A waveform optimization method for joint tracking and anti-jamming

Abstract

A waveform optimization method for joint tracking and anti-jamming, in the prior art, the state transition of the target is assumed to be fixed, the radar can directly observe the target state, without modeling the radar measurement process and state uncertainty, which oversimplifies the target tracking process. At the same time, only the spectrum occupation is optimized to improve the SINR and bandwidth, without considering more waveform parameters and the final tracking performance index. Therefore, it cannot reduce the radio frequency interference while improving the tracking performance, the application based on the proposed multi-step cost function for joint tracking and anti-jamming can optimize the frequency band occupation and waveform parameters at the same time, thereby improving the anti-jamming and target tracking performance; the proposed hybrid random-deterministic waveform optimization method has online learning ability, which can learn the behavior of radio frequency interference and the characteristics of target state transition by training from interactive experience samples.

Description

Technical Field

[0001] This invention relates to the field of radar waveform optimization technology, specifically a waveform optimization method for joint tracking and anti-jamming. Background Technology

[0002] Cognitive tracking radar (CTR) based on a fully adaptive architecture can achieve better tracking performance by dynamically optimizing waveforms. However, due to spectrum auctions and reallocation, current radar systems have to operate in congested spectrum environments. Because they coexist on the same frequency with other in-band radio frequency users (such as communication systems), the waveform agility tracking performance of CTR is affected by increasingly severe radio frequency interference (RFI).

[0003] Researchers have begun investigating how to improve tracking performance by optimizing the CTR waveform while mitigating RF interference from other in-band RF users. Ersin Selvi and R. Michael Buehrer first used Markov Decision Processes (MDPs) to describe the interaction between the CTR and the communication system. This team further extended this work, considering more types of communication interference and introducing a Sensing and Avoidance (SAA) approach for comparison. Mark Kozy introduced Deep Q-Networks (DQNs) to further reduce computational complexity. Charles E. Thornton introduced Dual Deep Recursive Q-Networks (DDRQNs) to further improve the average signal-to-interference-plus-noise ratio (SINR) and bandwidth, and conducted experimental analysis on Software-Defined Radar (SDRadar). While these MDP-based methods further improve target tracking performance in congested environments, they oversimplify the target tracking process by assuming fixed target state transitions and allowing direct observation of the target state without modeling the radar measurement process and state uncertainties. Furthermore, optimizing only the spectrum occupancy to improve SINR and bandwidth without considering other waveform parameters (such as pulse width) and the final tracking performance metrics (such as state estimation error) fails to improve tracking performance while reducing RF interference.

[0004] The following researchers have begun to consider how to improve upon the aforementioned limitations. Charles E. Thornton introduced a contextual gambling machine method to optimize the pulse width and modulation slope of the linear frequency modulated (LFM) signal to improve the root mean square error (RMSE) of target state estimation. R. Michael Buehrer further improved the RMSE of target tracking using a tree-to-tree weighted (CTW) method. Kristine Bell's proposed method can mitigate radio frequency interference and further improve the range estimation performance of the extended Kalman filter. The Bayesian meta-learning method proposed by Anthony F. Martone and Charles E. Thornton can further improve the sampling efficiency and online learning capability of waveform optimization.

[0005] It is evident that the aforementioned related work has begun to consider the uncertainties of target state transitions and noise measurements, and has optimized more waveform parameters to improve state estimation performance. However, the tracking waveform optimization problem under such spectrum congestion can essentially be viewed as a waveform optimization problem oriented towards joint tracking and anti-interference. To improve tracking performance while reducing radio frequency interference, it is necessary to jointly optimize the spectrum occupancy (i.e., frequency band selection) and waveform parameters of the cognitive tracking radar based on real-time sensing information. This requires not only considering state uncertainties but also the coupling correlation between tracking and anti-interference, including reusable information, interrelated task performance, and especially how to balance the relative importance of the two task performances. Researching this waveform optimization method oriented towards joint tracking and anti-interference is of great significance. Summary of the Invention

