Water surface target tracking method and system based on multi-physical parameter fusion

Abstract

The invention discloses a water surface target tracking method and system based on multi-physical parameter fusion, and the method comprises the steps: obtaining a physical layer observation parameter of a target through a water surface monitoring radar, and constructing a multi-dimensional nonlinear observation vector; establishing a multi-mode motion model set including constant speed, variable speed and turning, and realizing dynamic switching among motion modes through a Markov chain; adjusting a process noise covariance and an observation noise covariance based on a residual covariance estimation result in the sliding window by adopting an adaptive extended Kalman filtering algorithm; distributing weights according to the measurement variance of each physical parameter, optimizing the Kalman gain through a weighted least square method, and completing the updating and estimation of a target state; dynamic switching of motion modes is achieved through a Markov chain, and when state estimation residual errors of continuous preset times exceed a preset threshold value, model mismatch is judged, and a Markov chain model switching mechanism is triggered; according to the method, the sea condition adaptability, the calculation efficiency and the engineering expandability can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar target tracking, and in particular relates to a surface target tracking method and system based on multi-physical parameter fusion. Background Art

[0002] Surface target tracking technology is a core support for water traffic management, maritime surveillance, and navigation safety, and is widely used in areas such as Automatic Identification Systems (AIS), radar monitoring, and collaborative navigation of unmanned vessels. With the increasing density of shipping and the development of unmanned vessels, the demand for high-precision, robust, and real-time target tracking algorithms is becoming increasingly urgent.

[0003] Existing surface target tracking technologies are primarily based on the extended Kalman filter (EKF) and its improved algorithms, which achieve state prediction and update by linearizing nonlinear motion models. Typical approaches include filtering and estimating the uniform velocity model (CV) or uniform acceleration model (CA) in combination with observed data (such as range, orientation, and velocity). To enhance nonlinear adaptability, the interactive multi-model (IMM) improves maneuvering target tracking accuracy by combining multiple weighted motion models, while the particle filter (PF) employs Monte Carlo sampling to approximate the posterior probability distribution.

[0004] Traditional methods rely on single observation parameters and fixed motion models, and are difficult to adapt to multi-source interference and strong target maneuvering behavior in complex sea conditions. Although improved algorithms (such as IMM, PF, etc.) have improved tracking accuracy, they are difficult to meet the engineering requirements of multi-target tracking due to their high computational complexity and lack of real-time performance. As a result, existing technologies are difficult to effectively balance between sea condition adaptability, computational efficiency and engineering scalability. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a surface target tracking method based on multi-physical parameter fusion that can improve sea condition adaptability, computational efficiency and engineering scalability; on the other hand, to provide a surface target tracking system based on multi-physical parameter fusion.

[0006] Technical solution: The surface target tracking method of the present invention comprises the following steps:

[0007] (1) Obtaining the physical layer observation parameters of the target through the surface surveillance radar and constructing a multi-dimensional nonlinear observation vector can more comprehensively capture the dynamic characteristics of the target, avoid the error interference of a single data source, and provide a richer and more reliable information basis for subsequent processing;

[0008] (2) According to the ship's motion characteristics, a multi-mode motion model set including uniform speed, variable speed and turning is established The Markov chain is used to dynamically switch between motion modes, which can more accurately match the target's actual motion mode and reduce tracking errors caused by model mismatch. It is especially suitable for ships with complex maneuvers.

[0009] (3) Adopting the adaptive extended Kalman filter algorithm, based on the residual covariance estimation results within the sliding window, the process noise covariance and the observation noise covariance are dynamically adjusted. This can optimize the performance of the filter in real time and automatically adapt when the target suddenly changes speed or when the environmental interference increases, thus avoiding the tracking lag or divergence problems caused by the fixed noise parameters of the traditional method.

[0010] (4) Assigning weights based on the measurement variance of each physical parameter and optimizing the Kalman gain through weighted least squares method to complete the update and estimation of the target state, which can make more reasonable use of observation data, reduce the negative impact of low-quality data, and improve the overall tracking accuracy;

[0011] (5) Dynamic switching of motion modes is achieved through the Markov chain. When the state estimation residual exceeds the preset threshold for a preset number of consecutive times, it is determined to be a model mismatch and the Markov chain model switching mechanism is triggered. This can quickly correct the tracking deviation, avoid trajectory errors caused by "following the wrong model" for a long time, and enhance the robustness of the system.

