A waveform design method and system for a unmanned boat-borne radar to track moving targets on the sea surface

Abstract

The present invention discloses a waveform design method and system for an unmanned boat-borne radar to track moving targets on the sea surface, which relates to the technical field of radar communication and aims to solve the technical problem of inaccurate tracking of moving targets in a sea clutter environment. The technical key points of the present invention include: predicting the target state by using the marginalized particle filter algorithm and obtaining the predicted measurement value; generating a hypothesis tree according to the observation data; estimating the target state on each hypothesis branch by using the marginalized particle filter algorithm; calculating the association probability and updating the hypothesis weight by using the multiple hypothesis tracking algorithm, performing hypothesis pruning and fusion to obtain the final target state estimate; using multiple waveform selection criteria as models and determining the best criterion with the highest effective probability and the optimal transmission waveform parameters by using the interactive multiple criteria selection method. The present invention can effectively cope with false alarms caused by sea clutter, improve the performance of the unmanned boat-borne radar in dealing with complex tracking scenarios, and obtain more accurate and robust target tracking results.

Description

Technical Field

[0001] The present invention relates to the technical field of radar communication, and particularly relates to a waveform design method and system for an unmanned boatborne radar to track moving targets on the sea surface. Background Technique

[0002] In recent years, due to their flexible maneuverability and strong autonomy, unmanned boats have been increasingly used in the tracking and monitoring tasks of sea surface targets. Unmanned boats equipped with radar devices can effectively detect and track various moving targets on the sea surface, such as ships, small boats, and even unmanned surface platforms and low-altitude flying drones. These technologies have broad application prospects in the fields of maritime search and rescue, border patrol, and marine resource protection.

[0003] In traditional target tracking systems, radars usually estimate the target position and speed through a single tracking filter. With the complication of target motion behaviors, especially in the tracking tasks of highly maneuverable targets, a single filter often has difficulty coping with complex target state changes. Considering the target tracking mechanism and waveform selection in clutter scenarios, more and more research combines multiple algorithms to construct hybrid filters. The Probabilistic Data Association (PDA) algorithm effectively deals with false alarms by calculating the association probability between the measurement value and its predicted value; the Multiple Hypothesis Tracking (MHT) algorithm is also used to generate multiple hypotheses for target trajectory estimation, making it suitable for multi-target tracking in clutter backgrounds. These algorithms can be used to cope with complex clutter backgrounds and can be fused with filtering methods such as Unscented Kalman Filter (UKF), Square Root Cubature Kalman Filter (SCKF), and Particle Filter (PF) to process non-linear measurements and clutter, such as: "Variational Bayesian Target Tracking Algorithm in Clutter Interference Environment" by Yun Peng, Zheng Shiyou, Zhang Shicang, etc.; "Computer Simulation"; "Probabilistic Data Association Maneuvering Target Tracking Algorithm Based on Distance Weighting" by Chen Xiao, Li Ya'an, Li Yuxing, etc.; "Journal of Shanghai Jiao Tong University"; "Probabilistic Data Association Method for Space Target Tracking" by Xu Zhanwei, Wang Xin; "Acta Astronomica Sinica", etc.

[0004] In target tracking, the selection of the radar emission waveform is crucial for tracking accuracy. Traditional waveform selection methods are usually based on fixed criteria, which are difficult to optimize when facing rapidly changing target states (e.g., Cognitive radar target tracking waveform selection method based on reinforcement learning, Zhu Peikun, Liang Jing, Luo Zihan, etc.; Journal of Radars, 2023; Cognitive radar maneuvering target tracking algorithm based on information entropy criterion, Wang Shuliang, Bi Daping, Ruan Huailin, etc.; Acta Electronica Sinica, 2019). Therefore, more effective selection methods or simple and convenient switching methods are needed. To adapt to the changes in target states, the interacting multiple model (IMM) framework can be applied to waveform selection under multiple models, and flexibly perform adaptive adjustment among multiple waveform selection criteria according to the target state, so as to optimize the detection ability and tracking accuracy of the radar system.

[0005] Currently, existing unmanned boat radar tracking technologies still have problems such as insufficient tracking accuracy and inflexible waveform selection when facing complex sea surface maneuvering targets. How to effectively combine the filtering tracking algorithm with the radar emission waveform design to better cope with the mobility changes of sea surface targets and optimize the tracking performance by adaptively selecting the emission waveform has become an important direction of current technical research. Summary of the Invention

[0006] In view of the above problems, the present invention proposes a waveform design method and system for an unmanned boatborne radar to track sea surface maneuvering targets, aiming to provide a target tracking solution with high precision, high robustness and adaptive waveform selection ability in a complex sea environment.

[0007] According to one aspect of the present invention, a waveform design method for an unmanned boatborne radar to track sea surface maneuvering targets is proposed, and the method includes:

[0008] Predict the target state using the marginalized particle filter algorithm, and obtain the predicted measurement value based on the target state; the target state includes nonlinear state and linear state;

[0009] Generate a hypothesis tree according to the observation data;

[0010] Use the marginalized particle filter algorithm to estimate the target state on each hypothesis branch of the hypothesis tree;

[0011] Use the multiple hypothesis tracking algorithm to calculate the association probability and update the hypothesis weights, perform hypothesis pruning and fusion, and obtain the final target state estimate;

[0012] Use multiple waveform selection criteria as models, and use the interacting multiple criteria selection method to determine the best criterion with the highest effective probability and the optimal emission waveform parameters.

