Waveform design method and system for tracking sea surface maneuvering target by unmanned ship-mounted radar

Abstract

The invention discloses a waveform design method and system for tracking a sea surface maneuvering target by an unmanned ship-mounted radar, relates to the technical field of radar communication, and aims to solve the technical problem of inaccurate maneuvering target tracking in a sea surface clutter environment. The method is technically characterized by comprising the following steps: predicting a target state by using a marginalized particle filter algorithm, and obtaining a predicted measurement value; generating a hypothesis tree according to the observation data; performing target state estimation on each assumed branch by using a marginalized particle filter algorithm; a multi-hypothesis tracking algorithm is used to calculate an association probability and update a hypothesis weight, hypothesis pruning and fusion are carried out, and final target state estimation is obtained; a plurality of waveform selection criteria are used as a model, and an interactive multi-criterion selection method is utilized to determine an optimal criterion with the highest effective probability and an optimal transmitted waveform parameter. According to the method, false alarms caused by sea clutters can be effectively handled, the performance of the unmanned ship-mounted radar for processing complex tracking scenes can be improved, and a more accurate and robust target tracking result can be obtained.

Description

Technical Field

[0001] The present invention relates to the field of radar communication technology, and in particular to a waveform design method and system for tracking a sea surface mobile target by an unmanned boat-borne radar. Background Art

[0002] In recent years, unmanned boats have been increasingly used in tracking and monitoring sea targets due to their flexibility, mobility and strong autonomy. Equipped with radar equipment, unmanned boats can effectively detect and track various mobile targets on the sea, such as ships, small boats, even unmanned surface platforms, low-flying drones, etc. These technologies have broad application prospects in the fields of maritime search and rescue, border patrols, and marine resource protection.

[0003] In traditional target tracking systems, radars usually estimate the target position and velocity through a single tracking filter. With the complexity of target motion behavior, especially in the task of tracking targets with high maneuverability, a single filter is often difficult to cope with complex target state changes. Considering the target tracking mechanism and waveform selection in clutter scenes, more and more studies have combined multiple algorithms to construct hybrid filters. The probabilistic data association (PDA) algorithm effectively handles false alarms by calculating the association probability between the measured 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 deal with complex clutter backgrounds, and can be integrated with filtering methods such as unscented Kalman filter (UKF), square root volumetric Kalman filter (SCKF), particle filter (PF) to handle nonlinear 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 and Wang Xin; "Acta Astronomica Sinica", etc.

[0004] In target tracking, the selection of radar transmission waveform is crucial to tracking accuracy. Traditional waveform selection methods are usually based on fixed criteria, which are difficult to optimize when facing rapidly changing target states (such as: Cognitive radar target tracking waveform selection method based on reinforcement learning, Zhu Peikun, Liang Jing, Luo Zihan, etc.; Journal of Radar, 2023; Cognitive radar maneuvering target tracking algorithm based on information entropy criterion, Wang Shuliang, Bi Daping, Ruan Huailin, etc.; Journal of Electronics, 2019). Therefore, a more effective selection method or a simple and convenient switching method is needed. In order to adapt to the changes in target states, the interactive multi-model (IMM) framework can be applied to waveform selection under multiple models. According to the state of the target, it can flexibly and adaptively adjust between multiple waveform selection criteria, thereby optimizing the detection capability and tracking accuracy of the radar system.

[0005] At present, the existing unmanned boat radar tracking technology still has problems such as insufficient tracking accuracy and inflexible waveform selection when facing complex maneuvering targets on the sea surface. How to effectively combine the filter tracking algorithm with the radar transmission waveform design to better cope with the maneuverability changes of sea surface targets and optimize the tracking performance by adaptively selecting the transmission 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 unmanned boat-borne radar tracking of sea surface maneuvering targets, aiming to provide a target tracking solution with high precision, high robustness and adaptive waveform selection capability in a complex sea environment.

