An Online Evaluation Method for the Jamming Effect of Non-Cooperative Radar Based on Inverse Filtering Processing

Abstract

The present invention discloses a method for online evaluation of the non-cooperative radar jamming effect based on inverse filtering processing, which can invert the internal characteristics of the radar under two backgrounds of clutter-free and clutter-present, effectively reflect the radar tracking error, and thus realize non-cooperative online evaluation of the jamming effect of deception jamming such as range and velocity deception jamming, range and velocity dragging jamming, etc.; different inverse filtering algorithms are designed for the actual confrontation scenarios of clutter-free and clutter-present, including the inverse Kalman filtering algorithm and the inverse PDA filtering algorithm, and the estimation of the radar filtering result is obtained by inverse filtering of the opponent radar actions observed in real time in noise, so as to reflect the radar tracking error online; based on this, the designed jamming effect evaluation algorithm can online detect the qualitative results of successful / failed jamming and the specific moments of successful / failed jamming, with a relatively high accuracy; this method also makes an online adjustment of the jamming strategy based on the jamming effect evaluation results.

Description

Technical Field

[0001] The present invention relates to the field of radar electronic countermeasures, and in particular to an online evaluation method for the effect of non-cooperative radar towing jamming based on inverse filtering processing. Background Technique

[0002] With the gradual development of radar towards the intelligent direction, the anti-countermeasure ability of radar has been greatly improved, which brings huge challenges to traditional radar countermeasures, requiring the countermeasure side to construct a closed-loop cognitive countermeasure system including battlefield situation awareness, interference effect evaluation, and adaptive interference. Interference effect evaluation is the key link for the above-mentioned cognitive countermeasure system to achieve a closed loop. Only by accurately evaluating can the effect of interference implementation be timely and efficiently feedback, so as to optimize and adjust the interference strategy.

[0003] Interference effect evaluation refers to the process of qualitatively or quantitatively evaluating the damage or destruction suffered by a radar after interference is applied to the radar. Traditional interference effect evaluation methods are cooperative, requiring the radar side to provide certain experimental data, using the corresponding system functions or performances of the radar as evaluation indicators, and performing mathematical calculations on these indicators before and after being interfered according to certain evaluation criteria to achieve evaluation. Cooperative effectiveness evaluation criteria mainly include power criteria, information criteria, efficiency criteria, time criteria, etc. Specific evaluation calculation methods mainly include evaluation factor method, fuzzy comprehensive evaluation method, and intelligent evaluation method, etc. Different evaluation indicators and evaluation methods can be combined in specific applications. For example, a fuzzy neural network is introduced into the evaluation of the effect of deceptive interference, giving full play to the advantages of the evaluation factor method and the fuzzy comprehensive evaluation method while adopting the intelligent evaluation method, establishing a fuzzy comprehensive evaluation model, selecting the signal-to-jamming ratio, radar anti-interceptability, complexity of radar signal simulation, and time-domain resolution as the factor set, and using a radial basis function (RBF) neural network to determine the weights. The above-mentioned cooperative interference effect evaluation methods need to be cooperated by the interfered party to complete, and are mainly used in scenarios such as pre-war deduction evaluation to verify the feasibility of combat plans, etc., and are not applicable to real-time combat scenarios of non-cooperative real confrontation.

[0004] In non-cooperative confrontation scenarios, the jammer can only indirectly assess the jamming effect based on factors such as the radar's transmitted signal, beam switching, and platform maneuvers, as detected by its own reconnaissance. This assessment is based on changes in the radar signal received by the jammer's reconnaissance receiver before and after the jamming (such as carrier frequency, repetition rate, antenna scanning mode, signal polarization, and operating mode), combined with prior knowledge. These methods analyze the changes in the detected radar transmit signal to derive evaluation indicators at different levels, such as radar parameters, status, and mode, and then indirectly assess the jamming effect through comprehensive calculations. The evaluation indicator calculation process in these non-cooperative jamming effect methods relies heavily on expert experience and pre-war intelligence. Furthermore, the received radar transmit signal is the sole basis for evaluation, and the information content is very limited, failing to include actual information within the radar system. This presents significant limitations. Therefore, it is crucial to research non-cooperative online jamming effect evaluation methods that incorporate the impact of various signal processing steps within the radar system to support more authentic, highly reliable information.