[0013] Further, the prediction of the target state using the marginalized particle filter algorithm and obtaining the predicted measurement value based on the target state includes:

[0014] According to the state estimation vector obtained at time k-1 Estimation error covariance matrix And the triangular model of the target, the new particle prediction value is obtained through particle filtering:

[0015]

[0016] In the formula, Is the non-linear prediction state vector of the i-th particle at time k, Is the target non-linear state prediction vector, Is the non-linear state estimation vector of the i-th particle at time k-1, Is the linear state estimation vector of the target at time k-1, Is the non-linear state estimation vector of the target from time 0 to k-1 of the i-th particle, z 1:k-1 Is the target state measurement value from time 1 to k-1, A n Is the non-linear transformation matrix, Represents A n The transpose matrix of, Q n Is the non-linear part of the covariance matrix of the Gaussian process noise, f(·) represents the transfer function of the target non-linear state; n and l respectively represent the non-linear state and linear state of the target;

[0017] Calculate the target non-linear state prediction vector according to the following formula:

[0018]

[0019] In the formula, N is the total number of particles in the marginalized particle filter algorithm;

[0020] Calculate the linear state prediction vector of the target at time k according to the following formula:

[0021]

[0022] In the formula, Is the linear state prediction vector of the target at time k, Is the linear state prediction error covariance matrix of the target at time k, A l Is the linear transfer matrix, Is the residual, and there is Q l Is the linear part of the covariance matrix of the Gaussian process noise;

[0023] Calculate the predicted measurement value of the target according to the following formula:

[0024]

[0025] wherein is the predicted measurement value at time k, and h(·) represents a non-linear function, is the predicted state vector at time k and has

[0026] Furthermore, the generating of the hypothesis tree according to the observation data includes:

[0027] Regarding the random variables falling within the effective region of the predicted measurement value as clutter, the effective region refers to a region around the predicted measurement value with a threshold of g, and the size of this region is S k being the residual covariance; the clutter has a Poisson distribution in quantity and, as false alarms, together with the true measurement values from the target, constitutes all the observation data obtained in the radar received echo:

[0028] z b,k =[z k , c1, c2,..., c M-1

[0029] wherein, z b,k is the observation vector matrix, z k is the true measurement value from the target at time k, c M-1 is the false alarm caused by the (M - 1)-th sea clutter, and M represents the number of observation vectors;

[0030] Generating hypothesis branches based on the current measurement data, and each observation vector in the observation vector matrix is used as a possible target hypothesis:

[0031]

[0032] wherein represents the m-th hypothesis measurement value at time k.

[0033] Furthermore, the performing of target state estimation on each hypothesis branch of the hypothesis tree by using the marginalized particle filtering algorithm includes:

[0034] Assuming that the importance distribution only depends on the target state and the measurement value from the previous moment, the normalized importance weight is calculated by the following formula:

[0035]

[0036] wherein is the importance weight of the i-th particle at time k, is the normalization result of , is the predicted measurement value of the i-th particle at time k​ the residual, and there is R k is the measurement error covariance matrix at time k;

[0037] Using the normalized importance weights, the nonlinear state estimation vector of the hypothesis is obtained by particle filter resampling through the following formula:

[0038]

[0039] where is the nonlinear state estimation vector of the i-th particle of the m-th hypothesis at time k;

[0040] The linear state estimation vector of the hypothesis is obtained by Kalman filter through the following formula:

[0041]

[0042] where is the linear state estimation vector of the m-th hypothesis at time k, is the linear state estimation error covariance of the m-th hypothesis at time k, H k is the Jacobian matrix, s k,m is the residual and there is K k is the Kalman gain;

[0043] The linear estimated state vector and the nonlinear estimated state vector are combined through the following formula to obtain the total hypothesis state estimation vector:

[0044]

[0045] where is the total state estimation vector of the m-th hypothesis at time k, is the nonlinear estimated state vector of the m-th hypothesis at time k, and there is

[0046] Furthermore, the multi-hypothesis tracking algorithm is used to calculate the association probability and update the hypothesis weights, and hypothesis pruning and fusion are performed to obtain the final target state estimation, including:

[0047] The association probability between each hypothesis and the target state prediction value is calculated through the following formula:

[0048]

[0049] According to the association probability and the prior probability, the weight of each hypothesis is updated through Bayes' formula:

[0050]

[0051] where qk,m is the weight of the m-th hypothesis at time k, β m is the correlation probability between the m-th hypothesis and the predicted value of the target state, q k-1 is the prior probability at time k and also the posterior probability at time k - 1;

[0052] Perform hypothesis pruning based on the weights, directly sort and retain the I hypotheses with the highest weights;

[0053] Normalize the weights of the retained I hypotheses through the following formula:

[0054]

[0055] Perform hypothesis fusion through the following formula to obtain the final target state estimation vector and estimation error covariance:

[0056]

[0057] In the formula, is the target state estimation vector at time k, is the state estimation error covariance at time k, q k,i is the weight of the i-th hypothesis at time k, is q k,i The normalized result of, I is the number of hypotheses retained after hypothesis pruning.