[0007] According to one aspect of the present invention, a waveform design method for tracking a sea surface maneuvering target by an unmanned boat-borne radar is proposed, the method comprising:

[0008] A target state is predicted using a marginalized particle filter algorithm, and a predicted measurement value is obtained based on the target state; the target state includes a nonlinear state and a linear state;

[0009] Generate hypothesis trees based on observed data;

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

[0011] The multi-hypothesis tracking algorithm is used to calculate the association probability and update the hypothesis weights, perform hypothesis pruning and fusion, and obtain the final target state estimation;

[0012] Using multiple waveform selection criteria as a model, an interactive multi-criteria selection method is used to determine the best criterion with the highest effective probability and the optimal transmission waveform parameters.

[0013] Further, the predicting the target state by 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 Estimated error covariance matrix And the triangular model model of the target, obtain the new particle prediction value through particle filtering:

[0015]

[0016] In the formula, is the nonlinear prediction state vector of the ith particle at time k, is the target nonlinear state prediction vector, is the nonlinear state estimation vector of the ith particle at time k-1, is the linear state estimation vector of the target at time k-1, is the nonlinear state estimation vector of the target from the i-th particle 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, Indicates A n The transposed matrix, Q n is the nonlinear part of the covariance matrix of the Gaussian process noise, f(·) represents the transfer function of the nonlinear state of the target; n and l represent the nonlinear state and linear state of the target, respectively;

[0017] The target nonlinear state prediction vector is calculated according to the following formula:

[0018]

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

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

[0021]

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

[0023] The predicted measurement value of the target is calculated according to the following formula:

[0024]

[0025] In the formula, is the predicted measurement value at time k, h(·) represents a nonlinear function, is the predicted state vector at time k and

[0026] Further, generating a hypothesis tree according to the observed data includes:

[0027] The random variables falling within the effective region of the predicted measurement value are regarded as noise. The effective region refers to an area around the predicted measurement value with a threshold of g. The size of this area is S k is the residual covariance; the clutter is Poisson distributed in quantity and constitutes all the observation data obtained in the radar receiving echo as a false alarm together with the real measurement value from the target:

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

[0029] In the formula, 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-1th sea clutter, where M represents the number of observation vectors;

[0030] 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:

[0031]

[0032] In the formula, represents the mth hypothesized measurement value at time k.

[0033] Furthermore, the use of the marginalized particle filter algorithm to perform target state estimation on each hypothesis branch of the hypothesis tree includes:

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

[0035]

[0036] In the formula, is the importance weight of the i-th particle at time k, for The normalized result is is the predicted measurement value of the i-th particle at time k The residual of R k is the measurement error covariance matrix at time k;

[0037] The normalized importance weights are used to obtain the assumed nonlinear state estimation vector by resampling the particle filter using the following formula:

[0038]

[0039] In the formula, is the nonlinear state estimation vector of the m-th hypothesis ith particle at time k;

[0040] The assumed linear state estimation vector is obtained using Kalman filtering by the following formula:

[0041]

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

[0043] The linear estimated state vector and the nonlinear estimated state vector are combined by the following formula to obtain the total assumed state estimated vector:

[0044]

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

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

[0047] The probability of association between each hypothesis and the predicted value of the target state is calculated by the following formula:

[0048]

[0049] According to the associated probability and prior probability, the weight of each hypothesis is updated by the Bayesian formula:

[0050]

[0051] In the formula, qk,m is the weight of the m-th hypothesis at time k, β m is the association probability between the mth hypothesis and the target state prediction value, 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 weights, directly sorting and retaining the I hypotheses with the highest weights;

[0053] The retained I hypothesis weights are normalized by the following formula:

[0054]

[0055] The following formula is used to perform hypothesis fusion 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 ith hypothesis at time k, for q k,i is the normalized result of , and I is the number of hypotheses retained after hypothesis pruning.