[0006] The purpose of this invention is to address the problem in existing technologies that oversimplify the target tracking process by assuming fixed target state transitions and allowing radar to directly observe the target state without modeling the radar measurement process and state uncertainties. Furthermore, these methods only optimize spectrum occupancy to improve SINR and bandwidth, neglecting other waveform parameters (such as pulse width) and final tracking performance metrics (such as state estimation error). This results in a failure to improve tracking performance while reducing radio frequency interference. Therefore, this invention proposes a waveform optimization method for joint tracking and interference resistance.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] A waveform optimization method for joint tracking and anti-interference includes the following steps:

[0009] First, acquire radar echo data and define the confidence state for each radar. and the operation of each radar frequency band Then initialize the action value. and frequency band occupation strategy The radar confidence state includes target state and radio frequency interference state, for time steps. Perform the following steps in sequence: :

[0010] Step 1: Constructing Radar Confidence State ,Right now ,in, An estimate representing the state of radio frequency interference. This represents an estimate of the one-step predicted value of the target state. This represents the covariance of the predicted state error of the target. Indicates the identifier for a normal distribution;

[0011] Step 2: Based on radar confidence state Radar frequency band occupation strategy Generating radar band occupancy actions Radar frequency band occupation strategy Represented as:

[0012]

[0013] in, Indicates the confidence state with radar The number of related spectrum occupancy actions, This represents the rate of greed that gradually decreases over time. Indicates the value of an action;

[0014] Step 3: Radar band occupancy-based actions Generate spectral cost function and the spectral cost function Real-time spectral constraints for waveform parameter optimization;

[0015] Step 4: Based on radar confidence state Select waveform optimization criteria to generate conditional prediction Bayesian risk for target tracking. The waveform optimization criteria include the minimum mean square error criterion, the minimum verification gate volume criterion, and the maximum mutual information criterion.

[0016] Step 5: Based on the radar waveform type and waveform parameters, construct a radar waveform library, where the waveform types include linear frequency modulation (LFM) signals, power frequency modulation (PFM) signals, hyperbolic frequency modulation (HFM) signals, and exponential frequency modulation (EPM) signals, and the waveform parameters include the frequency modulation slope and pulse width;

[0017] Step 6: Randomly select radar waveform types based on the radar waveform library. And design radar waveform types Corresponding waveform cost function ;

[0018] Step 7: Based on the spectral cost function Conditional prediction of Bayesian risk and waveform cost function Construct the execution processor cost function And based on the processor cost function Waveform selection strategy ;

[0019] Step 8: Based on the real-time spectrum constraints derived from the waveform parameter optimization in Step 3, the processor cost function will then be executed. Weighting function in The optimal waveform parameters are obtained by setting the summation function, solving the equivalent constrained optimization problem, and then searching through a rectangular grid. :

[0020] in, The operator represents the trace of the corresponding matrix. Represents a determinant. and These are the measurement covariance matrix and the posterior estimation error covariance matrix, respectively. This represents the waveform parameters to be optimized. Including pulse width Frequency modulation rate and waveform type MMSE stands for Minimum Mean Square Error Criterion, MVGV stands for Minimum Validation Gate Volume Criterion, and MMI stands for Maximum Mutual Information Criterion. and These represent waveform types respectively. Corresponding pulse width The minimum and maximum values, and These represent waveform types respectively. Corresponding frequency modulation slope The minimum and maximum values, and These represent the pulse widths respectively. and frequency modulation slope The incremental step, This indicates the bandwidth of a sub-band. express The corresponding bandwidth Indicates frequency band occupancy action The corresponding bandwidth;

[0021] Step 9: Based on the optimal waveform parameters and frequency band occupancy actions The corresponding radar echo signal is obtained, and matched filtering and back-end radar data processing are performed based on the corresponding radar echo signal to update the radar confidence state. Updated confidence status Represented as ,in, Indicates based on target measurement value Target state estimation;

[0022] Step 10: Based on radar confidence state Updated radar confidence status and frequency band occupancy actions Generate reward function ;

[0023] Step 11: Based on the reward function Frequency band occupancy action Radar confidence status and radar confidence status Update action To obtain the updated action value For other confidence state action pairs that are not accessed, the corresponding Q-values ​​remain unchanged, i.e.