[0012] Preferably, the physical layer observation parameters described in step 1 include the received signal amplitude A k , received signal phase Doppler shift f k and the distance ρ calculated based on the time difference k , the multidimensional nonlinear observation vector is The multi-parameter complementary design greatly enhances the system's perception capability and significantly reduces the impact of noise interference (such as wave clutter and multipath effects) on a single parameter. It can provide more stable and comprehensive target feature information even in complex sea conditions, laying a data foundation for subsequent high-precision tracking.

[0013] Preferably, the received signal amplitude A k The calculation formula is:

[0014]

[0015] Among them, η is a constant related to radar reflection power, antenna gain, etc.

[0016] The received signal phase The calculation formula is:

[0017]

[0018] Where λ is the radar wavelength;

[0019] The Doppler shift f k The calculation formula is:

[0020]

[0021] in, is the radial velocity between the target and the radar;

[0022] The distance ρ calculated based on the time difference k The calculation formula is:

[0023]

[0024] Where c is the speed of light (c = 3 × 10 8 m / s), Δt is the time difference between the transmitted signal and the received signal.

[0025] Each parameter is quantitatively characterized through radar equations (amplitude), wavelength correlation (phase), velocity-frequency relationship (Doppler) and time delay measurement (distance). This not only ensures the clear physical meaning of the data, but also significantly improves the observation reliability through mutual verification between parameters (such as the coordinated verification of Doppler velocity and phase change rate). This full-parameter fusion based on the physical characteristics of electromagnetic waves fundamentally enhances the system's anti-interference ability and measurement accuracy in strong noise environments.

[0026] Preferably, the multi-mode motion model set described in step 2 include:

[0027]

[0028] Where: X CV 、X CA 、X CT are the state vectors of the uniform speed, variable speed and turning models respectively, F CV 、F CA 、F CT The state transfer matrices of the uniform speed, variable speed and turning models are (x k ,y k ) is the position of the target at time k; is the speed of the target at time k; is the acceleration of the target at time k; ω k is the angular velocity; T is the radar sampling period.

[0029] This multi-model collaborative architecture, combined with precise timing control of the radar sampling cycle, enables the system to simultaneously adapt to complex maneuvering scenarios such as ship cruising (constant speed), acceleration / braking (speed change) and turning (angular velocity change). It fundamentally solves the "model mismatch" problem that occurs when a single motion model changes dynamically when the target changes, and provides an accurate model library foundation for subsequent Markov chain intelligent switching.

[0030] Preferably, the process noise covariance adjustment process described in step 3 includes:

[0031] According to the current motion model, calculate the predicted state x k,k-1 and the predicted covariance P k,k-1 :

[0032] x k,k-1 =Fx k-1

[0033] P k,k-1 =FP k,k-1 F T +Q k-1

[0034] Among them, x k,k-1 is the state prediction value at the current moment, x k-1 is the state estimate of the previous moment, F is the state transfer matrix, P k,k-1 is the covariance prediction value at the current moment, Q k-1 is the process noise covariance matrix of the previous moment;

[0035] Calculate the residual vector r k =Z k -H k x k,k-1 , where H k is the Jacobian matrix, Z k is the observation value at the current moment;

[0036] The sliding window method is used to calculate the residual covariance matrix S k :

[0037]

[0038] Then the noise covariance is dynamically adjusted to:

[0039] Q k =αQ k-1 +(1-α)K k S k (K k ) T

[0040] Among them: K k is the Kalman gain matrix, and α is the forgetting factor.

[0041] This step effectively solves the problem of lag or divergence in maneuvering target tracking caused by fixed noise parameters in traditional Kalman filtering through closed-loop adjustment of "prediction-observation-feedback", realizes adaptive optimization of process noise, and improves steady-state tracking accuracy.

[0042] Preferably, the observation noise covariance adjustment process described in step 3 includes:

[0043] Set the initial value of the observation noise matrix R0;

[0044] The measurement variance of each physical layer observation parameter is updated every preset period, where the measurement variance of the amplitude is The calculation is as follows:

[0045]

[0046] Similarly, calculate the distance variance Phase variance Doppler shift variance

[0047] Then the observation noise is dynamically adjusted to:

[0048]

[0049] in: is the distance variance; is the amplitude variance; is the phase variance; is the Doppler frequency shift variance; the above variances are updated regularly.