[0058] Further, using multiple waveform selection criteria as a model, determining the best criteria with the highest effective probability and the optimal transmission waveform parameters using an interactive multi-criteria selection method includes:

[0059] Assuming there are L criteria, the predicted probability of each criterion is calculated based on the transition probability and prior probability:

[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 predicted probability of criterion i;

[0062] Traverse the pre-established waveform library, predict the target state at time k+1, and use the Kalman filter algorithm to predict the target state at time k+1 to obtain S k+1 ; Select the optimal transmission waveform parameters according to different criteria; wherein the waveform library is established as follows: the radar measurement error covariance R k The pulse length λ and the frequency sweep Δ in FAs a transmit waveform parameter that can be adaptively selected, and its range is determined according to actual needs, so as to construct a transmit waveform library Ψ;

[0063] The optimal transmission waveform parameters are selected according to different criteria; the likelihood probability of each criterion is calculated by 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 is the residual between the actual measured value and the predicted measured value at time k+1, and in is the predicted measurement value of criterion i at time k+1;

[0066] Update the weight of each criterion by:

[0067]

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

[0069] The criterion with the highest effective probability is selected as the best selection criterion, and its parameter selection result is applied as the optimal parameter to the transmission waveform at the next moment.

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

[0071] Further, selecting the optimal transmission waveform parameters using the maximum Q value criterion includes:

[0072] The entropy state is calculated 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] The real-time reward is calculated according to the following formula:

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

[0077] The cumulative discount reward is calculated according to the following formula:

[0078]

[0079] Where, ψ and ψ′ are the transmission waveform parameter combinations 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, 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];

[0080] The emission waveform parameters in the waveform library that maximize the cumulative discount reward It is expressed as:

[0081]

[0082] Where Ψ is the transmission waveform library.

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

[0084]

[0085] Further, selecting the optimal transmission waveform parameter by using the maximum mutual information criterion includes: calculating the optimal transmission waveform parameter according to the following formula:

[0086]

[0087] Further, selecting the optimal transmission waveform parameter by using the minimum wave gate criterion includes: calculating the optimal transmission waveform parameter according to the following formula:

[0088]

[0089] According to another aspect of the present invention, a waveform design system for tracking sea surface mobile targets by an unmanned boat-borne radar is provided, the system comprising:

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

[0091] A target state estimation module is configured to generate a hypothesis tree based on the observed data; perform target state estimation on each hypothesis branch of the hypothesis tree using a marginalized particle filter algorithm; calculate the association probability and update the hypothesis weight using a multi-hypothesis tracking algorithm, perform hypothesis pruning and fusion, and 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 an interactive multi-criteria selection method to determine the best criterion with the highest validity probability and the optimal transmission waveform parameters.

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

[0094] The present invention can effectively track maneuvering targets in composite linear and nonlinear states on the sea surface under high sea conditions, deal with false alarms caused by sea clutter, effectively combine the filter tracking algorithm with the radar transmission waveform design, better deal 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, and has the following advantages:

[0095] (1) For the target tracking problem in the sea clutter background, the present invention adopts a multi-hypothesis marginalized particle filter algorithm, uses the measurement values ​​analyzed in the received echo to form a hypothesis tree, and through hypothesis pruning and fusion, effectively solves the problem of sea clutter interference and enhances the anti-interference ability of target tracking. The marginalized particle filter is used to more accurately track highly maneuverable targets with variable states, providing a high-precision and high-robustness target tracking solution for unmanned boat-borne radars in complex sea environments.

