuvering magnetic targets, which solves the technical problems of low tracking accuracy and poor adaptability of existing magnetic target tracking methods when the target maneuvers or the system model is strongly nonlinear. This method not only adapts to the switching of the target's motion mode like IMM, but also intelligently adapts to the dynamic changes of the system process noise and observation noise through neural networks, thereby achieving higher accuracy and stronger robustness in complex and variable real scenarios.

[0008] To achieve the above purpose, the present application provides the following technical solutions:

[0009] The adaptive tracking method of a maneuvering magnetic target comprises the following steps: initializing an interactive multiple model (IMM) framework, wherein the IMM framework comprises a plurality of preset motion models representing different motion modes of the magnetic target, and transition probabilities between the motion models and initial probabilities of the motion models are set; initializing an adaptive kernel Kalman filter (AKKF) for each motion model in the IMM framework, wherein the initialization of the AKKF comprises setting an initial particle set of kernel mean embedding representing an initial probability density function of a state in a reproducing kernel Hilbert space, an initial kernel weight vector, and an initial kernel weight covariance matrix.

[0010] The method specifically comprises the following steps:

[0011] A physical model and a motion model of the target are established, and state variables of the tracked magnetic target are determined according to the models;

[0012] A state space model is constructed, and a motion state equation and a nonlinear observation equation of the magnetic target are obtained according to the determined state variables;

[0013] A double adaptive filtering tracking is performed: an IMM-AKKF-FNN model is constructed, wherein IMM represents an interactive multiple model, AKKF represents an adaptive kernel Kalman filter, and FNN represents a feedforward neural network; a maneuvering decision layer of the model adopts the IMM framework, a plurality of filters for different motion modes are run in parallel, and probability weighting is performed according to likelihoods of the motion models to adaptively cope with macro motion mode switching of the target; a nonlinear filtering layer of the model adopts the AKKF as a core state estimator inside each model of the IMM framework; and a noise perception layer is provided with a pre-trained FNN for each AKKF;

[0014] A working process of the IMM-AKKF-FNN model is as follows: at each tracking time, the FNN first adaptively estimates process noise covariance Q and observation noise covariance R of the AKKF for each motion model; then, each AKKF performs prediction and update by using the estimated Q and R; finally, the IMM framework performs motion model probability update and state fusion according to filtering results of the AKKFs to obtain a motion state of the target.

[0015] Further, a state space model is constructed, specifically comprising: assuming that a state of a tracked motion magnetic target at a discrete time k is represented as a state vector X k ; in the IMM framework, a dynamic state space model (DSSM) of a jth motion model M j can be represented as:

[0016] Equations of state:

[0017] Observation equation:

[0018] Among them, f j (·) is model M j The state transition function, h j (·) is model M j The observation function, i.e., the target physical model; and These are model M j The process noise and observation noise are respectively, and their covariance matrices are as follows: and

[0019] Furthermore, the observation function h j (·) Based on the magnetic dipole model, it is used to describe the nonlinear relationship between the target state and the magnetic field reading at the sensor:

[0020]

[0021] Where B(m,r) is the magnetic field generated by the target at the sensor observation point, m is the magnetic moment vector of the target, r is the relative position vector between the target and the sensor, and μ0 is the vacuum permeability.

[0022] Furthermore, the state variable x t The vector expression is:

[0023]

[0024] Where, ξ k ,η k ,ζ k For the target's position components. For the velocity component of the target, m ξ ,m η ,m ζ The magnetic moment component is the target.

[0025] Furthermore, the IMM framework performs motion model probability updates and state fusion based on the filtering results of each AKKF, specifically including the following steps:

[0026] S1: IMM Input Interaction: Calculate the mixed initial conditions of each motion model at the current time based on the probability and state of each motion model at the previous time.

[0027] S2: Parallel Model Filtering: For each motion model in the IMM framework, the following steps are performed independently and in parallel:

[0028] S21: FNN Noise Estimation: Using an FNN, estimate the process noise covariance of the motion model based on the characteristics of the current filtering state. and observation noise covariance

[0029] S22: AKKF State Estimation: Using AKKF and the state estimation obtained in step S21 and Make predictions and updates to obtain the state estimate and likelihood of the motion model;

[0030] S3: IMM Probability Update: Update the probability of each motion model based on the likelihood calculated for each motion model;

[0031] S4: IMM Output Fusion: Based on the updated motion model probabilities, the state estimates of each motion model are weighted and fused to obtain the final tracking result.