[0005] Inverse signal processing studies a system's external behavior or performance to infer its internal details. In recent years, due to its advantages in inferring the internal characteristics of a system, inverse signal processing has attracted widespread attention from researchers in fields such as artificial intelligence, control theory, machine learning, and electronic countermeasures. In the field of control, Kalman studied the inverse optimal control problem as early as 1964, aiming to determine the optimal cost criterion for a given control strategy. Inverse processing is more widely studied in the field of machine learning, primarily referring to inverse reinforcement learning (IRL), which involves inferring the reward function of an intelligent agent based on a given strategy or observed behavior. Recently, scholars have also conducted related research on inverse processing in the field of electronic countermeasures. For example, they use inverse reinforcement learning methods to detect whether a radar has undergone waveform optimization and infer the utility function of the waveform optimization, and use inverse filtering to estimate the accuracy of an adversary's sensors.

[0006] The classic inverse filtering problem primarily discusses how to estimate the filter input or sensor accuracy using the state posteriors output by Bayesian filtering. Since 1979, experts and scholars have studied the inverse filtering problem of Kalman filtering under linear Gaussian state-space models. Clustering algorithms can be used to solve the inverse filtering problem under discrete hidden Markov models (HMMs). In CAA systems, the application of inverse filtering algorithms for Kalman filtering, HMM filtering, and particle filtering can estimate the sensor accuracy of an adversary system by observing its behavior, providing a reference for adaptively adjusting jamming measures in the adversarial system. Therefore, inverse filtering can be used to obtain a posteriori estimates of the radar filter state and the characteristics of the radar's actual tracking filter-related information. This allows for processing radar motion, exploring the tracking results that drive radar motion under jamming conditions, and ultimately evaluating jamming effectiveness. Summary of the Invention

[0007] The present invention proposes a non-cooperative online interference effect evaluation method based on inverse filtering processing, which can reversely analyze the true tracking error of a radar according to changes in elements such as the platform maneuver, waveform selection, or resource scheduling actions of an opponent's radar, thereby evaluating in real time the impact of interference on radar tracking and adjusting the interference strategy online.

[0008] A non-cooperative online interference effect evaluation method based on inverse filtering processing includes the following steps:

[0009] S1. Establish an inverse filtering model according to the presence or absence of clutter, that is, determine the state equation and measurement equation of the inverse filtering model, specifically:

[0010] Our radar generates a motion state x according to its own motion mode k , where k = 1, 2,... represents discretized time, and x k represents the motion state at time k; the opponent's radar obtains a noisy observation value y k of the true motion state x k of our radar, performs tracking filtering to obtain an estimated value [[ID= to our motion state and takes an adaptive action u k ; we observe the adaptive action u k of the opponent's radar in noise and obtain the radar action a k ;

[0011] Slll. When there is no clutter in the background, the radar uses the Kalman filtering algorithm to obtain the inverse filtering state equation and measurement equation at time k, which are the following two formulas respectively:

[0012]

[0013] When there is clutter in the background, the radar uses the PDA filtering algorithm to obtain the inverse filtering state equation and measurement equation, which are the following two formulas respectively:

[0014]

[0015] Among them, represents the estimated value of our motion state at time k-1, v k is the measurement noise of the opponent's radar at the current time k, which is Gaussian white noise with a mean of zero, and R k is the measurement noise covariance at the current time k; μ k is the measurement noise of our side at the current time k; K k is the filtering gain at the current time k, C is the radar filtering measurement matrix, A is the radar state matrix, is the radar action matrix at the current time k, that is, our inverse filtering measurement matrix; P D and PG They are the radar detection probability and the probability that the measurement in the radar PDA filtering falls into the associated gate, respectively.

[0016] S12. Initialize the filtering parameters of the opponent's radar and the inverse filtering parameters of our side, including: the initial covariance of radar filtering ∑0, the initial estimated value of radar filtering the state matrix A of radar filtering, the covariance Q of radar filtering state noise, the measurement matrix C of radar, the covariance R of radar measurement noise, the covariance of inverse filtering measurement noise

[0017] S13. Simulate the filtering parameters of the opponent's radar according to the initialization parameters, including:

[0018] The predicted covariance at time K: Σ k|k-1 = AΣ k-1 A T + Q;

[0019] The innovation covariance at time K: S k = CΣ k|k-1 C T + R;

[0020] The filtering gain at time K:

[0021] where Σ k-1 represents the radar filtering covariance at time k - 1. When k = 1, it is taken as the initial value ∑0;

[0022] When K > 1, if there is no clutter in the background, the filtering covariance of the opponent's radar: Σ k-1 = (I - K k-1 C)Σ k-1|k-2 ;

[0023] If there is clutter in the background, then use the modified Riccati to calculate the filtering covariance:

[0024]

[0025] In the above formula, ∑ k-1|k-2 , S k-1 , K k-1 , V k-1 are the predicted covariance, innovation covariance, filtering gain and associated gate area at time k - 1, respectively; λ is the clutter density, and a, b, c are coefficients obtained by looking up the table according to expert experience;

[0026] S14. Calculate the inverse filtering model parameters at the current moment according to the filtering parameters of the other party's radar, including:

[0027] The state matrix:

[0028] State equation control matrix:

[0029] State noise:

[0030] S15. Observe the opponent's radar action a in real time in the noise k , record the true state x of our radar k , and use the observation set and our state to obtain the estimated value of the radar tracking filter result, which is divided into the following two steps:

[0031] (1) One-step prediction of inverse filtering to predict the opponent's estimation of our radar state at time k:

[0032] One-step prediction of the optimal estimation of the opponent's radar at time k:

[0033] Predict the inverse filtering error covariance at time k:

[0034] Among them, represents our estimation of the opponent's estimation at time k - 1; represents the error covariance of our radar inverse filtering at time k - 1;

[0035] (2) Use the measurement a of the radar action in the noise k to correct the one-step prediction result in (1).

[0036] Innovation covariance:

[0037] Filter gain:

[0038] Use the observed value to correct the one-step prediction result to obtain our estimation of the opponent's estimation:

[0039]

[0040] Update the error covariance of our radar inverse filtering:

[0041] S2. Estimate the tracking error of the corresponding dimension of the radar in real time through inverse filtering, specifically:

[0042] According to the parameter information in our estimation of the opponent's radar at time k , assuming that the true value of a certain parameter at time k is r k , after the opponent's radar performs tracking filtering, the estimated value of this parameter is After our inverse filtering processing, the estimation of is Then the radar range tracking error can be estimated as

[0043] S3. Detect the mutation points of the tracking error by using the opponent's radar tracking error obtained in S2, including the detection of sudden increase points and sudden decrease points:

[0044] S4. Qualitatively evaluate the success or failure of the interference effect by using the detection results of the mutation points.

[0045] Preferably, in S3, the method for detecting sudden increase points is as follows:

[0046] Continuously memorize the slope of the estimated tracking error curve Calculate the average value of the error slope up to the current k moment

[0047] After entering the towing period, when the growth amount of the average value of the error slope before a certain moment compared to the average value of the error slope at the previous moment is greater than the set threshold γ e1 At this time, record this moment as a candidate sudden increase point; if the growth amount of the average value of the error slope within the set time after this moment is also greater than the set threshold γ e1 , then record this moment as a sudden increase point.

[0048] Preferably, in S3, the method for detecting sudden decrease points is as follows:

[0049] Continuously memorize the slope of the estimated tracking error curve Calculate the average value of the error slope up to the current k moment

[0050] After entering the towing period, when the decrease amount of the average value of the error slope before a certain moment compared to the average value of the error slope at the previous moment is greater than the set threshold γ e2 At this time, record this moment as a candidate sudden decrease point; if the decrease amount of the average value of the error slope within the set time after this moment is also greater than the set threshold γ e2 , then record this moment as a sudden decrease point.

[0051] Preferably, in S4, the method for qualitatively evaluating the success or failure of the interference effect by using the detection results of the mutation points is as follows:

[0052] Case 1). If two consecutive sudden increase points are detected before the end of the towing period, it is determined that the interference is successful, and the successful moment is the moment of the second sudden increase point;

[0053] Case 2). If a sudden decrease point is detected before the end of the towing, it is determined that the interference fails, and the failure moment is the moment of the sudden decrease point;

[0054] Case 3). If only one sudden increase point is detected during the entire towing period, it is also determined that the interference fails, and the failure moment is the end moment of the towing period;

[0055] Case 4): If no sudden increase point is detected until the middle of the towing period, it is determined that the interference fails, and the failure time is the middle time of the towing period.