[0096] (2) For waveform parameter optimization, the present invention adopts an interactive multi-criteria selection method to simply and flexibly switch parameter selection strategies, further improving the adaptive adjustment capability of the radar system. Compared with the use of fixed waveforms or single criterion optimization methods, it has lower tracking errors and higher tracking accuracy, solving the problems of insufficient tracking accuracy and inflexible waveform selection in existing unmanned boat-borne radar tracking technology when facing complex maneuvering targets on the sea surface. 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, which 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 A block diagram of a waveform design method for tracking a sea surface mobile target by an unmanned boat-borne radar according to the present invention;

[0099] Figure 2 Select schematic diagrams for criteria in the tracking process;

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

[0101] Figure 4 A schematic diagram for selecting waveform parameters during tracking;

[0102] Figure 5 Root mean square error plot of the estimated state vector for the maneuvering target;

[0103] Figure 6 Figure 2 is a graph of tracking results using different waveform selection methods;

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

[0105] Figure 8 A comparison chart of the root mean square error of the target estimation state vector using different waveform selection methods. DETAILED DESCRIPTION

[0106] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0107] The present invention proposes a waveform design method for unmanned boat-borne radar tracking of sea surface maneuvering targets, namely, an unmanned boat-borne radar target tracking method that utilizes a multi-hypothesis marginalized particle filtering algorithm and an interactive multi-criteria selection method to select transmission waveform parameters, aiming to provide a target tracking solution with high precision, high robustness and adaptive waveform selection capability in a complex sea environment.

[0108] The embodiment of the present invention proposes a waveform design method for tracking a sea surface mobile target by an unmanned boat-borne radar, such as Figure 1 As shown, including:

[0109] S1. Predicting a target state using a marginalized particle filter algorithm, and obtaining a predicted measurement value based on the target state; the target state includes a nonlinear state and a linear state;

[0110] S2, generate a hypothesis tree based on the observed data;

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

[0112] S4, using the multi-hypothesis tracking algorithm to calculate the association probability and update the hypothesis weight, perform hypothesis pruning and fusion, and obtain the final target state estimation;

[0113] S5. Use multiple waveform selection criteria as a model and utilize an interactive multi-criteria selection method to determine the best criterion with the highest validity probability and the optimal transmission waveform parameters.

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

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

[0116]

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

[0118] w k The mean at time k is zero and the covariance matrix is ​​Q k Gaussian process noise, and: and are the nonlinear and linear Gaussian process noise at time k,

[0119] u k The mean at time k is zero and the measurement error covariance is R k The measurement noise is:

[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 Δ F is frequency sweep, T s is the effective pulse duration, η k is the signal-to-noise ratio at time k and:

[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, t and r are the positions of the radar receiver and transmitter respectively.

[0124] First, according to the state estimation vector obtained at time k-1 Estimated error covariance matrix The mixed state model of the target (i.e. the triangular model composed of linear state and nonlinear state) is used to obtain the new particle prediction value through particle filtering:

[0125]

[0126] is the nonlinear prediction state vector of the ith particle at time k, is the target nonlinear state prediction vector, is the nonlinear state estimation vector of the ith particle at time k-1, is the linear state estimation vector of the target at time k-1, is the nonlinear state estimation vector of the target from the i-th particle 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, Indicates A n The transposed matrix, Q n is the nonlinear part of the covariance matrix of the Gaussian process noise, represents the prior probability density function, f(·) represents the transfer function of the target nonlinear state;

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

[0128]

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

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

[0131]

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

[0133] The predicted measurement value of the target is calculated according to the following formula:

[0134]

[0135] is the predicted measurement value at time k, h(·) represents a nonlinear function, is the predicted state vector at time k and

[0136] Then S2 is executed, in which a hypothesis tree is generated based on the observed data.

[0137] According to an embodiment of the present invention, random variables falling within the effective region of the predicted measurement value are regarded as noise. The effective region refers to an area around the predicted measurement value with a threshold value of g. The size of the area is S k is the residual covariance; the clutter is Poisson distributed in quantity and constitutes all the observation data obtained in the radar receiving echo as a false alarm together with the real measurement value from the target:

[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, c M-1 is the false alarm caused by the M-1th sea clutter, where M represents the number of observation vectors;

[0140] 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:

[0141]

[0142] represents the mth hypothesized measurement value at time k.