[0024]

[0025] in, Indicates the learning rate. Indicates timing difference error. Represented as:

[0026]

[0027] in, Indicates the discount factor. Indicates when in radar confidence state At that time, based on frequency band occupancy strategy Take spectrum occupancy action The corresponding action value is expressed as:

[0028]

[0029] in, Indicates a state of confidence. Execute spectrum occupancy action at time Reaching radar confidence state Expected returns Representing the future The expected value related to the future confidence state in the step, where Indicates the use of frequency band occupancy strategies for evaluation The cumulative multi-step reward function;

[0030] Step 12: Based on the updated action value To obtain the radar frequency band occupation strategy ;

[0031] Step 13: Repeat the above steps iteratively until convergence is achieved, thus obtaining the optimal spectrum occupancy strategy. and optimal waveform selection strategy .

[0032] Furthermore, the spectral cost function Represented as:

[0033]

[0034] in, This represents the bandwidth of a sub-band, and the frequency band occupancy action. The corresponding bandwidth is expressed as , This represents the waveform parameters to be optimized. Including pulse width Frequency modulation rate and waveform type ,Right now , corresponding bandwidth Represented as:

[0035] .

[0036] Furthermore, the conditional prediction Bayesian risk Represented as:

[0037]

[0038] in, The operator represents the trace of the corresponding matrix. Represents a determinant. and These are the measurement covariance matrix and the posterior estimation error covariance matrix, respectively. and They are represented as follows:

[0039]

[0040] in, This represents the covariance of the predicted state error of the target. Represents the target measurement matrix. Describe the measurement error covariance. This represents the target motion error covariance. This represents the target state transition matrix.

[0041] Furthermore, the waveform cost function Represented as:

[0042] .

[0043] Furthermore, the waveform selection strategy Represented as:

[0044]

[0045]

[0046] Furthermore, the target measurement value Target state estimation Represented as:

[0047]

[0048] in, The one-step prediction value representing the target state. This indicates the Kalman filter gain.

[0049] Furthermore, the reward function Represented as:

[0050]

[0051]

[0052] in, This represents the reward corresponding to the echo signal-to-interference-plus-noise ratio. The signal-to-interference-plus-noise ratio (SIR) of the echo signal. The reward represents the number of sub-bands occupied by the cognitive tracking radar. This represents the reward for the cognitive tracking radar occupying the highest sub-frequency band.

[0053] Furthermore, the strategy used to evaluate frequency band occupancy... Cumulative multi-step reward function Represented as:

[0054] .

[0055] Furthermore, the radar frequency band occupancy strategy Represented as:

[0056]

[0057] in, Indicates confidence state The size of the action space occupied by the relevant spectrum.

[0058] Furthermore, the optimal spectrum occupancy strategy and optimal waveform selection strategy Represented as:

[0059]

[0060] in, Indicates a state of confidence. Below the strategy Optimal frequency band occupancy action, Represented as:

[0061]

[0062] in, Indicates spectrum occupancy strategy The optimal state value under the given conditions.

[0063] The beneficial effects of this invention are:

[0064] Based on the proposed multi-step cost function for joint tracking and anti-interference, this application proposes a waveform optimization method for joint tracking and anti-interference that can simultaneously optimize frequency band occupancy and waveform parameters, thereby improving anti-interference (i.e., interference avoidance) and target tracking performance. The hybrid stochastic-deterministic waveform optimization method proposed in this application has online learning capabilities and can learn the behavior of radio frequency interference and target state transition characteristics by training from interactive experience samples. Attached Figure Description

[0065] Figure 1 This is a diagram of a cognitive tracking radar framework based on a dual-controller architecture.