[0050] This step achieves real-time calibration of sensor errors by dynamically updating the measurement variance of each observation parameter; it automatically adjusts the confidence weight of each parameter according to different environmental conditions (such as amplitude fluctuations caused by wave interference and multipath effects affecting phase accuracy). When the error of a certain parameter increases (such as signal attenuation caused by heavy rain), its gain weight is reduced by increasing the corresponding variance value to avoid unreliable observations from contaminating the filtering results. Conversely, the contribution of high-precision parameters is increased. This adaptive noise reduction mechanism based on physical layer characteristics enables the system to maintain optimal observation fusion performance even in complex electromagnetic environments.

[0051] Preferably, the matrix corresponding to the weights in step 4 is:

[0052]

[0053] The Kalman gain is optimized as:

[0054]

[0055] Among them, Pk,k-1 is the covariance prediction value at the current moment, H k is the Jacobian matrix;

[0056] The state and covariance are updated as:

[0057] x k =x k,k-1 +K k r k

[0058] P k =(IK k H k )P k,k-1

[0059] Among them, x k is the estimated value of the state at the current moment; P k is the covariance estimate at the current moment.

[0060] This step optimizes the Kalman gain by introducing a weight matrix, achieving dynamic weighted fusion based on the real-time accuracy of each observation parameter, so that high-reliability parameters (such as low-variance observation data) obtain greater weight in state updates, while the influence of low-quality data is automatically suppressed; in the state and covariance update link, mathematical derivation is used to ensure that the estimated value always meets the minimum variance criterion, thereby significantly improving the estimation accuracy of target position, speed and other states; this data-driven intelligent weighting mechanism effectively solves the problem of poor environmental adaptability of traditional methods due to fixed weights, enabling the system to maintain millimeter-level tracking stability under complex sea conditions.

[0061] Preferably, the step 5 of dynamically switching the motion mode by using a Markov chain includes:

[0062] Define the pattern probability vector Indicates the probability that the target is in CV, CA, or CT motion modes at time k, satisfying

[0063] Define the transition probability matrix Π=[p nm ] 3×3 , where p nm Represents the probability of switching from the previous moment mode n to the current moment mode m, satisfying

[0064] Based on the pattern probability vector μ at the previous moment k-1 And the transition probability matrix π, predict the prior probability of each mode at the current moment:

[0065]

[0066] Compute the likelihood function for each model:

[0067]

[0068] in, Represents the current observation data Z k The degree of matching with the mth motion pattern; is the residual vector of the mth mode, where is the predicted value of the current state; is the residual covariance matrix; The smaller the covariance The closer it matches the actual error, the The larger the value, the more likely the current mode m is to be correct. This is the chi-square statistic, which is used to quantify the degree of misfit of the model;

[0069] Update the posterior probability using the Bayesian formula:

[0070]

[0071] The above formula is normalized to ensure If the prior probability of a model High residual matching High, then the posterior probability will increase significantly;

[0072] Select the model with the highest probability as the current valid model:

[0073] This step uses a Markov chain to achieve intelligent switching of motion modes, and dynamically evaluates the target motion state (constant speed CV, variable speed CA, turning CT) based on the mode probability vector and transition probability matrix. This data-driven adaptive mechanism effectively solves the switching lag problem of traditional multi-model algorithms and significantly improves tracking accuracy and stability under complex maneuvers.

[0074] Preferably, the triggering condition of the Markov chain model switching mechanism in step 5 is:

[0075] Define the chi-square statistic as Setting thresholds If satisfied 3 times in a row The current model is determined to be mismatched, and the model is switched, and the following operations are performed:

[0076] Select the new model with the highest probability in the Markov chain As the switching target, reset the process noise covariance Q k = 2Q0 and reset the state covariance matrix P k =P0.

[0077] The dual criteria of the chi-square statistic ensure that model switching is both sensitive and reliable: when the target's continuous maneuvers (such as long turns) cause the current model residual to deviate significantly, the system will not be falsely triggered by a single interference, but will only initiate the switch after three accumulated anomalies; after triggering, it will automatically select the new model with the highest probability (such as switching from uniform speed CV to turning CT), and reset the noise and state covariance to eliminate the influence of historical errors; this "delayed trigger + covariance reset" mechanism avoids frequent false switching while ensuring the rapidity and stability of model switching under sudden maneuvers, so that the tracking trajectory still maintains a smooth transition when the ship changes direction.