[0143] Then S3 is executed, in which the marginalized particle filter algorithm is used to estimate the target state on each hypothesis branch of the hypothesis tree.

[0144] According to an embodiment of the present invention, using a 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 measurement from the previous moment, the normalized importance weight can be calculated by the following formula:

[0146]

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

[0148] The assumed nonlinear state estimation vector is obtained by resampling the particle filter:

[0149]

[0150] is the nonlinear state estimation vector of the m-th hypothesis ith particle at time k; represents the normalized importance weight.

[0151] The assumed linear state estimation vector is obtained using Kalman filtering by the following formula:

[0152]

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

[0154] The linear estimated state vector and the nonlinear estimated state vector are combined by the following formula to obtain the total assumed state estimated vector:

[0155]

[0156] is the total state estimation vector of the m-th hypothesis at time k, is the nonlinear estimated state vector of the mth hypothesis at time k, and

[0157] Then S4 is executed. In S4, the multi-hypothesis tracking algorithm is used to calculate the association probability and update the hypothesis weight, 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 target state prediction value is calculated by the following formula:

[0159]

[0160] Then, the weight of each hypothesis is updated according to the associated probability and the prior probability through 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 mth hypothesis and the target state prediction value, q k-1 is the prior probability at time k, and also the posterior probability at time k-1;

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

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

[0165]

[0166] Then, the hypothesis fusion is performed through the following formula to obtain the final target state estimation vector and 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 ith hypothesis at time k, for q k,i is the normalized result of , and I is the number of hypotheses retained after hypothesis pruning.

[0169] Then, S5 is executed. In S5, a plurality of waveform selection criteria are used as a model, and an interactive multi-criteria selection method is used to determine the best criterion with the highest validity probability and the optimal transmission waveform parameters.

[0170] According to an embodiment of the present invention, assuming that there are L criteria, first, the prediction probability of each criterion is calculated based on the transition probability and the prior probability:

[0171]

[0172] 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.

[0173] Then, the waveform library is traversed to select the optimal transmission waveform parameters according to different criteria; wherein the waveform library is pre-established as follows: the radar measurement error covariance R k The pulse length λ and the frequency sweep Δ in F As the transmit waveform parameter that can be adaptively selected, its range is determined according to actual needs, so as to construct the transmit waveform library Ψ.

[0174] Then, the likelihood probability of each criterion is calculated by the following formula:

[0175]

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

[0177] Then, the weight of each criterion is updated by:

[0178]

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

[0180] Then, the criterion with the highest effective probability is selected as the best selection criterion, and its parameter selection result is applied as the optimal parameter to the transmission waveform at the next moment.

[0181] In this embodiment, preferably, Figure 2 As shown, the waveform library is traversed and the optimal transmission waveform parameters are selected according to different criteria, including:

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

[0183] a) Selecting the optimal transmission waveform parameters using the maximum Q value criterion; including:

[0184] The entropy state is calculated according to the following formula:

[0185]

[0186] ES k+1 and ESk are the entropy states at time k+1 and time k respectively;

[0187] The real-time reward is calculated according to the following formula:

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

[0189] The cumulative discount reward is calculated according to the following formula:

[0190]

[0191] ψ and ψ′ are both transmit waveform parameter combinations in the transmit waveform library and ψ and ψ′ are different. k (ψ) and Q k (ψ′) are the cumulative discounted rewards corresponding to ψ and ψ′ at time k, 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];

[0192] The emission waveform parameters in the waveform library that maximize the cumulative discount reward It is expressed as:

[0193]

[0194] Ψ is the transmission waveform library.

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

[0196]

[0197] c) Selecting the optimal transmission waveform parameters using the maximum mutual information criterion; Calculating 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 wave gate criterion according to the following formula:

[0200]

[0201] Follow the above steps recursively to complete the waveform design of the continuous tracking task.

[0202] The technical effect of the present invention is further verified through experiments.