[0058] Furthermore, use multiple waveform selection criteria as a model and utilize the interactive multi-criteria selection method to determine the best criterion with the highest effective probability and the optimal transmit waveform parameters, including:

[0059] Assume there are L criteria, and calculate the prediction probability of each criterion according to the transition probability and prior probability as:

[0060]

[0061] In the formula, p ji is the transition probability from criterion j to criterion i, is the effective probability of criterion j at time k, is the prediction probability of criterion i;

[0062] Traverse the pre-established waveform library, predict the target state at time k + 1, and predict the target state at time k + 1 through the Kalman filtering algorithm to obtain S k+1 ; Select the optimal transmit waveform parameters according to different criteria; among them, the waveform library is established as follows: the pulse length λ and sweep frequency Δ in the radar measurement error covariance R k in FAs an adaptively selectable transmit waveform parameter, its range is determined according to actual requirements, thereby constructing a transmit waveform library Ψ;

[0063] Select the optimal transmit waveform parameter according to different criteria; calculate the likelihood probability of each criterion through the following formula:

[0064]

[0065] In the formula, is the likelihood probability of the i-th criterion, is the residual covariance at time k + 1, and there is is the residual between the actual measurement value and the predicted measurement value at time k + 1, and there is where is the predicted measurement value of criterion i at time k + 1;

[0066] Update the weight of each criterion through the following formula:

[0067]

[0068] In the formula, is the effective probability of criterion i at time k + 1, and it is also the weight of criterion i;

[0069] Select the criterion with the highest effective probability as the best selection criterion, and use its parameter selection result as the optimal parameter in the transmit waveform at the next moment.

[0070] Furthermore, the different criteria include: maximum Q-value criterion, minimum mean square error criterion, maximum mutual information criterion, minimum waveform criterion.

[0071] Furthermore, using the maximum Q-value criterion to select the optimal transmit waveform parameter includes:

[0072] Calculate the entropy state according to the following formula:

[0073]

[0074] In the formula, ES k+1 and ES k are the entropy states at time k + 1 and time k respectively;

[0075] Calculate the real-time reward according to the following formula:

[0076] r k =log(1+|ES k+1 -ES k |)sign(ES k+1 -ES k );

[0077] Calculate the cumulative discount reward according to the following formula:

[0078]

[0079] In the formula, both ψ and ψ′ are combinations of transmission waveform parameters in the transmission waveform library, and Q k (ψ) and Q k (ψ′) are the cumulative discount rewards corresponding to ψ and ψ′ at time k respectively, and Q k+1 (ψ) is the cumulative discount reward corresponding to ψ at time k + 1, α is the learning rate, γ is the discount factor and γ ∈ [0, 1];

[0080] The transmission waveform parameters in the waveform library that maximize the cumulative discount reward are expressed as:

[0081]

[0082] In the formula, Ψ is the transmission waveform library.

[0083] Furthermore, using the minimum mean square error criterion to select the optimal transmission waveform parameters includes: calculating the optimal transmission waveform parameters according to the following formula:

[0084]

[0085] Furthermore, using the maximum mutual information criterion to select the optimal transmission waveform parameters includes: calculating the optimal transmission waveform parameters according to the following formula:

[0086]

[0087] Furthermore, using the minimum gate criterion to select the optimal transmission waveform parameters includes: calculating the optimal transmission waveform parameters according to the following formula:

[0088]

[0089] According to another aspect of the present invention, a waveform design system for an unmanned boat-borne radar to track moving targets on the sea surface is proposed. The system includes:

[0090] A predicted measurement value calculation module configured to predict the target state using the marginalized particle filter algorithm and obtain the predicted measurement value based on the target state; the target state includes a non-linear state and a linear state;

[0091] A target state estimation module configured to generate a hypothesis tree according to the observation data; perform target state estimation on each hypothesis branch of the hypothesis tree using the marginalized particle filter algorithm; calculate the association probability and update the hypothesis weight using the multiple hypothesis tracking algorithm, and perform hypothesis pruning and fusion to obtain the final target state estimation;

[0092] The optimal transmission waveform determination module is configured to use multiple waveform selection criteria as a model and utilize the interactive multi-criteria selection method to determine the best criterion with the highest effective probability and the optimal transmission waveform parameters.

[0093] The beneficial technical effects of the present invention are as follows:

[0094] The present invention can effectively track maneuvering targets in the compound linear and non-linear states of the sea surface under high sea conditions, cope with false alarms caused by sea clutter, effectively combine the filtering tracking algorithm and the radar transmission waveform design, better cope with the maneuverability changes of sea surface targets, and more flexibly select the transmission waveform to optimize the tracking performance, enhance the robustness and accuracy of tracking. Its advantages are as follows:

[0095] (1) For the problem of target tracking in the sea clutter background, the present invention adopts the multi-hypothesis marginalized particle filter algorithm, forms a hypothesis tree using the measurement values obtained from the received echo analysis, and effectively solves the problem of sea clutter interference through hypothesis pruning and fusion, enhancing the anti-interference ability of target tracking. Using marginalized particle filter to more accurately track strongly maneuvering targets with variable states, providing a target tracking solution with high precision and high robustness for unmanned surface vehicle-mounted radars in complex sea surface environments.

[0096] (2) For waveform parameter optimization, the present invention adopts the interactive multi-criteria selection method, simply and flexibly switches the parameter selection strategy, further improves the adaptive adjustment ability of the radar system, has lower tracking error and higher tracking accuracy compared with using fixed waveforms or single-criterion optimization methods, and solves the problems of insufficient tracking accuracy and inflexible waveform selection in the existing unmanned surface vehicle-mounted radar tracking technology when facing complex sea surface maneuvering targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings. The accompanying drawings, together with the following detailed description, are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0098] Figure 1 It is a block diagram of a waveform design method for an unmanned surface vehicle-mounted radar to track sea surface maneuvering targets according to the present invention;

[0099] Figure 2 It is a schematic diagram of criterion selection during the tracking process;

[0100] Figure 3 It is a schematic diagram of the maneuvering target movement trajectory and tracking result;

[0101] Figure 4 It is a schematic diagram of waveform parameter selection during the tracking process;

[0102] Figure 5 It is the root mean square error graph of the estimated state vector of the maneuvering target;

[0103] Figure 6 It is the tracking result graph using different waveform selection methods;

[0104] Figure 7 It is the schematic diagram of parameter selection using different waveform selection methods;

[0105] Figure 8 It is the comparison graph of the root mean square error of the estimated state vector of the target using different waveform selection methods. Specific implementation manner

[0106] In order to enable those skilled in the art to better understand the solution of the present invention, the exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are only a part of the embodiments or examples of the present invention, rather than all of them. Based on the embodiments or examples in the present invention, all other embodiments or examples obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0107] The present invention proposes a waveform design method for an unmanned boatborne radar to track sea surface maneuvering targets, that is, an unmanned boatborne radar target tracking method that uses the multi-hypothesis marginalized particle filter algorithm and the interactive multi-criterion selection method to select the transmitted waveform parameters, aiming to provide a target tracking solution with high precision, high robustness and adaptive waveform selection ability in a complex sea surface environment.