[0078] The surface target tracking system of the present invention comprises:

[0079] Radar observation module, used to obtain the physical layer observation parameters of the target through surface surveillance radar and construct multi-dimensional nonlinear observation vectors;

[0080] The motion model building module is used to build a multi-mode motion model set including uniform speed, variable speed and turning according to the ship's motion characteristics. And the dynamic switching between motion modes is achieved through Markov chain;

[0081] An adaptive filtering module is used to dynamically adjust the process noise covariance and the observation noise covariance based on the residual covariance estimation results within the sliding window using an adaptive extended Kalman filter algorithm;

[0082] The weighted fusion optimization module is used to assign weights based on the measurement variance of each physical parameter, optimize the Kalman gain through the weighted least squares method, and complete the update and estimation of the target state;

[0083] The dynamic switching decision module is used to realize dynamic switching of motion modes through Markov chain. When the state estimation residual exceeds the preset threshold for a consecutive preset number of times, it is determined to be a model mismatch and the Markov chain model switching mechanism is triggered.

[0084] Beneficial effects: Compared with the existing technology, the present invention has the following significant advantages: 1. It can improve sea condition adaptability, computational efficiency and engineering scalability; 2. The multi-mode motion model combined with the Markov chain intelligent switching strategy greatly improves the tracking accuracy of complex maneuvering targets; 3. Based on the sliding window residual estimation and probability-driven model switching, the real-time performance of the algorithm is significantly optimized; 4. Through the chi-square test and continuous trigger mechanism, the instantaneous interference signal is effectively filtered, which significantly improves the stability under extreme working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0086] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0087] like Figure 1 As shown, the surface target tracking method of the present invention includes the following steps:

[0088] Step 1: Use the surface surveillance radar to obtain the target's physical layer observation parameters, including the received signal amplitude, phase, Doppler frequency shift, and distance calculated based on time difference, and construct a multidimensional nonlinear observation vector as follows:

[0089]

[0090] Where: k is the target distance; A k is the received signal amplitude; is the phase of the received signal; f k is the Doppler frequency shift. The specific parameter definitions and physical meanings are as follows:

[0091] Time difference distance ρ k :

[0092]

[0093] Where: c is the speed of light (c = 3 × 10 8 m / s); Δt is the time difference between the transmitted signal and the received signal.

[0094] Received signal amplitude A k :

[0095]

[0096] Where: η is a constant related to the radar system parameters and target characteristics, and depends on several factors:

[0097] Radar transmit power: The greater the radar transmit power, the greater the received signal amplitude, and the value of η will increase accordingly;

[0098] Antenna gain: The higher the antenna gain, the greater the received signal amplitude, and the value of η will also increase;

[0099] Target radar cross-section: The larger the target's radar cross-section, the stronger the reflected signal, and the larger the value of η;

[0100] Propagation loss: The signal will be affected by atmospheric attenuation, rain attenuation, etc. during the propagation process, which will also affect the value of η.

[0101] In the radar equation, the received signal power P r Distance to target ρ k The relationship can be expressed as:

[0102]

[0103] Where: P t is the radar transmission power; G t is the transmitting antenna gain; G r is the receiving antenna gain; λ is the radar wavelength; σ is the radar cross section (RCS) of the target; and L is the system loss factor.

[0104] Received signal amplitude A k and the received signal power P r The relationship can be expressed as:

[0105]

[0106] Therefore, the received signal amplitude A k Distance to target ρ k The relationship can be expressed as:

[0107]

[0108] Among them: The constant η can be expressed as:

[0109]

[0110] Since the specific value of η depends on the radar system parameters and target characteristics, it usually needs to be determined through experiments or system calibration. The following are some reference values of typical parameters:

[0111] Radar transmit power P t : Typical values range from a few kilowatts to tens of kilowatts;

[0112] Antenna gain G t and G r : Typical values are 30dB to 40dB;

[0113] Radar wavelength λ: typically a few centimeters to tens of centimeters (for example, the wavelength of an X-band radar is about 3 cm);

[0114] Target radar cross-sectional area σ: Typical values range from a few square meters to tens of square meters (for example, a small ship is about 10m 2 , large ships may exceed 100m 2 );

[0115] System loss factor L: Typical values range from a few dB to more than ten dB;

[0116] Assumption: P t =10kW, G t =G r =1000(30dB),λ=0.03m(X band),σ=10m 2, L = 10 (10dB), then the constant η can be estimated as:

[0117]

[0118] Therefore, the relationship between the received signal amplitude and the target distance can be expressed as:

[0119]

[0120] Received signal phase

[0121]

[0122] Where: λ is the radar wavelength.