[0032] Furthermore, in step S21, the FNN is pre-trained through offline supervised learning. This training process includes constructing a training dataset containing input feature vectors and corresponding real noise covariance labels, and using a backpropagation algorithm to minimize the prediction error.

[0033] Furthermore, in step S21, the input feature vector of the FNN includes one or more of the following:

[0034] Statistical characteristics calculated based on the historical information sequence of each motion model;

[0035] The IMM probability vector of the previous time step;

[0036] Kinematic features extracted from the fused state estimate of the previous time step.

[0037] Furthermore, in step S22, the prediction steps of AKKF include: extracting proposal particles, calculating proposal kernel weights, and predicting state particles and kernel weights.

[0038] Furthermore, in step S22, the AKKF update steps include:

[0039] Calculate the kernel Kalman gain in, For the predicted kernel weight covariance matrix, G yy Let κ be the Gram matrix of the observed particle, κ be the regularization parameter, and I be the identity matrix.

[0040] And using K k Update kernel weight vector and kernel weight covariance matrix

[0041] Further, at each tracking time instant, the method of Scheme 1 performs the following main operations:

[0042] Firstly, an IMM input interaction step is performed, which calculates the mixed initial state estimate and the mixed initial covariance for each motion model at the current tracking time instant, according to the probabilities of the motion models at the previous tracking time instant, the state estimates and covariances output by the AKKFs of the models, and the preset transition probabilities between the motion models.

[0043] Then, for each motion model in the IMM framework, its corresponding AKKF is run in parallel to perform state estimation. This process specifically includes: firstly, a prediction step of the AKKF is performed based on the mixed initial state estimate and the mixed initial covariance of the model obtained from the IMM input interaction step. The prediction step propagates the particles representing the state probability distribution through the state transition function of the motion model, and predicts a predicted kernel weight vector and a predicted kernel weight covariance matrix in the reproducing kernel Hilbert space. Secondly, magnetic target observation data collected by a sensor (such as a magnetometer) at the current tracking time instant is obtained. Thirdly, based on the predicted state particles obtained by the AKKF prediction step and the currently obtained magnetic target observation data, and in combination with the observation function of the motion model, an update step of the AKKF is performed. The update step calculates a kernel Kalman gain through the kernel Kalman rule, and updates the kernel weight vector and the kernel weight covariance matrix accordingly, and finally calculates the state estimate and the corresponding covariance of the magnetic target at the current time instant under the assumption of the motion model. Fourthly, the likelihood of the motion model under the current observation data is calculated according to the result of the AKKF update step.

[0044] Next, an IMM model probability update step is performed, which updates the probability of each motion model at the current tracking time instant according to the likelihood calculated for each motion model in the parallel model filtering step and the model transition information at the previous tracking time instant, so as to reflect the matching degree of each model with the current actual motion mode of the target.

[0045] Finally, an IMM output interaction step (also referred to as a state fusion step) is performed, which weights and fuses the state estimate and the covariance output by each motion model in the parallel model filtering step according to the updated probability of each motion model obtained in the model probability update step, so as to obtain the final state estimate and the final covariance of the magnetic target at the current tracking time instant.

[0046] Scheme 2: An adaptive tracking system of a maneuvering magnetic target, comprising:

[0047] A system model construction module is configured to establish a target physical model and a motion model, and determine a state variable;

[0048] A state equation determination module is configured to obtain a motion state equation and a nonlinear observation equation of the magnetic target;

[0049] a dual adaptive filtering module, which is internally integrated with:

[0050] a model interaction unit for realizing the hybrid and fusion functions of interactive multiple model (IMM);

[0051] a noise adaptive unit composed of a feedforward neural network (FNN) for online estimating the covariance of process noise and observation noise;

[0052] a state estimation unit composed of an adaptive kernel Kalman filter (AKKF) for performing recursive estimation of state under the driving of the system model interaction unit and the noise adaptive unit.