[0066] Figure 2 This is the overall flowchart of this application. Detailed Implementation

[0067] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0068] Specific implementation method one: Refer to Figure 1 This embodiment specifically describes a waveform optimization method for joint tracking and anti-interference, comprising:

[0069] Step 1: Construct a radar waveform library based on specific radar waveform types and parameters; and define the confidence state for each radar waveform. and radar frequency band occupancy actions Initialize Q value and frequency band occupation strategy For time steps Perform the following steps in sequence:

[0070] Step 2: Obtain the received and processed radar echo data, and construct the radar confidence state. The radar confidence state includes the target state and the radio frequency interference state. Based on the radar confidence state... Radar frequency band occupation strategy and combined Method to generate radar band occupancy actions .

[0071] Step 3: Radar band occupancy-based actions Generate frequency spectrum cost function This serves as a real-time spectral constraint for subsequent waveform parameter optimization. Based on radar confidence state. By selecting specific waveform optimization criteria (i.e., minimum mean square error criterion (MMSE), minimum validation gate volume criterion (MVGV), and maximum mutual information criterion (MMI)), a conditional prediction Bayesian risk for target tracking is generated. Design specific radar waveform types based on a specific waveform library structure. Corresponding waveform cost function .

[0072] Step 4: Based on Spectrum Constraints Conditional prediction of Bayesian risk and waveform cost function Construct the execution processor cost function Waveform selection strategy To minimize the processor cost function, optimal waveform parameters are obtained by performing a rectangular grid search on a specific waveform library.

[0073] Step 5: Radar Receiver Processing and Waveform Parameters and frequency band occupancy actions The corresponding echo signal updates the radar confidence state. This includes spectral measurement Estimate radio frequency interference status and based on target measurement value Estimate target state Based on the old radar confidence state Updated radar confidence status and frequency band occupancy actions Generate a reward function related to radar jamming avoidance and bandwidth utilization. .

[0074] Step Six: Based on the above-mentioned rewards Frequency band occupancy action and radar confidence status Update radar confidence status - action pair The corresponding Q-value. Based on the updated action value. ,according to Method to update radar frequency band occupancy strategy .

[0075] This invention formulates the tracking waveform optimization problem under spectrum congestion as a joint tracking and anti-interference waveform optimization problem (WO-JTAI). Based on a multi-step objective function oriented towards joint tracking and anti-interference, a hybrid stochastic-deterministic waveform optimization method (HSODO) for WO-JTAI is proposed to simultaneously optimize spectrum occupancy and waveform parameters to improve tracking performance and mitigate radio frequency interference. Specifically, firstly, based on a partially observable Markov decision process (POMDP) ​​model for WO-JTAI, a multi-step objective function for JTAI is proposed. By incorporating a criterion based on tracking accuracy and a tradeoff between bandwidth utilization and interference avoidance, a coupling relationship is established between spectrum occupancy, waveform parameters, and the potential long-term performance of joint tracking and anti-interference. Secondly, to develop an efficient solution method for the proposed objective function, the WO-JTAIHSODO method based on a novel CTR framework with a dual-controller structure is proposed by decoupling the objective function and solving it sequentially. This two-step decoupling method, based on imperfect state information caused by uncertain state transitions and noise measurements, iteratively performs spectral occupancy optimization based on time-difference Q-learning and waveform parameter optimization based on deterministic optimization (DO) until convergence to the optimal strategy. The technical problems to be solved include:

[0076] (1) In a spectrum congestion environment, to jointly optimize frequency band occupancy and waveform parameters to improve joint tracking and anti-interference performance, it is necessary to establish a cost function for tracking waveform optimization under spectrum congestion to reveal the coupling relationship between spectrum occupancy, waveform parameters, and joint tracking and anti-interference performance. At the same time, it is also necessary to evaluate the impact of current frequency band occupancy and waveform parameter selection on future expected rewards. This cost function, which can reflect the waveform agility mechanism, is the foundation and prerequisite for tracking waveform optimization. Currently, research in this area is still in its early stages.

[0077] (2) Based on the above waveform optimization mechanism, the joint optimization of frequency band occupancy and waveform parameters faces a nonlinear, multivariate, and high-dimensional optimization problem. It is necessary to design an efficient solution method to reduce computational complexity while maintaining long-term performance and meet the real-time requirements of adaptive waveform optimization for cognitive tracking radar. At present, research in this area is still insufficient.