[0123] Doppler shift f k :

[0124]

[0125] in: is the radial velocity between the target and the radar.

[0126] In the established multidimensional nonlinear observation vector, the amplitude A k Affected by environmental attenuation, but the phase Sensitive to distance changes, Doppler shift f k It can detect sudden changes in velocity, but is easily disturbed by the motion of the carrier; multi-dimensional parameter fusion can be cross-validated to suppress the influence of a single noise source; the observation equation contains nonlinear terms such as amplitude and phase, which need to be linearized through extended Kalman filtering.

[0127] Step 2: Based on the ship's motion characteristics, a multi-mode motion model set including uniform speed, variable speed and turning is established. And the probability switching of motion mode is realized through Markov chain;

[0128] The state vector of the uniform velocity model (CV) is defined as:

[0129]

[0130] Where: (x k ,y k ) is the position of the target at time k; is the velocity of the target at time k.

[0131] The state transfer matrix of the uniform velocity model (CV) is:

[0132]

[0133] Where: T is the radar sampling period.

[0134] The state vector of the variable speed model (CA) is defined as:

[0135]

[0136] in: is the acceleration of the target at time k.

[0137] The state transfer matrix of the variable speed model (CA) is:

[0138]

[0139] The turning model (CT) state vector is defined as:

[0140]

[0141] Where: k is the angular velocity;

[0142] The state transfer matrix of the turning model (CT) is:

[0143]

[0144] Step 3: Design an adaptive extended Kalman filter algorithm to dynamically adjust the process noise covariance Q based on the sliding window residual covariance estimation k and the observation noise covariance P k ;

[0145] According to the current motion model, calculate the predicted state x k,k-1 and the predicted covariance P k,k-1 :

[0146] x k,k-1 =Fx k-1

[0147] P k,k-1 =FP k-1 F T +Q k-1

[0148] Where: x k,k-1 is the predicted value of the current state; x k-1 is the state estimate of the previous moment; F is the state transfer matrix; P k,k-1 is the covariance prediction value at the current moment; Q k-1 is the process noise covariance matrix at the previous moment.

[0149] The initial values of the parameters are set as:

[0150]

[0151] Calculate the residual vector rk :

[0152] r k =Z k -H k x k,k-1

[0153] Among them: H k is the Jacobian matrix, Z k is the observed value at the current moment.

[0154] Then the sliding window method is used to calculate the residual covariance matrix S k :

[0155]

[0156] Then the noise covariance is dynamically adjusted to:

[0157] Q k =αQ k-1 +(1-α)K k S k (K k ) T

[0158] Among them: K k is the Kalman gain matrix; α controls the decay rate of historical information.

[0159] In the method of the present invention, the sliding window length N=10; α=0.95;

[0160] The initial value of the observation noise matrix R0 = diag(16, 0.25, 0.01, 25).

[0161] The measurement variance of each physical parameter is updated every 10 cycles, among which the measurement variance of amplitude The calculation is as follows:

[0162]

[0163] Similarly, calculate the distance variance Phase variance Doppler shift variance

[0164] Then the observation noise is dynamically adjusted to:

[0165]

[0166] Step 4: Dynamically assign weights based on the measurement variance of each physical parameter, optimize the Kalman gain through weighted least squares, and perform state update and estimation;

[0167] The weight matrix is defined as:

[0168]

[0169] Kalman gain optimization:

[0170]

[0171] State and covariance update:

[0172] x k =x k,k-1 +K k r k

[0173] P k =(IK k H k )P k,k-1

[0174] Where: x k is the estimated value of the state at the current moment; P k is the covariance estimate at the current moment.

[0175] Step 5: Dynamically switch the motion mode through the Markov chain. Hypothesis testing is used to determine model mismatch. If the residual exceeds the threshold for three consecutive times, the Markov chain model switch is triggered.

[0176] Pattern probability vector:

[0177] Define the pattern probability vector Indicates the probability that the target is in each motion mode (CV, CA, CT) at time k, satisfying In the method of the present invention, μ0=[0.9,0.05,0.05] T , by default the initial speed model is dominated by the uniform velocity model.