[0053] The present application has the following beneficial effects:

[0054] (1) Dual adaptive is realized, and robustness is extremely strong: The present application creatively constructs the dual adaptive mechanism of "IMM adaptive motion mode" and "FNN adaptive noise environment". When the target is maneuvering, IMM is responsible for model switching; when the noise is changing, FNN is responsible for adjusting Q and R. This synergistic effect makes the present method have much higher robustness and tracking accuracy than traditional IMM-UKF or IMM-AKKF methods with fixed parameters in the complex scene where maneuvering and noise time-varying occur simultaneously.

[0055] (2) The nonlinear processing accuracy is improved: The present application takes AKKF as the core filter, which has stronger approximation ability for nonlinear models than UKF, does not require Gaussian assumption, and can more accurately transmit and update the probability distribution of state, especially suitable for strong nonlinear observation models such as magnetic dipoles.

[0056] (3) The parameter setting problem is solved, and the practicality is higher: In traditional filtering algorithms, the setting of Q and R matrices usually depends on expert experience, which is difficult to set and cannot adapt to changes. The present application makes it intelligent and adaptive through FNN, reduces the dependence on artificial parameter adjustment, and makes the algorithm more feasible and superior in actual deployment.

[0057] Other advantages, objects, and features of the present application will be in part apparent and in part pointed out hereinafter in the specification, and will be observed in the practice of the application. The objects and other advantages of the present application can be realized and attained by the structure particularly pointed out in the specification as follows. BRIEF DESCRIPTION OF DRAWINGS

[0058] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred detailed description of the present application will be given below in combination with the drawings, in which:

[0059] Figure 1 Overall flowchart of the adaptive tracking method for maneuvering magnetic targets provided in the embodiments of the present invention

[0060] Figure 2 A detailed flowchart of the adaptive tracking method for maneuvering magnetic targets provided in this embodiment of the invention;

[0061] Figure 3 This is a simulated target motion trajectory diagram used in the embodiments of the present invention;

[0062] Figure 4 This is a comparison diagram of the tracking trajectory and the actual trajectory of the IMM-AKKF method in this embodiment of the invention;

[0063] Figure 5 for Figure 4 A magnified detail of the middle section of the trajectory;

[0064] Figure 6 This is a comparison diagram of the tracking trajectory and the actual trajectory of the IMM-AKKF method without using FNN in an embodiment of the present invention;

[0065] Figure 7 for Figure 6 A magnified detail of the middle section of the trajectory;

[0066] Figure 8 This is a graph showing the probability changes over time for the CV and CT models of the IMM framework in this embodiment of the invention.

[0067] Figure 9 This is a graph showing the probability changes over time for the CV and CT models of the IMM framework without using FNN in this embodiment of the invention.

[0068] Figure 10 This is a graph showing the position tracking error curves of the IMM-AKKF method in the X and Y directions in an embodiment of the present invention.

[0069] Figure 11 This is a position tracking error curve in the X and Y directions of the IMM-AKKF method in an embodiment of the present invention when FNN is not used. Detailed Implementation

[0070] The present application can also be embodied in a different specific form, and the various details of the specification can be modified in various ways without departing from the spirit of the application. It should be noted that the drawings provided in the following examples are only intended to illustrate the basic concept of the present application, and the following examples and features in the examples can be combined with each other without conflict.

[0071] The accompanying drawings are only used for illustrative purposes, and the representations are only schematic diagrams, not physical drawings, and should not be understood as limiting the present application. In order to better illustrate the embodiments of the present application, some components in the drawings may be omitted, enlarged or reduced, and do not represent the actual size of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions in the drawings may be omitted.

[0072] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that if the terms "upper", "lower", "left", "right", "front", "back" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only used for illustrative purposes, and should not be understood as limiting the present application. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0073] Please refer to Figures 1-11 The embodiment of the present application provides a new method for tracking a moving magnetic target by deeply integrating a feedforward neural network (FNN) adaptive noise estimation, an interactive multiple model (IMM) framework and an adaptive kernel Kalman filter (AKKF). The core idea of the method is to introduce a pre-trained FNN based on the IMM-AKKF framework, so that it can adaptively estimate and adjust the process noise covariance Q and the observation noise covariance R required by each AKKF filter in real time according to the features in the filtering process, thereby overcoming the defects that the Q and R matrices in the traditional filter are fixed or difficult to set, and greatly improving the adaptability and robustness of the system to complex dynamic and unknown noise environment.