[0056] Preferably, in S4, when it is Case 1), the interference ends at the success time until the next towing cycle arrives.

[0057] Preferably, in S4, when it is Case 2), the towing is immediately stopped at the failure time, and the towing speed is reduced in the next towing cycle.

[0058] Preferably, in S4, when it is Case 3), the next interference cycle is started at the failure time, and the towing speed is increased.

[0059] Preferably, in S4, when it is Case 4), the towing is stopped and the next interference cycle is started, and the towing speed is reduced.

[0060] Advantages of the present invention:

[0061] The present invention proposes an online evaluation method for radar interference effect based on inverse filtering processing, which can inversely sense the target tracking error inside the radar system, so as to realize non-cooperative online interference effect evaluation for deception jamming such as range and velocity deception jamming, range and velocity towing jamming, etc.; this method first designs algorithms for inverse filtering processing in actual confrontation scenarios with and without clutter, specifically including inverse Kalman filtering algorithm and inverse PDA filtering algorithm. The processing algorithm can use actions of the opponent radar such as waveform selection, resource scheduling, and platform movement observed in real time in noise to inversely filter and obtain an estimate of the radar filtering result, and online estimate and sense the tracking error of the radar; then, based on the filtering estimation result of the radar tracking error, this method designs an interference effect evaluation algorithm that can online judge the success / failure of interference and the success / failure time, with a relatively high accuracy. Finally, this method also proposes an improvement method for the interference strategy based on the evaluation. Brief Description of the Drawings

[0062] Figure 1 It is a flow chart of the online evaluation method for interference effect realized by the present invention.

[0063] Figure 2 It is a hierarchical view of the working principle of the radar system and the inverse processing of the radar system.

[0064] Figure 3 It is a schematic diagram of the application scenario for estimating the radar tracking error by inverse filtering processing.

[0065] Figure 4 It is a schematic diagram of the mathematical model of the inverse filtering processing process proposed by the present invention.

[0066] Figure 5Flow chart of the inverse Kalman filtering algorithm under clutter-free background implemented by the present invention.

[0067] Figure 6 Flow chart of the inverse PDA filtering algorithm under clutter background implemented by the present invention.

[0068] Figure 7 Flow chart of the online evaluation of the range gate pull-off (RGPO) jamming effect based on inverse filtering processing of the present invention.

[0069] Figure 8 Flow chart of the radar anti-RGPO jamming strategy in the embodiment.

[0070] Figure 9 Graph of the evaluation result of the range gate pull-off (RGPO) jamming effect obtained in the embodiment.

[0071] Figure 10 Graph of the adjustment process of the range gate pull-off (RGPO) jamming strategy obtained in the embodiment. Detailed implementation manners

[0072] The present invention proposes a non-cooperative online jamming effect evaluation method based on inverse filtering processing. The detailed implementation manners are as follows:

[0073] S1. Establish an inverse filtering model according to the presence or absence of clutter, that is, determine the state equation and measurement equation of the inverse filtering model.

[0074] According to the radar tracking principle, the radar tracking process is summarized as a process as shown in Figure 3 where the left side is our side, i.e., the countermeasure side. k = 1, 2,..., N represents the discretized time. Our radar generates the motion state x Figure 3 according to its own motion mode. The opponent's radar obtains the noisy observation value y k of our true motion state x k through its sensors, performs tracking filtering to obtain the estimated value k of our motion state, and takes adaptive actions u such as platform maneuvering, waveform selection, resource scheduling, etc. Our side observes the adaptive actions u [[ID=4!]] k of the opponent's radar in noise and obtains the observed radar action a k . The inverse filtering problem is to estimate the opponent's radar's estimation of our state k under the condition of the known noisy measurement sequence a 1:k of the radar action and our true state sequence x 0:k . Let the estimation of the opponent's radar's estimation of our state obtained by our side be The inverse filtering problem can be characterized by the following formula: [[ID=5!]]

[0075] ​

[0076] S11. Select different inverse filtering state equations and measurement equations according to the presence or absence of clutter.