[0108] An embodiment of the present invention proposes a waveform design method for an unmanned boatborne radar to track sea surface maneuvering targets, as Figure 1 shown, including:

[0109] S1. Predict the target state using the marginalized particle filter algorithm and obtain the predicted measurement value based on the target state; the target state includes a non-linear state and a linear state;

[0110] S2. Generate a hypothesis tree according to the observation data;

[0111] S3. Use the marginalized particle filter algorithm to estimate the target state on each hypothesis branch of the hypothesis tree;

[0112] S4. Use the multi-hypothesis tracking algorithm to calculate the association probability and update the hypothesis weights, perform hypothesis pruning and fusion, and obtain the final target state estimate;

[0113] S5. Use multiple waveform selection criteria as a model, and use the interactive multi-criteria selection method to determine the best criterion with the highest effective probability and the optimal transmit waveform parameters.

[0114] The method starts from S1. In S1, the marginalized particle filter algorithm is used to predict the target state, and the predicted measurement value is obtained based on the target state.

[0115] According to the embodiments of the present invention, the marginalized particle filter algorithm is used to construct a sea surface low-altitude maneuvering target motion model, and the target state is a triangular model composed of a linear state and a non-linear state:

[0116]

[0117] where x k is the measurement state vector of the maneuvering target at time k, and there are and are the non-linear state vector and the linear state vector of the maneuvering target at time k respectively, f(·) represents the transfer function of the target non-linear state, A n and A l represent the non-linear and linear transfer matrices respectively, h(·) is the measurement function, z k is the measurement value of the target at time k. n and l represent the non-linear state and the linear state of the target respectively.

[0118] w k is the Gaussian process noise with zero mean and covariance matrix Q k at time k, and there are: and are the non-linear and linear Gaussian process noises at time k respectively,

[0119] u k is the measurement noise with zero mean and measurement error covariance R k at time k, and there are:

[0120]

[0121] c is the speed of light, f0 is the carrier frequency, λ is the pulse length, b is the frequency modulation slope and there is Δ F is the frequency sweep, T s is the effective pulse duration, η k is the signal-to-noise ratio at time k and there are:

[0122]

[0123] d0 is the distance from the radar to the maneuvering target when the signal-to-noise ratio is 0 dB, p kis the position of the maneuvering target at time k, where t and r are the positions of the radar receiver and transmitter, respectively.

[0124] First, based on the state estimation vector obtained at time k - 1 the estimation error covariance matrix and the target's hybrid state model (i.e., the triangular model composed of linear and nonlinear states mentioned above), the new particle prediction values are obtained through particle filtering:

[0125]

[0126] is the nonlinear prediction state vector of the i-th particle at time k, is the target's nonlinear state prediction vector, is the nonlinear state estimation vector of the i-th particle at time k - 1, is the target's linear state estimation vector at time k - 1, is the target's nonlinear state estimation vector of the i-th particle from time 0 to k - 1, z 1:k-1 is the target state measurement value from time 1 to k - 1, A n is the nonlinear transformation matrix, represents the transpose matrix of A n Q n is the nonlinear part of the covariance matrix of the Gaussian process noise, represents the prior probability density function, and f(·) represents the transfer function of the target's nonlinear state;

[0127] The target's nonlinear state prediction vector is calculated according to the following formula:

[0128]

[0129] N is the total number of particles in the marginalized particle filtering framework;

[0130] The target's linear state prediction vector at time k is calculated according to the following formula:

[0131]

[0132] is the target's linear state prediction vector at time k, is the target's linear state prediction error covariance matrix at time k, A l is the linear transfer matrix, is the residual, and there is Q l is the linear part of the covariance matrix of the Gaussian process noise, N k and L kIt is an intermediate process quantity for calculating the linear prediction vector, reflecting the mutual influence between the non-linear and linear states;

[0133] Calculate the predicted measurement value of the target according to the following formula:

[0134]

[0135] is the predicted measurement value at time k, and h(·) represents a non-linear function. is the predicted state vector at time k and has

[0136] Then execute S2. In S2, generate a hypothesis tree according to the observation data.

[0137] According to the embodiment of the present invention, a random variable falling within the effective region of the predicted measurement value is regarded as clutter. The effective region refers to a region around the predicted measurement value with a threshold of g, and the size of this region is S k is the residual covariance; the clutter is Poisson distributed in number and, together with the true measurement value from the target, constitutes all the observation data obtained in the radar received echo as false alarms:

[0138] z b,k = [z k , c1, c2,..., c M-1 ;

[0139] z b,k is the observation vector matrix, z k is the true measurement value from the target at time k, and c M-1 is the false alarm caused by the (M - 1)-th sea clutter, and M represents the number of observation vectors;

[0140] Generate hypothesis branches based on the current measurement data. Each observation vector in the observation vector matrix is used as a possible target hypothesis:

[0141]

[0142] represents the m-th hypothesis measurement value at time k.