[0203] The system state is the three-dimensional position and velocity of the target, that is: The target initial state is It obeys the discrete time system dynamic model. The measured values ​​include radial distance, radial velocity, azimuth and elevation. The actual trajectory of the target in the XYZ three-dimensional space is as follows: Figure 3 shown.

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

[0205]

[0206] The multi-hypothesis marginalized particle filter algorithm (MH-MPF) is used for target tracking, and the interactive multi-criteria selection method is used for waveform selection. The simulation tracking results are as follows: Figure 3 As shown in Figure 2, the waveform parameter selection process is as follows: Figure 4 As shown in Figure 2, the root mean square error of the state estimation is Figure 5 The average root mean square error ARMSE of different target states is shown in Table 1.

[0207] Based on the multi-hypothesis marginalized particle filter algorithm, different methods are used for waveform design. The tracking results, waveform parameter selection process and RMSE comparison are shown in the figure below. Figure 6 , 7 ,8, and ARMSE are shown in Table 2.

[0208] Table 1 Average root mean square error (ARMSE) of waveform selection by MH-MPF algorithm tracking IMCS method

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

[0210] Table 2 Comparison of ARMSE with different waveform selection methods

[0211]

[0212]

[0213] The present invention combines multi-hypothesis tracking with marginalized particle filter algorithm and applies it to the tracking of maneuvering targets of sea surface unmanned boat-borne radar under clutter background, and adopts interactive multi-criteria selection method to adaptively select radar transmission waveform parameters. Compared with the existing filtering algorithm waveform design method, the present invention can better adapt to the tracking scene, cope with the interference of sea surface clutter, effectively combine the filtering tracking algorithm with the radar transmission waveform design, better cope with the maneuverability change of sea surface targets, more flexibly select the transmission waveform to optimize the tracking performance, and enhance the robustness and accuracy of tracking. The application of the multi-hypothesis marginalized particle filter algorithm and radar waveform design method of the present invention can enable the unmanned boat-borne radar to adaptively, stably and accurately track maneuvering targets in complex sea surface environments.

[0214] Another embodiment of the present invention provides a waveform design system for tracking sea surface mobile targets by an unmanned boat-borne radar, the system comprising:

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

[0216] A target state estimation module is configured to generate a hypothesis tree based on the observed data; perform target state estimation on each hypothesis branch of the hypothesis tree using a marginalized particle filter algorithm; calculate the association probability and update the hypothesis weight using a multi-hypothesis tracking algorithm, perform hypothesis pruning and fusion, and obtain the final target state estimation;

[0217] The optimal transmission waveform determination module is configured to use multiple waveform selection criteria as a model and utilize an interactive multi-criteria selection method to determine the best criterion with the highest validity probability and the optimal transmission waveform parameters.

[0218] The function of a waveform design system for tracking sea surface mobile targets by an unmanned boat-borne radar in an embodiment of the present invention can be described by the waveform design method for tracking sea surface mobile targets by an unmanned boat-borne radar as mentioned above. Therefore, for the parts not described in detail in the system embodiment, please refer to the above method embodiment and will not be repeated here.

[0219] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.

Claims

1. A waveform design method for tracking sea surface mobile targets by unmanned boat-borne radar, characterized in that: include: The target state is predicted using a marginalized particle filter algorithm, and a predicted measurement value is obtained based on the target state; The target state includes a nonlinear state and a linear state; Generate hypothesis trees based on observed data; The marginalized particle filter algorithm is used to estimate the target state on each hypothesis branch of the hypothesis tree; The multi-hypothesis tracking algorithm is used to calculate the association probability and update the hypothesis weights, perform hypothesis pruning and fusion, and obtain the final target state estimation; Using multiple waveform selection criteria as a model, an interactive multi-criteria selection method is used to determine the best criterion with the highest effective probability and the optimal transmission waveform parameters.