[0077] When there is no clutter in the background, the radar adopts the Kalman filtering algorithm, and the algorithm flow is as Figure 5 shown. The inverse filtering state equation and measurement equation of the inverse filtering model are respectively the following two formulas:

[0078]

[0079] When there is clutter in the background, the radar adopts the PDA filtering algorithm, and the algorithm flow is as Figure 6 shown. The inverse filtering state equation and measurement equation of the inverse filtering model are respectively the following two formulas:

[0080]

[0081] where v k is the measurement noise of the opponent's radar, which is Gaussian white noise with zero mean, and R k is the measurement noise covariance of the opponent's radar. μ k is the measurement noise of our side, K k is the radar filtering gain, C is the radar filtering measurement matrix, A is the radar state matrix, is the radar action matrix, that is, the inverse filtering measurement matrix of our side. P D and P G are respectively the radar detection probability and the probability that the measurement falls into the associated gate in the radar PDA filtering.

[0082] S12. Initialize the filtering parameters of the opponent's radar and the inverse filtering parameters of our side, including: the initial covariance of radar filtering ∑0, the initial estimated value of radar filtering the radar filtering state matrix A, the radar filtering state noise covariance Q, the radar measurement matrix C, the radar measurement noise covariance R, the inverse filtering measurement noise covariance the inverse filtering measurement matrix

[0083] S13. Simulate the filtering parameters of the opponent's radar according to the initialized parameters, including:

[0084] The predicted covariance at time K: Σ k|k-1 = AΣ k-1 A T + Q

[0085] The innovation covariance at time K: S k = CΣ k|k-1 C T + R

[0086] The filtering gain at time K:

[0087] Among them, Σ k-1 represents the radar filtering covariance at time k - 1. When k = 1, it is taken as the initial value ∑0;

[0088] When K > 1, if there is no clutter in the background, the opponent's radar filtering covariance: Σ k-1 =(I - K k-1 C)Σ k-1|k-2 ;

[0089] If there is clutter in the background, the modified Riccati is used to calculate the filtering covariance:

[0090]

[0091] In the above formula, ∑ k-1|k-2 , S k-1 , K k-1 , V k-1 are the predicted covariance, innovation covariance, filtering gain, and associated gate area at time k - 1 respectively. The associated gate area can be calculated from the innovation covariance according to different gate shapes. λ is the clutter density. The values of the coefficients a, b, and c are as described in the literature "He You, Xiu Jianjuan, Zhang Jingwei, etc. Radar Data Processing and Applications (Second Edition)", and can be obtained by looking up the table according to the expert experience based on the observation dimension and association threshold.

[0092] S14. Calculate the inverse filtering model parameters at the current moment according to the opponent's radar filtering parameters, including:

[0093] State matrix:

[0094] If the radar takes actions according to the prefabricated function, then the measurement matrix at each moment is calculated according to the radar prefabricated function.

[0095] State equation control matrix: F k-1 =CK k , without clutter;

[0096] F k-1 =CK k P D P G , with clutter;

[0097] State noise:

[0098] S15. Observe the opponent's radar action a k in real - time in the noise and record our true state x k . Using the observation set and our state, obtain the estimated value of the radar tracking filtering result, which is mainly divided into the following two steps:

[0099] (1) One-step prediction of inverse filtering to predict the opponent's estimation of our radar state at time k:

[0100] One-step prediction of the optimal estimation of the opponent's radar at time k:

[0101] Predict the inverse filtering error covariance at time k:

[0102] Where, represents our estimation of the opponent's estimation at time k - 1; represents the error covariance of our radar inverse filtering at time k - 1;

[0103] (2) Use the measurement a of the radar action in noise k to correct the one-step prediction result in (1).

[0104] Innovation:

[0105] Gain:

[0106] Use the observed value to correct the one-step prediction result to obtain our estimation of the opponent's estimation:

[0107]

[0108] Update the error covariance of our radar inverse filtering: Return to (1) to perform the prediction at time k + 1.

[0109] S2. Real-time estimate the tracking error of the radar in the corresponding dimension through inverse filtering.

[0110] Taking the distance dimension as an example, our estimation of the opponent's radar estimation at time k is including distance and speed information. Assume that the true value of the relative distance between us and the radar at time k is r k , and the estimated value of the relative distance obtained after the opponent's radar performs tracking filtering is After our inverse filtering process, the estimation of is Then the radar distance tracking error can be estimated as

[0111] S3. Use the opponent's radar tracking error obtained in S2 to detect the mutation point of the distance tracking error

[0112] The principle of range gate pull-off jamming defines the following three types of mutation points:

[0113] 1) Starting towing mutation point: Assume that the interference signal during the towing pause period can successfully capture the range gate. After entering the towing period, the towing interference starts to take effect, and the radar range tracking error experiences the first sudden increase. This point is called the starting towing mutation point.