[0143] Then execute S3. In S3, use the marginalized particle filter algorithm to perform target state estimation on each hypothesis branch of the hypothesis tree.

[0144] According to the embodiment of the present invention, using the marginalized particle filter algorithm to perform target state estimation on each hypothesis branch includes:

[0145] Assuming that the importance distribution depends only on the target state and the measurements from the previous moment, the normalized importance weights can be calculated by the following formula:

[0146]

[0147] is the importance weight of the i-th particle at time k, is the normalization result of, is the predicted measurement value of the i-th particle at time k the residual of, and there is R k is the measurement error covariance matrix at time k;

[0148] The non-linear state estimation vector of the hypothesis is obtained by particle filter resampling:

[0149]

[0150] is the non-linear state estimation vector of the i-th particle of the m-th hypothesis at time k; represents the normalized importance weights.

[0151] The linear state estimation vector of the hypothesis is obtained by Kalman filter through the following formula:

[0152]

[0153] is the linear state estimation vector of the m-th hypothesis at time k, is the linear state estimation error covariance of the m-th hypothesis at time k, H k is the Jacobian matrix, K k is the Kalman gain, s k,m is the residual and there is

[0154] The linear estimation state vector and the non-linear estimation state vector are combined through the following formula to obtain the total hypothesis state estimation vector:

[0155]

[0156] is the total state estimation vector of the m-th hypothesis at time k, is the non-linear estimation state vector of the m-th hypothesis at time k, and there is

[0157] Then, S4 is executed. In S4, the multi-hypothesis tracking algorithm is used to calculate the association probability and update the hypothesis weights, and hypothesis pruning and fusion are performed to obtain the final target state estimation.

[0158] According to an embodiment of the present invention, first, the association probability between each hypothesis and the predicted value of the target state is calculated by the following formula:

[0159]

[0160] Then, according to the association probability and the prior probability, the weight of each hypothesis is updated by the Bayesian formula:

[0161]

[0162] q k,m is the weight of the m-th hypothesis at time k, β m is the association probability between the m-th hypothesis and the predicted value of the target state, q k-1 is the prior probability at time k and also the posterior probability at time k - 1;

[0163] Then, hypothesis pruning is performed according to the weights, and the I hypotheses with the highest weights are directly sorted and retained;

[0164] Then, the weights of the retained I hypotheses are normalized by the following formula:

[0165]

[0166] Then, hypothesis fusion is performed by the following formula to obtain the final target state estimation vector and the estimation error covariance:

[0167]

[0168] is the target state estimation vector at time k, is the state estimation error covariance at time k, q k,i is the weight of the i-th hypothesis at time k, is the normalization result of q k,i and I is the number of hypotheses retained after hypothesis pruning.

[0169] Then, S5 is executed. In S5, multiple waveform selection criteria are used as the model, and the interactive multi-criteria selection method is used to determine the best criterion with the highest effective probability and the optimal transmit waveform parameters.

[0170] According to an embodiment of the present invention, assuming there are L criteria, first, the predicted probability of each criterion is calculated according to the transition probability and the prior probability as:

[0171]

[0172] p ji is the transition probability from criterion j to criterion i, is the effective probability of criterion j at time k, The predicted probability for criterion i.

[0173] Then, traverse the waveform library and select the optimal transmitted waveform parameters according to different criteria; among them, the waveform library is pre-established as follows: the radar measurement error covariance R k The pulse length λ and the frequency sweep Δ F in are used as the adaptively selectable transmitted waveform parameters, and their ranges are determined according to actual requirements, so as to construct the transmitted waveform library Ψ.

[0174] Then, calculate the likelihood probability of each criterion through the following formula:

[0175]

[0176] is the likelihood probability of the i-th criterion, is the residual covariance at time k + 1, and there is is the residual between the actual measurement value and the predicted measurement value at time k + 1, and there is where is the predicted measurement value of criterion i at time k + 1.

[0177] Then, update the weight of each criterion through the following formula:

[0178]

[0179] is the effective probability of criterion i at time k + 1, and it is also the weight of criterion i;

[0180] Then, select the criterion with the highest effective probability as the best selection criterion, and apply its parameter selection result as the optimal parameter to the transmitted waveform at the next moment.

[0181] In this embodiment, preferably, as Figure 2 shown, traverse the waveform library and select the optimal transmitted waveform parameters according to different criteria, including:

[0182] Predict the target state at time k + 1, and predict the target state at time k + 1 through the Kalman filter algorithm to obtain S k+1 ;

[0183] a) Select the optimal transmitted waveform parameters using the maximum Q-value criterion; including:

[0184] Calculate the entropy state according to the following formula:

[0185]

[0186] ES k+1 and ESk The entropy states at times k + 1 and k respectively;

[0187] Calculate the real-time reward according to the following formula:

[0188] r k = log(1 + |ES k+1 - ES k |) sign(ES k+1 - ES k );

[0189] Calculate the cumulative discounted reward according to the following formula:

[0190]

[0191] Both ψ and ψ′ are combinations of transmission waveform parameters in the transmission waveform library and ψ and ψ′ are different. Q k (ψ) and Q k (ψ′) are the cumulative discounted rewards corresponding to ψ and ψ′ at time k respectively. Q k+1 (ψ) is the cumulative discounted reward corresponding to ψ at time k + 1. α is the learning rate and γ is the discount factor with γ ∈ [0, 1];

[0192] The transmission waveform parameters in the waveform library that maximize the cumulative discounted reward are expressed as:

[0193]

[0194] Ψ is the transmission waveform library.