2. The waveform design method for tracking sea surface mobile targets by an unmanned boat-borne radar according to claim 1 is characterized in that: The method of predicting the target state by 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 Estimated error covariance matrix And the triangular model of the target, the new particle prediction value is obtained through particle filtering: In the formula, is the nonlinear prediction state vector of the ith particle at time k, is the target nonlinear state prediction vector, is the nonlinear state estimation vector of the ith particle at time k-1, is the linear state estimation vector of the target at time k-1, is the nonlinear state estimation vector of the target from the i-th particle 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, Indicates A n The transposed matrix, Q n is the nonlinear part of the covariance matrix of the Gaussian process noise, and f(·) represents the transfer function of the target nonlinear state; represents the prior probability density function; n and l represent the nonlinear state and linear state of the target respectively; The target nonlinear state prediction vector is calculated according to the following formula: Where N is the total number of particles in the marginalized particle filter algorithm; The linear state prediction vector of the target at time k is calculated according to the following formula: In the formula, is the linear state prediction vector of the target at time k, is the target linear state prediction error covariance matrix at time k, A l is the linear transfer matrix, is the residual, and Q l is the linear part of the covariance matrix of the Gaussian process noise; The predicted measurement value of the target is calculated according to the following formula: In the formula, is the predicted measurement value at time k, h(·) represents a nonlinear function, is the predicted state vector at time k and 3. The waveform design method for tracking sea surface mobile targets by an unmanned boat-borne radar according to claim 2 is characterized in that: Generating a hypothesis tree according to the observed data comprises: The random variables falling within the effective region of the predicted measurement value are regarded as noise. The effective region refers to an area around the predicted measurement value with a threshold of g. The size of this area is S k is the residual covariance; the clutter is Poisson distributed in quantity and constitutes all the observation data obtained in the radar receiving echo as a false alarm together with the real measurement value from the target: With b,k =[of k ,c1,c2,...,c M-1 ] In the formula, 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-1th sea surface clutter, where 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 mth hypothesized measurement value at time k.

4. The waveform design method for tracking sea surface mobile targets by an unmanned boat-borne radar according to claim 3 is characterized in that: The method of using the marginalized particle filter algorithm to estimate the target state on each hypothesis branch of the hypothesis tree includes: Assuming that the importance distribution depends only on the target state and the measurement from the previous moment, the normalized importance weight is calculated by the following formula: In the formula, is the importance weight of the i-th particle at time k, for The normalized result is is the predicted measurement value of the i-th particle at time k The residual of R k is the measurement error covariance matrix at time k; The normalized importance weights are used to obtain the assumed nonlinear state estimation vector by resampling the particle filter using the following formula: In the formula, is the nonlinear state estimation vector of the m-th hypothesis ith particle at time k; The assumed linear state estimation vector is obtained using Kalman filtering as follows: In the formula, is the linear state estimation vector of the mth hypothesis at time k, is the error covariance of the m-th assumed linear state estimation at time k, H k is the Jacobian matrix, s k,m is the residual and K k is the Kalman gain; The linear estimated state vector and the nonlinear estimated state vector are combined by the following formula to obtain the total assumed state estimation vector: In the formula, is the total state estimation vector of the m-th hypothesis at time k, is the nonlinear estimated state vector of the mth hypothesis at time k, and 5. The waveform design method for tracking sea surface mobile targets by unmanned boat-borne radar according to claim 4 is characterized in that: The method of using a multi-hypothesis tracking algorithm to calculate the association probability and update the hypothesis weight, perform hypothesis pruning and fusion, and obtain the final target state estimation includes: The probability of association between each hypothesis and the predicted value of the target state is calculated by the following formula: According to the associated probability and prior probability, the weight of each hypothesis is updated by the Bayesian formula: In the formula, q k,m is the weight of the m-th hypothesis at time k, β m is the association probability between the mth hypothesis and the target state prediction value, q k-1 is the prior probability at time k, and also the posterior probability at time k-1; Perform hypothesis pruning based on weights, directly sorting and retaining the I hypotheses with the highest weights; The retained I hypothesis weights are normalized by the following formula: The following formula is used to perform hypothesis fusion to obtain the final target state estimation vector and estimation error covariance: 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 ith hypothesis at time k, for q k,i is the normalized result of , and I is the number of hypotheses retained after hypothesis pruning.