[0078] Example:

[0079] According to the appendix Figure 1and attached Figure 2 The implementation process of this invention is described in detail, and the method includes the following steps:

[0080] Step 1: Construct a radar waveform library based on specific radar waveform types and parameters. Waveform types include Linear Frequency Modulation (LFM), Power Frequency Modulation (PFM), Hyperbolic Frequency Modulation (HFM), and Exponential Frequency Modulation (EFM); waveform parameters include modulation slope and pulse width.

[0081] Step 2: For each radar confidence state and the operation of each radar frequency band Initialize Q value and frequency band occupation strategy .

[0082] Step 3: Construct the radar confidence state based on the received and processed radar echo data. The radar confidence state includes the target state and the radio frequency interference state, i.e. .

[0083] Step 4: Based on radar confidence state Radar frequency band occupation strategy Generating radar band occupancy actions The radar frequency band occupancy action can be represented as

[0084]

[0085] in Is it related to confidence state? The number of related spectrum occupancy actions, It is a greed rate that gradually decreases over time. This radar frequency band occupancy strategy. use The method suggests that any frequency band occupancy action has a probability of being selected, but the greedy action with the highest Q value has the highest probability. The aim is to retain a certain degree of exploratory nature while also considering the development and utilization of the current optimal frequency band occupancy action. This indicates the frequency band occupancy strategy, which tells the cognitive tracking radar how to operate in the radar confidence state. Lower optimization frequency band occupancy ;

[0086] Step 5: Radar band occupancy-based actions Generate frequency spectrum cost function This serves as a real-time spectral constraint for subsequent waveform parameter optimization. The spectral cost function... It can be represented as

[0087]

[0088] in This represents the bandwidth of a sub-band, and the frequency band occupancy action. The corresponding bandwidth can be expressed as Waveform parameters to be optimized Including pulse width Frequency modulation rate and waveform type ,Right now Specific waveform parameters corresponding bandwidth It can be represented as

[0089]

[0090] Step Six: Based on Radar Confidence State By selecting specific waveform optimization criteria (i.e., minimum mean square error criterion (MMSE), minimum validation gate volume criterion (MVGV), and maximum mutual information criterion (MMI)), a conditional prediction Bayesian risk for target tracking is generated. Conditional prediction of Bayesian risk Characterized based on previous measurement sequences The predictive tracking performance is equivalent to the expectation of a specific probability distribution. Since target state transitions and target measurement models are typically complex and nonlinear, there is no exact solution for predicting conditional Bayesian risk. In the linear additive white Gaussian noise (AWGN) model, the conditional predictive Bayesian risk under different waveform optimization criteria... It can be represented as

[0091]

[0092] Among them, the conditional prediction Bayesian risk based on MMSE optimizes the mean square error and is widely used in waveform agility tracking applications. The operator represents the trace of the corresponding matrix; secondly, the conditional prediction Bayesian risk based on MVGV can be written as a measurement covariance matrix. The determinant is designed to reduce false alarms and clutter in the verification gate by controlling its volume. The determinant is represented; finally, the MMI-based sub-reward optimizes the mutual information between target measurement and target state prediction. Minimize the intersection of the prediction error ellipse and the measurement error ellipse. and Let be the measurement covariance matrix and the posterior estimation error covariance matrix, respectively, which can be expressed as:

[0093]

[0094] in This represents the covariance of the predicted state error of the target. Represents the target measurement matrix. Describe the measurement error covariance. This represents the target motion error covariance. This represents the target state transition matrix.

[0095] Step 7: Design specific radar waveform types based on a specific waveform library structure. Corresponding waveform cost function , can be represented as

[0096]

[0097] in and These represent waveform types respectively. Corresponding pulse width The minimum and maximum values; and These represent waveform types respectively. Corresponding frequency modulation slope The minimum and maximum values; and These represent the pulse widths respectively. and frequency modulation slope The incremental step.