[0195] b) Select the optimal transmission waveform parameters using the least mean square error criterion; calculate the optimal transmission waveform parameters of the least mean square error criterion according to the following formula:

[0196]

[0197] c) Select the optimal transmission waveform parameters using the maximum mutual information criterion; calculate the optimal transmission waveform parameters of the maximum mutual information criterion according to the following formula:

[0198]

[0199] d) Select the optimal transmission waveform parameters using the minimum waveform criterion. Calculate the optimal transmission waveform parameters of the minimum waveform criterion according to the following formula:

[0200]

[0201] Recursively loop according to the above steps to complete the waveform design for the continuous tracking task.

[0202] Further verify the technical effect of the present invention through experiments.

[0203] The system state is the three-dimensional position and velocity of the target, i.e.: The initial state of the target is Subject to the discrete-time system dynamic model, the measurement values include radial distance, radial velocity, azimuth angle, and elevation angle. The true trajectory of the target in the X-Y-Z three-dimensional space is as Figure 3 shown.

[0204] Select waveform parameters pulse width and sweep frequency to establish the waveform library as follows:

[0205]

[0206] Use the Multiple Hypothesis Marginalized Particle Filter algorithm (MH-MPF) for target tracking and the Interactive Multiple Criteria Selection method for waveform selection. The obtained simulation tracking results are as Figure 3 shown, the waveform parameter selection process is as Figure 4 shown, the root mean square error of state estimation is as Figure 5 shown, and the average root mean square error ARMSE of different target states is shown in Table 1.

[0207] Based on the Multiple Hypothesis Marginalized Particle Filter algorithm, different methods are used for waveform design. The obtained tracking results, waveform parameter selection process, and RMSE comparison are respectively as Figure 6 , 7 , shown in Figure 8, and the ARMSE is shown in Table 2.

[0208] Table 1 Average Root Mean Square Error (ARMSE) of Tracking IMCS Method Waveform Selection by MH-MPF Algorithm

[0209] ARMSE x position (m) y position (m) z position (m) x velocity (m / s) y velocity (m / s) z velocity (m / s) MH-MPF 2.0119 1.5316 1.0454 0.2104 0.2260 0.3018

[0210] Table 2 Comparison of ARMSE of Different Waveform Selection Methods

[0211]

[0212]

[0213] The present invention combines multiple hypothesis tracking with marginalized particle filtering algorithm and applies it to the tracking of maneuvering targets by a sea surface unmanned boat-borne radar in a clutter background. The interactive multi-criterion selection method is used to adaptively select the radar transmission waveform parameters. Compared with the existing waveform design methods of filtering algorithms, the present invention can better adapt to the tracking scenario, cope with sea clutter interference, effectively combine the filtering tracking algorithm with the radar transmission waveform design, better cope with the maneuverability changes of sea surface targets, more flexibly select the transmission waveform to optimize the tracking performance, and enhance the robustness and accuracy of tracking. By applying the multi-hypothesis marginalized particle filtering algorithm and the radar waveform design method of the present invention, the unmanned boat-borne radar can adaptively, stably and accurately track maneuvering targets in a complex sea environment.

[0214] Another embodiment of the present invention proposes a waveform design system for a sea surface maneuvering target tracking by an unmanned boat-borne radar. The system includes:

[0215] A predicted measurement value calculation module configured to predict the target state using the marginalized particle filtering algorithm and obtain the predicted measurement value based on the target state; the target state includes a non-linear state and a linear state;

[0216] A target state estimation module configured to generate a hypothesis tree according to the observation data; perform target state estimation on each hypothesis branch of the hypothesis tree using the marginalized particle filtering algorithm; calculate the association probability and update the hypothesis weight using the multiple hypothesis tracking algorithm, perform hypothesis pruning and fusion, and obtain the final target state estimation;

[0217] An optimal transmission waveform determination module configured to use multiple waveform selection criteria as a model and determine the best criterion and the optimal transmission waveform parameters with the highest effective probability using the interactive multi-criterion selection method.

[0218] The functions of the waveform design system for a sea surface maneuvering target tracking by an unmanned boat-borne radar in an embodiment of the present invention can be illustrated by the aforementioned waveform design method for a sea surface maneuvering target tracking by an unmanned boat-borne radar. Therefore, for the parts not described in detail in the system embodiment, reference can be made to the above method embodiment, which will not be elaborated here.

[0219] Although the present invention is described according to a limited number of embodiments, those skilled in the art in this technical field will understand that other embodiments can be conceived within the scope of the present invention thus described. For the scope of the present invention, the disclosure of the present invention is illustrative rather than restrictive, and the scope of the present invention is defined by the appended claims.