[0178] Transition probability matrix:

[0179] Define the transition probability matrix Π=[p nm ] 3×3 , where p nm Represents the probability of switching from the previous moment mode n to the current moment mode m, satisfying Since the ship has inertia, it usually maintains the current mode (such as constant speed) for a short time, so the diagonal element p nn Set to a larger value (such as 0.7-0.9); the non-diagonal elements are distributed according to the actual maneuvering characteristics and rules of the ship. For example, the probability of switching from uniform speed (CV) to acceleration (CA) or turning (CT) is low (such as 0.05-1); the probability of switching from turning (CT) to uniform speed (CV) is high (such as 0.1-0.2); in the method of the present invention, the specific values of ∏ are as follows:

[0180]

[0181] Likelihood function:

[0182]

[0183] in: Represents the current observation data Z k The degree of matching with the mth motion pattern; is the residual vector of the mth mode; is the residual covariance matrix; The smaller the covariance The closer it matches the actual error, the The larger the value, the more likely the current mode m is to be correct. This is the chi-square statistic, which is used to quantify the degree of misfit of the model.

[0184] Mode probability update and switching:

[0185] Based on the previous moment pattern probability μ k-1 And the transfer matrix ∏, predict the prior probability of each mode at the current moment:

[0186]

[0187] For each model m, calculate its likelihood value Reflects the observed data Z k The degree of fit with the model.

[0188] Update the posterior probability using the Bayesian formula:

[0189]

[0190] The above formula is normalized to ensure If the predicted probability of a model High residual matching High, then the posterior probability will increase significantly.

[0191] Select the model with the highest probability as the current valid model:

[0192]

[0193] The chi-square statistic is defined as:

[0194]

[0195] The threshold value in the present invention is set as:

[0196]

[0197] If satisfied 3 times in a row The current model is judged to be mismatched, and then the model is switched to select the new model with the highest probability in the Markov chain. Reset the process noise covariance Q of the model k =2Q0, improve the model's adaptability to ship maneuvers; reset the model's covariance matrix P k =P0, to avoid the accumulation of historical errors.

[0198] Hypothesis testing based on the chi-square distribution can quantify the model mismatch risk; the continuously triggered dynamic switching mechanism can effectively suppress instantaneous interference (such as sea clutter) and has strong anti-noise capability.

Claims

1. A surface target tracking method based on multi-physical parameter fusion, characterized in that: The following steps are involved: (1) Obtain the physical layer observation parameters of the target through the surface surveillance radar and construct a multi-dimensional nonlinear observation vector; (2) According to the ship's motion characteristics, a multi-mode motion model set including uniform speed, variable speed and turning is established And the dynamic switching between motion modes is achieved through Markov chain; (3) Adopting the adaptive extended Kalman filter algorithm, the process noise covariance and the observation noise covariance are dynamically adjusted based on the residual covariance estimation results within the sliding window; (4) Assign weights based on the measurement variance of each physical parameter, optimize the Kalman gain through weighted least squares method, and complete the update and estimation of the target state; (5) Dynamic switching of motion modes is achieved through Markov chain. When the state estimation residual exceeds the preset threshold for a preset number of consecutive times, it is determined to be a model mismatch and the Markov chain model switching mechanism is triggered.

2. The surface target tracking method according to claim 1, characterized in that: The physical layer observation parameters described in step 1 include the received signal amplitude A k , received signal phase Doppler shift f k and the distance ρ calculated based on the time difference k , the multidimensional nonlinear observation vector is 3. The surface target tracking method according to claim 2, characterized in that: The received signal amplitude A k The calculation formula is: Among them, η is a constant related to radar reflection power, antenna gain, etc. The received signal phase The calculation formula is: Where λ is the radar wavelength; The Doppler shift f k The calculation formula is: in, is the radial velocity between the target and the radar; The distance ρ calculated based on the time difference k The calculation formula is: Where c is the speed of light (c = 3 × 10 8 m / s), Δt is the time difference between the transmitted signal and the received signal.

4. The surface target tracking method according to claim 1, characterized in that: The multimodal motion model set described in step 2 include: Where: X CV 、X CA 、X CT are the state vectors of the uniform speed, variable speed and turning models respectively, F CV 、F CA 、F CT are the state transfer matrices of the uniform speed, variable speed and turning models respectively, (x k ,y k ) is the position of the target at time k; is the speed of the target at time k; is the acceleration of the target at time k; ω k is the angular velocity; T is the radar sampling period.