[0098] Step 8: Based on Spectrum Constraints Conditional prediction of Bayesian risk and waveform cost function Construct the execution processor cost function Waveform selection strategy , can be represented as

[0099]

[0100] in This indicates the waveform selection strategy, which tells the cognitive tracking radar how to operate in the radar confidence state. and frequency band occupancy actions Optimize waveform parameters . The processor cost function for execution can be expressed as:

[0101]

[0102] in It is a weighting function in the field of multi-objective optimization, and its specific form depends on the characteristics of the cost function and the application scenario.

[0103] Step Nine: Obtain the optimal waveform parameters by solving the equivalent constrained optimization problem: Apply the formula... Weighting function in If we set it as a summation function, then we can optimize the waveform parameters by solving the following equivalent constrained optimization problem, denoted as:

[0104]

[0105] The optimal waveform parameters are found by performing a rectangular grid search on a specific waveform library because this method has low computational cost and works well in practice.

[0106] Step 10: Radar Receiver Processing and Waveform Parameters and frequency band occupancy actions The corresponding echo signal updates the radar confidence state. The confidence state can be represented as This includes spectral measurements. Estimate radio frequency interference status and based on target measurement value Estimate target state , can be represented as

[0107]

[0108] in The one-step prediction value representing the target state. This indicates the Kalman filter gain.

[0109] Step 11: Based on the old confidence state Updated confidence status and frequency band occupancy actions Generate reward function , can be represented as

[0110]

[0111] in

[0112]

[0113] in This is a sub-reward for frequency band occupancy, and it is in a confidence state. Frequency band occupation action is taken below The reward received later This is the reward corresponding to the echo signal-to-interference-plus-noise ratio (SINR). The signal-to-interference-plus-noise ratio (SIR) of the echo signal plays a crucial role in range-Doppler processing. It is a reward for the number of sub-bands occupied by the cognitive tracking radar. This is a reward for the cognitive tracking radar occupying the highest sub-band. The larger the bandwidth, the higher the ranging resolution.

[0114] Step Twelve: Based on the above-mentioned rewards Frequency band occupancy action Compared to the old radar confidence state and new radar confidence status Update radar confidence status - action pair The corresponding Q value remains unchanged for other unvisited confidence state action pairs.

[0115]

[0116] in It's the learning rate. It is the timing difference error, defined as

[0117]

[0118] change

[0119] in Indicates the discount factor. Indicates when in radar confidence state At that time, based on strategy Take spectrum occupancy action The corresponding action value is denoted as

[0120]

[0121] Among them, formula The first item is that it is in a radar confidence state. Execute spectrum occupancy action at time Arrival radar confidence state Expected returns, the second item is related to the future. The expected value related to the future confidence state in the step. Among them It is used to evaluate frequency band occupancy strategies. The cumulative multi-step reward function is expressed as:

[0122]

[0123] Step Thirteen: Based on the updated action value ,according to Method to update radar frequency band occupancy strategy , It can be represented as

[0124]

[0125] in Is it related to confidence state? The size of the relevant spectrum occupying action space, since the spectrum occupies a relatively small amount of action space. It can simultaneously handle state uncertainty and anticipated future returns for joint tracking and interference resistance. It is a greed rate that gradually decreases over time.

[0126] In summary, as Figure 2 As shown, the HSODO method proposed in this application iteratively performs frequency band occupancy optimization based on time-difference Q-learning and waveform parameter optimization based on deterministic optimization until it converges to the optimal spectrum occupancy strategy. and optimal waveform selection strategy Optimal spectrum occupancy strategy and optimal waveform selection strategy It can be represented as

[0127]

[0128] in In a state of confidence Below the strategy The optimal frequency band occupancy action can be expressed as

[0129]

[0130] in Based on spectrum occupancy strategy The proposed HSODO method is essentially a decoupled two-step iterative method, which may produce local optima in some time steps.