Claims

1. A waveform design method for a unmanned boat-borne radar to track moving targets on the sea surface, characterized in that, Including: Predict the target state using the marginalized particle filter algorithm and obtain the predicted measurement value based on the target state; The target state includes a non-linear state and a linear state; Generate a hypothesis tree according to the observed data; Use the marginalized particle filter algorithm to estimate the target state on each hypothesis branch of the hypothesis tree; including: Assume that the importance distribution only depends on the target state and the measurement value from the previous moment, then the normalized importance weight is calculated by the following formula: wherein is the importance weight of the i-th particle at the k-th moment, is the normalization result of; is the predicted measurement value of the i-th particle at the k-th moment the residual of, and there is represents the m-th hypothetical measurement value at the k-th moment; R k is the measurement error covariance matrix at the k-th moment; N is the total number of particles in the marginalized particle filter algorithm; Use the normalized importance weight to obtain the estimated vector of the non-linear state of the hypothesis by particle filter resampling through the following formula: wherein, is the non-linear state estimation vector of the i-th particle of the m-th hypothesis at the k-th moment; is the non-linear predicted state vector of the j-th particle at the k-th moment; Obtain the estimated vector of the linear state of the hypothesis by Kalman filter through the following formula: In the formula, is the linear state estimation vector of the m-th hypothesis at time k, is the linear state prediction vector of the target at time k, is the linear state prediction error covariance matrix of the target at time k, is the linear state estimation error covariance of the m-th hypothesis at time k, H k is the Jacobian matrix, s k,m is the residual and has h(·) represents the non-linear function, is the predicted state vector at time k and has is the non-linear state prediction vector of the target, is the linear state prediction vector of the target at time k; K k is the Kalman gain; Combine the linear estimated state vector and the non-linear estimated state vector through the following formula to obtain the total hypothesis state estimated vector: wherein, is the total state estimation vector of the m-th hypothesis at time k, is the non-linear estimated state vector of the m-th hypothesis at time k, and there is Use the multiple hypothesis tracking algorithm to calculate the association probability and update the hypothesis weight, perform hypothesis pruning and fusion to obtain the final target state estimate; including: Calculate the association probability between each hypothesis and the predicted value of the target state through the following formula: where, R k is the measurement error covariance matrix at time k; Update the weight of each hypothesis through the Bayesian formula according to the association probability and the prior probability; where q k,m is the weight of the m-th hypothesis at time k, β m is the association probability between the m-th hypothesis and the predicted value of the target state, q k-1 is the prior probability at time k and also the posterior probability at time k-1; Perform hypothesis pruning according to the weight, directly sort and retain the I hypotheses with the highest weight; Normalize the weights of the retained I hypotheses through the following formula: Perform hypothesis fusion through the following formula to obtain the final target state estimated vector and the estimated error covariance; Wherein, is the target state estimation vector at time k, is the state estimation error covariance at time k, q k,i is the weight of the i-th hypothesis at time k, is the normalization result of q k,i and I is the number of hypotheses remaining after hypothesis pruning; Use multiple waveform selection criteria as a model and use the interactive multi-criteria selection method to determine the best criterion with the highest effective probability and the optimal transmission waveform parameters.

2. A waveform design method for tracking moving targets on the sea surface by an unmanned boat-borne radar according to claim 1, characterized in that, The predicting the target state using the marginalized particle filter algorithm and obtaining the predicted measurement value based on the target state includes: According to the state estimation vector obtained at time k-1 Estimation error covariance matrix and the triangular model of the target, the new particle prediction value is obtained through particle filtering: Wherein, is the non - linear predicted state vector of the i - th particle at time k, is the target non - linear state prediction vector, is the non - linear state estimation vector of the i - th particle at time k - 1, is the linear state estimation vector of the target at time k - 1, is the non - linear state estimation vector of the target from time 0 to k - 1 for the i - th particle, z 1:k-1 are the target state measurement values from time 1 to k - 1, A n is the non - linear transformation matrix, denotes the transpose matrix of A n Q n is the non - linear part of the covariance matrix of the Gaussian process noise, and f(·) represents the transfer function of the target non - linear state; represents the prior probability density function; n and l respectively represent the non - linear state and the linear state of the target; Calculate the target non-linear state prediction vector according to the following formula: In the formula, N is the total number of particles in the marginalized particle filter algorithm; Calculate the linear state prediction vector of the target at time k according to the following formula: In the formula, is the linear state prediction vector of the target at time k, is the linear state prediction error covariance matrix of the target at time k, A l is the linear transfer matrix, is the residual, and there is Q l is the linear part of the covariance matrix of the Gaussian process noise; Calculate the predicted measurement value of the target according to the following formula: wherein, is the predicted measurement value at time k, h(·) represents a non-linear function, is the predicted state vector at time k and there is 3. A waveform design method for tracking moving targets on the sea surface by an unmanned boat-borne radar according to claim 2, characterized in that The generating the hypothesis tree according to the observed data includes: Random variables falling within the effective region of the predicted measurement value are regarded as clutter. The effective region refers to an area around the predicted measurement value with a threshold of g, and the size of this area is S k the residual covariance; the clutter has a Poisson distribution in quantity and, together with false alarms and true measurement values from the target, constitutes all the observed data obtained from the radar received echo: z b,k = [z k , c1, c2,..., c M-1 ​ where z b,k is the observation vector matrix, and z k is the true measurement value from the target at time k, c M-1 is the false alarm caused by the (M - 1)-th sea clutter, and M represents the number of observation vectors; Generate hypothesis branches based on the current measurement data, and each observation vector in the observation vector matrix is used as a possible target hypothesis: In the formula, represents the m-th hypothesized measurement value at time k.

4. A waveform design method for tracking moving targets on the sea surface by an unmanned boat-borne radar according to claim 3, characterized in that The using multiple waveform selection criteria as a model and using the interactive multi-criteria selection method to determine the best criterion with the highest effective probability and the optimal transmission waveform parameters includes: Assume there are L criteria, and calculate the predicted probability of each criterion according to the transition probability and the prior probability as: where p ji is the transition probability from criterion j to criterion i, is the effective probability of criterion j at time k, is the predicted probability of criterion i; Traverse the pre-established waveform library, predict the target state at the (k + 1)th moment, and predict the target state at the (k + 1)th moment through the Kalman filtering algorithm to obtain S k+1 ; Select the optimal transmission waveform parameters according to different criteria; among them, the waveform library is established as follows: the pulse length λ and the frequency sweep Δ k in the radar measurement error covariance R F are used as adaptively selectable transmission waveform parameters, and their ranges are determined according to actual requirements, thereby constructing the transmission waveform library Ψ; Select the optimal transmission waveform parameters according to different criteria; calculate the likelihood probability of each criterion through the following formula: wherein, is the likelihood probability of the i-th criterion, is the residual covariance at the (k + 1)-th moment, and there is is the residual between the actual measurement value and the predicted measurement value at the (k + 1)-th moment, and there is where is the predicted measurement value of the criterion i at the (k + 1)-th moment; Update the weight of each criterion through the following formula: wherein, is the effective probability of criterion i at the (k + 1)-th moment and also the weight of criterion i; Select the criterion with the highest effective probability as the best selection criterion, and use its parameter selection result as the optimal parameter and apply it to the transmission waveform of the next moment.