[0074] 1) System model

[0075] It is assumed that the state of the moving magnetic target to be tracked at discrete time k is represented as a state vector X k In the IMM framework, for the jth motion model M jThe dynamic state space model (DSSM) of which can be represented as:

[0076] State equation:

[0077] Observation equation:

[0078] where f j (·) is the state transition function of the model M j , h j (·) is the observation function of the model M j . and are the process noise and observation noise under the model M j , respectively, whose covariance matrices are and

[0079] In a magnetic target tracking application, the state vector X k usually contains the kinematic parameters of the target, such as position, velocity, etc., and the magnetic moment parameters of the target, for example: where ξ k , η k , ζ k are the position components of the target, are the velocity components of the target, and m ξ , m η , m ξ are the magnetic moment components of the target. The observation vector Z k is the magnetic field measurement data obtained by one or more magnetometer sensors. The observation function h j (·) is based on the magnetic dipole model, which describes the nonlinear relationship between the state of the target and the magnetic field readings at the sensor:

[0080]

[0081] where m is the magnetic moment vector of the target, r is the relative position vector between the target and the sensor, and μ0 is the vacuum permeability.

[0082] 2) Workflow of IMM-AKKF-FNN model

[0083] Referring to Figure 1 , the main steps of the method in a complete tracking cycle are as follows:

[0084] S1: Initialization, including:

[0085] (1) IMM framework initialization:

[0086] Select N motion models Examples include uniform motion (CV) models and uniform turning (CT) models.

[0087] Set the Markov transition probability matrix between models as Π=[π ij ].

[0088] Set the initial probabilities for each motion model.

[0089] (2) Initialization of AKKF for each model (for each model M) j ):

[0090] M initial particles are drawn from the prior distribution p(X0).

[0091] Initialize kernel weight vector and covariance matrix

[0092] Choose a kernel function k(·,·), such as a Gaussian kernel, and set the regularization parameters κ and λ. K .

[0093] (3) Load the pre-trained FNN model: Load the pre-trained FNN weights and bias parameters (W,b).

[0094] S2: Iterative filtering (times k = 1, 2, ...), specifically including the following steps:

[0095] S21: IMM input interaction;

[0096] This step is for each model M j The AKKF filter provides a mixed initial condition that incorporates all model information from the previous time step.

[0097] Calculate the mixture probability Where the normalization factor in Let be the model probability of the i-th motion model at the previous time k-1.

[0098] Computational model M j Mixed initial state in Let be the state estimate of the i-th motion model output by the i-th AKKF filter at the previous time k-1.

[0099] Computational model M j Mixed initial covariance in Let k-1 be the state estimate at the previous time. The corresponding error covariance matrix.

[0100] S22: Parallel Model Filtering

[0101] For each motion model M in the IMM framework j (j = 1, ..., N), execute the following steps independently and in parallel:

[0102] S221: Adaptive estimation of noise covariance based on FNN;

[0103] Before performing AKKF filtering, a pre-trained FNN is first invoked to estimate the optimal noise covariance matrix for the current model j. and

[0104] 1) Constructing the input feature vector This vector is formed by fusing various pieces of information that reflect the current filtering state and model dynamics, such as:

[0105] The statistical characteristics calculated based on the historical information sequence of model j include the information mean and information variance.

[0106] The probability vector of the IMM model at the previous time step (k-1).

[0107] Kinematic features extracted from the state estimate after fusion from the previous time step (k-1).

[0108] 2) Forward propagation of FNN: FNN receives the input vector Then perform forward propagation calculations and output the original values.

[0109] 3) Construction of the covariance matrix: To ensure the non-negativity of the diagonal elements of the covariance matrix, the original output of the FNN is... Apply the Softplus activation function, and then use the diag(·) function to construct the diagonal covariance matrix. and

[0110] S222: AKKF proposes particle extraction and reweighting, including:

[0111] Extracting the mean and covariance: based on model M j Embedded from the posterior kernel mean at the previous time step k-1 Extract the mean and covariance of the states.

[0112] Extracting proposal particles: Randomly select M proposal particles from a probability distribution (e.g., a Gaussian distribution) that matches the above mean and covariance.