[0114] 2) Successful mutation point: After the starting towing mutation point appears during the towing period, the radar tracking error continues to increase. When the tracking gate is towed away from the true target echo, the radar tracking error experiences the second sudden increase. This point is denoted as the successful mutation point.

[0115] 3) Failure mutation point: If during the towing period, due to a large towing speed, the interference signal breaks away from the range tracking gate or is successfully recognized and countered by the radar anti - interference, the radar tracking error will decrease at the failure moment. This point is denoted as the failure mutation point.

[0116] The design of the tracking error mutation point detection method is as follows: Continuously memorize the slope of the estimated tracking error curve and calculate the mean value of the error slope up to the current moment k:

[0117]

[0118] After entering the towing period, when the growth of the mean value of the error slope before a certain moment (denoted as moment k1) compared to the mean value of the error slope at the previous moment (denoted as moment k1 - 1) is greater than the set threshold γ e1 then moment k1 is denoted as a candidate sudden increase point. Perform the same processing on the mean value of the error slope from k1 + 1 to k1 + Δk t , where Δk t is the cumulative determination times. If the growth of the error mean value is greater than the set threshold γ e1 in all cases, then moment k1 is denoted as a sudden increase point, and recalculate the mean value of the error slope from moment k1 to the current moment k, that is:

[0119]

[0120] If the first detected sudden increase point during the towing period is the starting towing mutation point, and if the radar tracking error continues to increase after detecting the starting towing mutation point and a second sudden increase point is detected, then it is the successful mutation point. The detection of the sudden decrease point is similar to the above - mentioned sudden increase point detection method, that is, memorize the slope of the estimated tracking error curve and calculate the mean value of the curve slope. When the continuous cumulative decrease of the error mean value from a certain moment k2 for Δk t times is greater than the set threshold, then it is determined that moment k2 is the sudden decrease point, which is the failure mutation point.

[0121] S4. Use the detection results of the mutation points to qualitatively evaluate the interference effect as successful / failed, obtain the specific successful / failed moments, and finally adjust the interference strategy.

[0122] For the evaluation of interference effects and strategy adjustment, there are the following four situations, and the specific process is as Figure 7 shown below.

[0123] 1) If a successful mutation point is detected before the end of the towing period, it is determined that the interference is successful. The successful moment is the moment when the successful mutation point is detected. The interference should end at this moment until the next towing cycle arrives.

[0124] 1) If a sudden increase point is detected twice before the end of the towing period, it is determined that the interference is successful. The successful moment is the moment when the second sudden increase point is detected. The interference should end at this moment until the next towing cycle arrives.

[0125] 2) If a failed mutation point is detected before the end of towing, it is determined that the interference fails. The failure moment is the moment when the failed mutation point is detected. Towing should be stopped immediately at this moment, and the towing speed should be reduced in the next towing cycle because this situation is caused by the large towing speed, resulting in the towing signal deviating from the gate or being recognized and countered by the radar anti-jamming.

[0126] 3) If only the starting towing point is detected during the entire towing period, it is also determined that the interference fails. The failure moment is the end moment of the towing period. The next interference cycle should be started, and the towing speed should be increased because there is always a real target echo within the radar gate at the current towing speed;

[0127] 4) If no starting towing mutation point is detected until the middle of the towing period, it is determined that the interference fails. The failure moment is the middle moment of the towing period. Since the towing speed is too large, the interference signal deviates from the tracking gate or is recognized by the radar anti-jamming at the beginning of the towing. Towing should be stopped and the next interference cycle should be started, and the towing speed should be reduced.

[0128] Example:

[0129] Construct the following confrontation scenario. Assume that the confrontation is carried out in a two-dimensional plane space. The confrontation scenario set in the experiment is as follows: The enemy radar is an active homing guidance radar seeker, with a pulsed Doppler radar system. The specific scenario is air-to-air, and the missile attacks the carrier target head-on, tracking the target's distance and speed. Under this scenario, meteorological clutter is mainly considered, which is reflected as false measurement points within the associated gate during radar probabilistic data association and approximately follows a Poisson distribution within the associated gate. The simulation step size Δt = 0.01s.