6. The waveform design method for tracking sea surface mobile targets by unmanned boat-borne radar according to claim 5 is characterized in that: The method of using multiple waveform selection criteria as a model and utilizing an interactive multi-criteria selection method to determine the best criteria and the best transmission waveform parameters with the highest effective probability includes: Assuming there are L criteria, the predicted probability of each criterion is calculated based on the transition probability and prior probability: 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 predicted probability of criterion i; Traverse the pre-established waveform library, predict the target state at time k+1, and use the Kalman filter algorithm to predict the target state at time k+1 to obtain S k+1 ; Select the optimal transmission waveform parameters according to different criteria; wherein the waveform library is established as follows: the radar measurement error covariance R k The pulse length λ and the frequency sweep Δ in F As a transmit waveform parameter that can be adaptively selected, and its range is determined according to actual needs, so as to construct a transmit waveform library Ψ; The optimal transmission waveform parameters are selected according to different criteria; the likelihood probability of each criterion is calculated by the following formula: In the formula, is the likelihood probability of the i-th criterion, is the residual covariance at time k+1, and is the residual between the actual measured value and the predicted measured value at time k+1, and in is the predicted measurement value of criterion i at time k+1; Update the weight of each criterion by: In the formula, is the effective probability of criterion i at time k+1, which is also the weight of criterion i; The criterion with the highest effective probability is selected as the best selection criterion, and its parameter selection result is applied as the optimal parameter to the transmission waveform at the next moment.

7. The waveform design method for tracking sea surface mobile targets by unmanned boat-borne radar according to claim 6 is characterized in that: The different criteria include: maximum Q value criterion, minimum mean square error criterion, maximum mutual information criterion, and minimum waveform criterion.

8. The waveform design method for tracking sea surface mobile targets by unmanned boat-borne radar according to claim 7 is characterized in that: The optimal transmit waveform parameters selected using the maximum Q value criterion include: The entropy state is calculated according to the following formula: In the formula, ES k+1 and ES k are the entropy states at time k+1 and time k respectively; The real-time reward is calculated according to the following formula: r k =log(1+|ES k+1 -IS k |)sign(ES k+1 -IS k ); The cumulative discount reward is calculated according to the following formula: Where, ψ and ψ′ are the transmission waveform parameter combinations 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, 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 emission waveform parameters in the waveform library that maximize the cumulative discount reward It is expressed as: Where Ψ is the transmission waveform library.

9. The waveform design method for tracking sea surface mobile targets by unmanned boat-borne radar according to claim 8 is characterized in that: Selecting the optimal transmission waveform parameters using the minimum mean square error criterion 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 wave gate criterion includes: calculating the optimal transmission waveform parameters according to the following formula:

10. A waveform design system for tracking sea surface mobile targets by unmanned boat-borne radar, characterized in that: include: a predicted measurement value calculation module configured to predict a target state using a marginalized particle filter algorithm and obtain a predicted measurement value based on the target state; The target state includes a nonlinear state and a linear state; a target state estimation module configured to generate a hypothesis tree based on the observed data; The marginalized particle filter algorithm is used to estimate the target state on each hypothesis branch of the hypothesis tree; the multi-hypothesis tracking algorithm is used to calculate the association probability and update the hypothesis weight, perform hypothesis pruning and fusion, and obtain the final target state estimation; The optimal transmission waveform determination module is configured to use multiple waveform selection criteria as a model and utilize an interactive multi-criteria selection method to determine the best criterion with the highest validity probability and the optimal transmission waveform parameters.

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