[0113] Compute proposal kernel weights: Compute the corresponding proposal kernel weight vector and covariance matrix for this set of new proposal particles and Perform basis transformation.

[0114] S223: AKKF prediction, including:

[0115] Particle propagation: Propagate the proposal particles through the state transition function f j (·) of the model M j and add process noise samples (sampled from ), to obtain the predicted state particles

[0116] Predicted kernel weights: The predicted kernel weight vector and covariance matrix are: where V k is the transition residual matrix.

[0117] S224: AKKF update, including:

[0118] Generate observation particles: Map the predicted state particles to the observation space through the observation function h j (·) of the model M j and add observation noise samples (sampled from ), to obtain a set of virtual observation particles

[0119] Update kernel weights: Obtain the real observation data Z k at the current time k, and update the kernel weight vector and covariance matrix using the kernel Kalman filtering rule:

[0120] Compute the kernel Kalman gain: where is the predicted kernel weight covariance matrix, G yy is the Gram matrix of the observation particles, and κ is the regularization parameter, and I is the identity matrix;

[0121] Update the kernel weight vector: where is the kernel function vector between the current real observation data Z k and all virtual observation particles .

[0122] Update the kernel weight covariance matrix:

[0123] Compute model state output: extract model M from updated posterior kernel mean embedding j State estimate at time k and covariance

[0124] S225: Compute likelihood: compute likelihood of model M j under current observation Z k

[0125] S23: IMM model probability update: update probability of each model according to the likelihood computed by the model

[0126] S24: IMM output fusion: weight fusion of parallel filtering results of all models j, to get the final state estimate of the magnetic target at current time k and final covariance P k .

[0127] The above steps S21 to S24 are executed in a loop at each tracking time, so as to realize continuous and adaptive tracking of the maneuvering magnetic target.

[0128] Simulation experiment:

[0129] The simulation verification experiment is carried out for the IMM-AKKF framework. In order to verify the effectiveness of the core filtering framework adopted by the present application, the performance of the interactive multiple model-adaptive kernel Kalman filter (IMM-AKKF) in processing the maneuvering magnetic target tracking problem is simulated and verified. The experiment aims to prove that the core framework can effectively cope with the target maneuvering behavior and the inherent strong nonlinear problem of the system, thereby laying a foundation for the effectiveness of the overall scheme of the present application (i.e. further introducing the FNN noise adaptive module).

[0130] 1) Simulation scene and parameter setting

[0131] Target motion trajectory:

[0132] A simulation motion trajectory of a magnetic target is set, as shown in Figure 2 The trajectory contains two typical stages to test the maneuvering adaptability of the IMM framework:

[0133] Stage one: (0-80 seconds): the target moves at a constant speed (3, 3, 0) m / s in a straight line (CV).

[0134] Stage two: (81-160 seconds): the target moves at a constant speed of 2 rad / s in a turning motion (CT), simulating target maneuvering.

[0135] ​​​Phase three: (161-240 seconds): target resumes (3, 3, 0) m / s constant velocity straight motion (CV). Sensor layout:

[0136] Three triaxial vector magnetometers are laid out, with coordinates as follows: sensor 1 (-5m, 0, 0), sensor 2 (0, 0, 0), and sensor 3 (5m, 0, 0).

[0137] The initial position of the target is (0m, 0m, 0m), and the initial magnetic moment is set to (0, 0, 50) A·m 2 .

[0138] Noise model settings:

[0139] In this embodiment, to verify the performance of the core framework under ideal conditions, the process noise and observation noise are set as fixed parameter Gaussian white noise.

[0140] The standard deviation of the observation noise is set to 10pT.

[0141] Implementation algorithm:

[0142] The interactive multiple model-adaptive kernel Kalman filter (IMM-AKKF) method is used for tracking.

[0143] Key parameter settings:

[0144] IMM framework: the motion model set includes constant velocity (CV) model and constant turn (CT) model. The transition probability matrix between models

[0145] AKKF parameters: Gaussian kernel is used for kernel function, kernel bandwidth sigma = 150, regularization parameters kappa, λK are set to 1e-5.

[0146] 2) Simulation results and performance analysis

[0147] 100 Monte Carlo experiments are performed, and the root mean square error (RMSE) of position is used as the core performance evaluation index.