[0131] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A waveform optimization method for joint tracking and anti-interference, characterized in that... Includes the following steps: First, acquire radar echo data and define the confidence state b for each radar and the frequency band occupancy action β for each radar. Then, initialize the action value q(b,β) and the frequency band occupancy strategy π. β (β|b), the radar confidence state includes the target state and the radio frequency interference state, and the following steps are executed sequentially for time step k, k = 1,...,N: Step 1: Construct radar confidence state b k-1 ,Right now in, An estimate representing the state of radio frequency interference. P represents the estimate of the one-step prediction of the target state. k|k-1 This represents the covariance of the predicted state error of the target. Indicates the identifier for a normal distribution; Step 2: Based on radar confidence state b k-1 Radar frequency band occupation strategy Generating radar band occupancy action β k Radar frequency band occupation strategy Represented as: in, Indicates the radar confidence state b k-1 The relevant spectrum occupancy number of actions, ∈ (0,1) represents the greed rate that gradually decreases over time, q k Indicates the value of an action; Step 3: Radar band occupancy action β k Generate the spectral cost function C B (θ k |β k ), and the spectral cost function C B (θ k |β k () as a real-time spectral constraint for waveform parameter optimization; Step 4: Based on radar confidence state b k-1 Select waveform optimization criteria to generate conditional prediction Bayesian risk for target tracking. The waveform optimization criteria include the minimum mean square error criterion, the minimum verification gate volume criterion, and the maximum mutual information criterion. Step 5: Based on the radar waveform type and waveform parameters, construct a radar waveform library, where the waveform types include linear frequency modulation (LFM) signals, power frequency modulation (PFM) signals, hyperbolic frequency modulation (HFM) signals, and exponential frequency modulation (EPM) signals, and the waveform parameters include the frequency modulation slope and pulse width; Step Six: Based on the radar waveform library, randomly select radar waveform type w type And design radar waveform type w type The corresponding waveform cost function R Θ (λ,k r |w type ); Step 7: Based on the spectral cost function C B (θ k |β k Conditional prediction of Bayesian risk and waveform cost function R Θ (λ,k r |w type Construct the execution processor cost function L. C,Θ,B (θ k |z 1:k-1 ;θ 1:k-1 ), and according to the execution processor cost function L C,Θ,B (θ k |z 1:k-1 ;θ 1:k-1 Waveform selection strategy π θ (θ k |b k-1 ,β k ); Step 8: Based on the real-time spectrum constraints derived from the waveform parameter optimization in Step 3, the processor cost function L will then be executed. C,Θ,B (θ k |z 1:k-1 ;θ 1:k-1 Weighting function in ) The optimal waveform parameters are obtained by setting the summation function, solving the equivalent constrained optimization problem, and then searching through a rectangular grid. Where Tr[·] operator represents the trace of the corresponding matrix, det[·] represents the determinant, and S k (θ k ) and P k|k (θ k θ represents the measurement covariance matrix and the posterior estimation error covariance matrix, respectively. k θ represents the waveform parameters to be optimized. k Including pulse width λ, frequency modulation rate k r and waveform type w type MMSE stands for Minimum Mean Square Error Criterion, MVGV stands for Minimum Validation Gate Volume Criterion, and MMI stands for Maximum Mutual Information Criterion. and These represent waveform types w respectively. type The corresponding minimum and maximum values ​​of the pulse width λ. and These represent waveform types w respectively. type The corresponding frequency modulation slope k r The minimum and maximum values, and Let λ represent the pulse width and k represent the frequency modulation slope, respectively. r The step increment, ΔB, represents the bandwidth of a sub-band, B θ (θ k ) represents θ k The corresponding bandwidth, B β (β k ) indicates frequency band occupancy action β k The corresponding bandwidth; Step 9: Based on the optimal waveform parameters and frequency band occupancy action β k The corresponding radar echo signal is obtained, and matched filtering and back-end radar data processing are performed based on the corresponding radar echo signal to update the radar confidence state b. k The updated confidence state b k Represented as in, Indicates based on the target measurement value z k Target state estimation; Step 10: Based on radar confidence state b k-1 Updated radar confidence status b k and frequency band occupancy action β k Generate reward function Step 11: Based on the reward function Frequency band occupancy action β k Radar confidence state b k-1 and radar confidence state b k Update action (b) k-1 ,β k ), to obtain the updated action value q k+1 (b k-1 For other unvisited confidence state-action pairs, the corresponding Q-value remains unchanged, i.e. Where, α k (b k-1 ,β k )∈(0,1) represents the learning rate, δ k δ represents the timing difference error. k Represented as: Where γ∈(0,1) represents the discount factor, q k (b k-1 ,β k ) indicates that when in radar confidence state b k-1 At that time, based on frequency band occupancy strategy Take spectrum occupancy action β k The corresponding action value is expressed as: in, Indicates a state of confidence (b) k-1 Execute spectrum occupancy action β at time k Reaching radar confidence state b k Expected returns This represents the expected value associated with the future confidence state in the next L1 step, where Indicates the use of frequency band occupancy strategies for evaluation The cumulative multi-step reward function; Step 12: Based on the updated action value q k+1 (b k-1 ,β), to obtain the radar frequency band occupancy strategy Step 13: Repeat the above steps iteratively until convergence is achieved, thus obtaining the optimal spectrum occupancy strategy. and optimal waveform selection strategy 2. The waveform optimization method for joint tracking and anti-interference as described in claim 1, characterized in that... The spectral cost function C B (θ k |β k ) is represented as: Where ΔB represents the bandwidth of a sub-band, and the band occupancy action β k The corresponding bandwidth is expressed as θ k θ represents the waveform parameters to be optimized. k Including pulse width λ, frequency modulation rate k r and waveform type w type ,Right now θ k corresponding bandwidth Represented as:

3. The waveform optimization method for joint tracking and anti-interference as described in claim 2, characterized in that... The conditional prediction Bayesian risk Represented as: Where Tr[·] operator represents the trace of the corresponding matrix, det[·] represents the determinant, and S k (θ k ) and P k|k (θ k S represents the measurement covariance matrix and the posterior estimation error covariance matrix, respectively. k (θ k ) and P k|k (θ k They are represented as follows: Among them, P k|k-1 H represents the covariance of the predicted state error of the target. k Represents the target measurement matrix, R(θ) k Q represents the measurement error covariance. k-1 F represents the target motion error covariance. k-1 This represents the target state transition matrix.

4. The waveform optimization method for joint tracking and anti-interference as described in claim 3, characterized in that... The waveform cost function R Θ (λ,k r |w type ) is represented as:

5. A waveform optimization method for joint tracking and anti-interference as described in claim 4, characterized in that... The waveform selection strategy π θ (θ k |b k-1 ,β k ) is represented as: Where, π θ (θ k |b k-1 ,β k () indicates the waveform selection strategy. This represents the weighting function for the multi-objective optimization domain.

6. A waveform optimization method for joint tracking and anti-interference as described in claim 5, characterized in that... The target measurement value z k Target state estimation Represented as: Where, x k|k-1 K represents the one-step prediction of the target state. k (θ k ) represents the Kalman filter gain.

7. A waveform optimization method for joint tracking and anti-interference as described in claim 6, characterized in that... The reward function Represented as: Among them, R SINR (·) indicates the reward corresponding to the echo signal-to-interference-plus-noise ratio. R represents the signal-to-interference-plus-noise ratio (SIR) of the echo signal. B (β k R represents the reward for the number of subbands occupied by the cognitive tracking radar. H (β k This indicates the reward for the cognitive tracking radar occupying the highest sub-frequency band.

8. A waveform optimization method for joint tracking and anti-interference according to claim 7, characterized in that... The strategy for evaluating frequency band occupancy Cumulative multi-step reward function Represented as:

9. A waveform optimization method for joint tracking and anti-interference as described in claim 8, characterized in that... The radar frequency band occupancy strategy Represented as: in, Indicates confidence state b k-1 The size of the action space occupied by the relevant spectrum.

10. A waveform optimization method for joint tracking and anti-interference according to claim 9, characterized in that... The optimal spectrum occupancy strategy and optimal waveform selection strategy Represented as: Wherein, β*(b k-1 ) indicates confidence state b k-1 Below the strategy Optimal frequency band occupancy action, Represented as: in, Indicates spectrum occupancy strategy The optimal state value under the given conditions.

Images