5. The surface target tracking method according to claim 1, characterized in that: The process noise covariance adjustment process described in step 3 includes: According to the current motion model, calculate the predicted state x k,k-1 and the predicted covariance P k,k-1 : x k,k-1 =Fx k-1 P k,k-1 =FP k,k-1 F T +Q k-1 Among them, x k,k-1 is the state prediction value at the current moment, x k-1 is the state estimate of the previous moment, F is the state transfer matrix, P k,k-1 is the covariance prediction value at the current moment, Q k-1 is the process noise covariance matrix of the previous moment; Calculate the residual vector r k =Z k -H k x k,k-1 , where H k is the Jacobian matrix, Z k is the observation value at the current moment; The sliding window method is used to calculate the residual covariance matrix S k : Then the noise covariance is dynamically adjusted to: Q k =αQ k-1 +(1-α)K k S k (K k ) T Among them: K k is the Kalman gain matrix, and α is the forgetting factor.

6. The surface target tracking method according to claim 1, characterized in that: The observation noise covariance adjustment process described in step 3 includes: Set the initial value of the observation noise matrix R0; The measurement variance of each physical layer observation parameter is updated every preset period, where the measurement variance of the amplitude is The calculation is as follows: Similarly, calculate the distance variance Phase variance Doppler shift variance Then the observation noise is dynamically adjusted to: in: is the distance variance; is the amplitude variance; is the phase variance; is the Doppler frequency shift variance; the above variances are updated regularly.

7. The surface target tracking method according to claim 1, characterized in that: The matrix corresponding to the weights described in step 4 is: The Kalman gain is optimized as: Among them, P k,k-1 is the covariance prediction value at the current moment, H k is the Jacobian matrix; The state and covariance are updated as: x k =x k,k-1 +K k r k P k =(I-K k H k )P k,k-1 Among them, x k is the estimated value of the state at the current moment; P k is the covariance estimate at the current moment.

8. The surface target tracking method according to claim 1, characterized in that: The dynamic switching of the motion mode by using the Markov chain described in step 5 includes: Define the pattern probability vector Indicates the probability that the target is in CV, CA, or CT motion modes at time k, satisfying Define the transition probability matrix Π=[p nm ] 3×3 , where p nm Represents the probability of switching from the previous moment mode n to the current moment mode m, satisfying Based on the pattern probability vector μ at the previous moment k-1 And the transition probability matrix π, predict the prior probability of each mode at the current moment: Compute the likelihood function for each model: in, Represents the current observation data Z k The degree of matching with the mth motion pattern; is the residual vector of the mth mode, where is the predicted value of the current state; is the residual covariance matrix; The smaller the covariance The closer it matches the actual error, the The larger the value, the more likely the current mode m is to be correct. This is the chi-square statistic, which is used to quantify the degree of misfit of the model; Update the posterior probability using the Bayesian formula: The above formula is normalized to ensure If the prior probability of a model High residual matching High, then the posterior probability will increase significantly; Select the model with the highest probability as the current valid model:

9. The surface target tracking method according to claim 1, characterized in that: The triggering conditions for the Markov chain model switching mechanism described in step 5 are: Define the chi-square statistic as Setting thresholds If satisfied 3 times in a row The current model is determined to be mismatched, and the model is switched, and the following operations are performed: Select the new model with the highest probability in the Markov chain As the switching target, reset the process noise covariance Q k = 2Q0 and reset the state covariance matrix P k =P0.

10. A surface target tracking system based on multi-physical parameter fusion, characterized in that: include: Radar observation module, used to obtain the physical layer observation parameters of the target through surface surveillance radar and construct multi-dimensional nonlinear observation vectors; The motion model building module is used to build a multi-mode motion model set including uniform speed, variable speed and turning according to the ship's motion characteristics. And the dynamic switching between motion modes is achieved through Markov chain; An adaptive filtering module is used to dynamically adjust the process noise covariance and the observation noise covariance based on the residual covariance estimation results within the sliding window using an adaptive extended Kalman filter algorithm; The weighted fusion optimization module is used to assign weights based on the measurement variance of each physical parameter, optimize the Kalman gain through the weighted least squares method, and complete the update and estimation of the target state; The dynamic switching decision module is used to realize dynamic switching of motion modes through Markov chain. When the state estimation residual exceeds the preset threshold for a consecutive preset number of times, it is determined to be a model mismatch and the Markov chain model switching mechanism is triggered.

Images