[0148] Qualitative analysis:

[0149] As shown in the tracking trajectory comparison chart Figure 3 , Figure 4 indicates that the IMM-AKKF method used in this embodiment can closely follow the true trajectory of the target, and there is no divergence phenomenon in both the constant velocity straight motion phase and the constant turn maneuver phase, proving the stability and effectiveness of the algorithm. As shown in Figure 6 , Figure 7The tracking trajectory comparison chart shows that the IMM-AKKF method used in the embodiment has a significant decline in tracking effect when the noise suddenly increases in the third stage without using FNN, which proves the effectiveness of the FNN algorithm.

[0150] As Figure 8 shown in the model probability change curve, in stage one, the probability of the CV model dominates; when the target enters stage two and starts to turn, the probability of the CT model rises rapidly and becomes the dominant model; when the target enters stage three and returns to straight line, the probability of the CV model again dominates. This proves that the IMM framework can accurately identify the switching of the target motion mode. And Figure 9 as shown in the model probability change curve, without using FNN, when the noise suddenly increases in the third stage, the algorithm detects that the target appears rapid jitter, and the probabilities of the CV and CT models compete with each other, resulting in a decline in tracking effect.

[0151] Quantitative analysis:

[0152] To further quantitatively evaluate the tracking accuracy, Table 1 lists the average position RMSE statistics of the IMM-AKKF method in the three different motion stages, and Table 2 lists the average speed RMSE statistics of the IMM-AKKF method in the three different motion stages. At the same time, the errors of X and Y positions during the entire motion process are shown in Figure 10 and Figure 11

[0153] Table 1: Average position RMSE of IMM-AKKF method in each stage (unit: m)

[0154] Algorithm Stage One Stage Two Stage Three IMM-AKKF (without FNN) 0.8272 0.8043 39.5059 IMM-AKKF (with FNN) 0.7841 0.7973 3.8289

[0155] Table 2: Average speed RMSE of IMM-AKKF method in each stage (unit: m / s)

[0156] Algorithm Stage One Stage Two Stage Three IMM-AKKF (without FNN) 0.2838 0.3314 5.4188 IMM-AKKF (with FNN) 0.2978 0.3248 1.6156

[0157] From the data in Table 1 and Table 2, it can be seen that the method maintains a low tracking error in the three stages, and the tracking error without FNN is significantly greater than that with FNN, which proves the high precision characteristics of AKKF as the core filter in processing the magnetic dipole nonlinear observation model, and the tracking stability of the FNN algorithm when noise mutation occurs.

[0158] 3) Experimental conclusion

[0159] ​The results of the simulation experiment show that the IMM-AKKF as the core filtering framework of the application can successfully and accurately track the nonlinear magnetic target with maneuvering under the condition of stable noise characteristics. This fully verifies the feasibility and basic performance of the technical route.

[0160] However, the experiment is also based on an ideal assumption that the system noise (Q, R) is fixed and known. In real complex application scenarios, factors such as environmental electromagnetic interference and target state changes will cause the system noise to fluctuate in real time and unknown. In this case, the performance of the IMM-AKKF framework with fixed parameters will decrease. This introduces the FNN noise adaptive module into the application to realize online estimation and compensation of time-varying noise, thereby obtaining a more robust complete technical solution, and provides sufficient technical motivation and necessity.

[0161] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the application and not to limit it. Although the application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the application can be modified or replaced equivalently without departing from the purpose and scope of the technical solutions, which should be covered in the scope of the claims of the application.

Claims

1. A method of adaptive tracking of a motorized magnetic target, characterized in that, The method comprises: establishing a target physical model and a motion model, and determining state variables of the tracked magnetic target according to the models; constructing a state space model, and obtaining a motion state equation and a nonlinear observation equation of the magnetic target according to the determined state variables; performing double adaptive filtering tracking: constructing an IMM-AKKF-FNN model, including a maneuver decision layer, a nonlinear filtering layer and a noise perception layer, wherein IMM represents an interactive multiple model, AKKF represents an adaptive kernel Kalman filter, and FNN represents a feedforward neural network; the maneuver decision layer adopts an IMM framework, and runs multiple filters for different motion modes in parallel, and performs probability weighting according to the likelihoods of the motion models, so as to adaptively cope with the macro motion mode switching of the target; the nonlinear filtering layer adopts AKKF as a core state estimator inside each model of the IMM framework; and the noise perception layer is provided with a pre-trained FNN for each AKKF; a working process of the IMM-AKKF-FNN model is as follows: at each tracking time, the FNN first adaptively estimates process noise covariance Q and observation noise covariance R that are most suitable for the AKKF for each motion model; then, each AKKF performs prediction and updating by using the estimated Q and R; finally, the IMM framework performs motion model probability updating and state fusion according to the filtering results of each AKKF, to obtain the motion state of the target.