5. A waveform design method for an unmanned boat-borne radar to track moving targets on the sea surface according to claim 4, characterized in that, The different criteria include: the maximum Q value criterion, the minimum mean square error criterion, the maximum mutual information criterion, and the minimum waveform criterion.

6. A waveform design method for an unmanned boat-borne radar to track moving targets on the sea surface according to claim 5, characterized in that Using the maximum Q value criterion to select the optimal transmission waveform parameters includes: Calculate the entropy state according to the following formula: where ES k+1 and ES k are the entropy states at the (k + 1)-th and k-th moments respectively; Calculate the real-time reward according to the following formula: r k = log(1 + |ES k+1 -ES k |) sign(ES k+1 -ES k ); Calculate the cumulative discounted reward according to the following formula: where ψ and ψ′ are both combinations of transmission waveform parameters in the transmission waveform library, Q k (ψ) and Q k (ψ′) are the cumulative discounted rewards corresponding to ψ and ψ′ at time k, respectively, and Q k+1 (ψ) is the cumulative discounted reward corresponding to ψ at time k + 1, α is the learning rate, γ is the discount factor and γ ∈ [0, 1]; The transmission waveform parameters in the waveform library that maximize the cumulative discounted reward Expressed as: In the formula, Ψ is the transmission waveform library.

7. A waveform design method for an unmanned boat-borne radar to track moving targets on the sea surface according to claim 6, characterized in that, Using the minimum mean square error criterion to select the optimal transmission waveform parameters includes: calculating the optimal transmission waveform parameters according to the following formula: Selecting the optimal transmission waveform parameters using the maximum mutual information criterion includes: calculating the optimal transmission waveform parameters according to the following formula: Selecting the optimal transmission waveform parameters using the minimum gate criterion includes: calculating the optimal transmission waveform parameters according to the following formula:

8. A waveform design system for an unmanned boat-borne radar to track moving targets on the sea surface, characterized in that, Including: A predicted measurement value calculation module configured to predict the target state using the marginalized particle filter algorithm and obtain the predicted measurement value based on the target state; The target state includes a non-linear state and a linear state; A target state estimation module configured to generate a hypothesis tree according to the observed data; Using the marginalized particle filter algorithm to perform target state estimation on each hypothesis branch of the hypothesis tree, including: If the assumed importance distribution depends only on the target state and the measurement value from the previous moment, the normalized importance weight is calculated by the following formula: wherein, is the importance weight of the i-th particle at the k-th moment, is the normalization result of; is the predicted measurement value of the i-th particle at the k-th moment the residual of, and there is indicating the m-th assumed measurement value at the k-th moment; R k is the measurement error covariance matrix at the k-th moment; N is the total number of particles in the marginalized particle filter algorithm; Using the normalized importance weight to obtain the estimated vector of the non-linear state of the hypothesis by particle filter resampling according to the following formula: wherein, is the non-linear state estimation vector of the i-th particle of the m-th hypothesis at the k-th moment; is the non-linear predicted state vector of the j-th particle at the k-th moment; Obtaining the estimated vector of the linear state of the hypothesis by Kalman filtering according to the following formula: wherein, is the linear state estimation vector of the m-th hypothesis at time k, is the linear state prediction vector of the target at time k, is the linear state prediction error covariance matrix of the target at time k, is the linear state estimation error covariance of the m-th hypothesis at time k, H k is the Jacobian matrix, s k,m is the residual and there is h(·) represents a non-linear function, is the predicted state vector at time k and there is is the non-linear state prediction vector of the target, is the linear state prediction vector of the target at time k; K k is the Kalman gain; Combining the linear estimated state vector and the non-linear estimated state vector according to the following formula to obtain the total hypothesis state estimated vector: wherein, is the total state estimation vector of the m-th hypothesis at time k, is the non-linear estimated state vector of the m-th hypothesis at time k, and there is Using the multiple hypothesis tracking algorithm to calculate the association probability and update the hypothesis weight, perform hypothesis pruning and fusion to obtain the final target state estimation, including: Calculating the association probability between each hypothesis and the predicted value of the target state according to the following formula: where R k is the measurement error covariance matrix at time k; Updating the weight of each hypothesis through the Bayesian formula according to the association probability and the prior probability; where q k,m is the weight of the m-th hypothesis at time k, β m is the association probability between the m-th hypothesis and the predicted target state, and q k-1 is the prior probability at time k and also the posterior probability at time k-1; Performing hypothesis pruning according to the weight, directly sorting and retaining the top I hypotheses with the highest weight; Normalizing the weights of the retained I hypotheses according to the following formula: Performing hypothesis fusion according to the following formula to obtain the final target state estimated vector and the estimated error covariance: wherein, is the target state estimation vector at time k, is the state estimation error covariance at time k, q k,i is the weight of the i-th hypothesis at time k, is the normalization result of q k,i and I is the number of hypotheses retained after hypothesis pruning; An optimal transmission waveform determination module configured to use multiple waveform selection criteria as a model and use the interactive multi-criteria selection method to determine the best criterion with the highest effective probability and the optimal transmission waveform parameters.

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