2. The method of adaptive tracking of a motorized magnetic target of claim 1, wherein, constructing a state space model, specifically including: assuming that the state of the tracked moving magnetically target at a discrete time instant k is represented as a state vector X k ; in the IMM framework, for the jth moving model M j , whose dynamic state space model is represented as: State equation: Observation equation: where f j (·) is the state transition function of the model M j j (·) is the observation function of the model M j , i.e., the target physical model; and are the process noise and observation noise under the model M j , respectively, whose covariance matrices are and ​ 3. The method of claim 2, wherein, Observation function h j (·) Based on the magnetic dipole model, used to describe the nonlinear relationship between the target state and the magnetic field readings at the sensor: B (m, r) is a magnetic field generated by the target at a sensor observation point, m is a magnetic moment vector of the target, r is a relative position vector between the target and the sensor, and μ0 is a vacuum permeability.

4. The method of claim 2, wherein, The state variable x t The vector expression for x is where ξ k ,η k ,ζ k are the position components of the target, are the velocity components of the target, m ξ ,m η ,m ζ are the magnetic moment components of the target.

5. The method of claim 1, wherein, The IMM framework performs motion model probability updating and state fusion according to the filtering results of each AKKF, and specifically comprises the following steps: S1: IMM input interaction: calculating mixed initial conditions of each motion model at the current time according to the probabilities and states of each motion model at the previous time; S2: parallel model filtering: for each motion model in the IMM framework, the following steps are independently and in parallel performed: S21: FNN noise estimation: using FNN, estimate the process noise covariance of this motion model according to the current filter state characteristics and the observation noise covariance S22: AKKF state estimation: AKKF is adopted, and the state estimation and likelihood under the motion model are obtained by using the results obtained in step S21 and prediction and update are performed, and the state estimation and likelihood under the motion model are obtained; S3: IMM probability updating: updating the probabilities of each motion model according to the likelihoods calculated for the motion models; S4: IMM output fusion: performing weighted fusion on the state estimates of each motion model according to the updated motion model probabilities, to obtain a final tracking result.

6. The method of adaptive tracking of a motorized magnetic target of claim 5, wherein, In step S21, the FNN is pre-trained in a manner of offline supervised learning, and the training process includes constructing a training data set containing an input feature vector and a corresponding real noise covariance label, and minimizing a prediction error by using a back propagation algorithm.

7. The method of claim 5, wherein, In step S21, the input feature vector of the FNN includes one or more of the following: statistical features calculated based on a historical innovation sequence of each motion model; an IMM probability vector at the previous time; kinematics features extracted from the fused state estimate at the previous time.

8. The method of claim 5, wherein, In step S22, the prediction step of the AKKF includes: extracting proposal particles, calculating proposal kernel weights, and predicting state particles and kernel weights.

9. The method of claim 5, wherein, In step S22, the updating step of the AKKF includes: Computing the kernel Kalman gain where, is the predicted kernel weight covariance matrix, G yy is the Gram matrix of the observations, κ is a regularization parameter, and I is the identity matrix. and kernel weights are updated using K k updating the kernel weight vector and kernel weight covariance matrix 10. A system for adaptive tracking method for a motorized magnetic target as claimed in claim 5, characterized in that, The system comprises: A system model construction module is configured to establish a target physical model and a motion model and determine a state variable; A state equation determination module is configured to obtain a motion state equation and a nonlinear observation equation of the magnetic target; The double adaptive filtering module has the following components integrated therein: A model interaction unit is configured to realize a mixing and fusing function of the IMM; A noise adaptive unit is configured by a FNN and is configured to estimate covariance of process noise and observation noise on line; A state estimation unit is configured by an AKKF and is configured to perform recursive estimation of the state under driving of the system model interaction unit and the noise adaptive unit.

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