[0130] The radar is an active homing guidance radar seeker with a pulsed Doppler radar system, and the specific scenario is air-to-air. A rectangular coordinate system is established with the initial position of the radar as the origin. At the initial moment, the distance between the missile and the target is 14.1 Km, and the height difference between the missile and the target is 1 Km. That is, the target is located at [1000 m, 1000 m] at the initial moment, the missile attacks the target head-on, the initial flight speed of the missile is [400 m / s, 500 m / s], and the radar seeker designs an optimal guidance law using the linear quadratic Gaussian theory. The carrier target moves in a uniform straight line along the negative x-axis with a speed of [200 m / s, 0 m / s]. The radar uses a probabilistic data association (PDA) filter to track the target in clutter. The tracking gate is a rectangular gate, the target detection probability is 1, the probability that the target falls within the gate is 0.9997, and the clutter density is 0.0001. The target (ourside) uses range gate pull-off jamming, and the radar side identifies and suppresses range gate pull-off jamming based on PDA filtering technology. The predicted value of the PDA filter at the current moment is compared with the optimal estimate obtained by true filtering, and interference is identified based on this, and then the range gate pull-off jamming is countered by memorizing the moving speed of the range gate. The anti-jamming process is as Figure 8 shown.

[0131] The jammer adopts self-defense range gate pull-off jamming, which starts 1 s after the simulation begins and performs uniform backward pulling with a 10-s pull-off jamming period. The range gate pull-off settings are as follows:

[0132] 1) Hold-off period: The duration of the hold-off period is 1 s. In the experiment, the ratio of the pulse amplitude of the jamming signal to the pulse amplitude of the echo signal is set to 1.4, and then it is maintained for a period of time to allow the jamming signal to capture the range gate. The time delay of our side's retransmitted jamming pulse is ignored, and it is ensured that the range gate can be successfully captured during the hold-off period.

[0133] 2) Pull-off period: The initial pull-off period duration is set to 7 s in the simulation. The pull-off speed is 500 m / s.

[0134] 3) Shutdown period: The shutdown period is set to 2 s, and a total of 10 s is a pull-off cycle.

[0135] The specific algorithm implementation process is as follows:

[0136] S1. Select the inverse PDA filtering algorithm under clutter for inverse filtering

[0137] S11. The inverse filtering model is:

[0138]

[0139]

[0140] S12. Initialize the parameters of the inverse filtering algorithm, including the initial covariance of filtering, the initial estimated value of radar filtering, the radar filtering state matrix, the radar filtering state noise covariance, the radar measurement matrix, the radar measurement noise covariance, and the inverse filtering measurement noise covariance.

[0141] S13. Simulate the enemy radar filtering parameters according to the initialized parameters, including:

[0142] Prediction covariance: Σ k|k-1 = AΣ k-1 A T + Q

[0143] Innovation covariance: S k = CΣ k|k-1 C T + R

[0144] Filter gain:

[0145] Calculate the filtering covariance using the modified Riccati, where a, b, and c take values 0.37, 2.57, and 0.997 respectively:

[0146]

[0147] S14. Calculate the inverse filtering model parameters at the current moment according to the enemy filtering parameters, including:

[0148] State matrix:

[0149] State equation control matrix:

[0150] State noise:

[0151] S15. Observe the radar action a k in real time in the noise. In this experiment, it is the radar guidance law, and record our true state x k . Use the observation set, our state, and the parameters obtained in S1 to perform inverse filtering to obtain the estimated value of the radar tracking filtering result, which is mainly divided into the following two steps:

[0152] (1) One-step prediction of inverse filtering to predict the enemy's optimal estimate of our state.

[0153] One-step prediction of the opponent's radar optimal estimate:

[0154] Predict the inverse filtering error covariance:

[0155] (2) Use the measurement a k of the radar action in the noise.Correct the one-step prediction result of S31.

[0156] Innovation:

[0157] Gain:

[0158] Use the observation value to correct the one-step prediction result to obtain the optimal estimate of the enemy's estimate:

[0159]

[0160] Update the error covariance of our inverse filter:

[0161] S2. Real-time estimate the radar range tracking error through inverse filtering:

[0162] S3. Real-time plot the radar range tracking error curve as Figure 9 shown. When the towing speed is v j = 500 m / s, both the true and estimated tracking error curves detect sudden drops at 2.4 s, indicating that the jamming fails. The reason for the failure is that the towing speed is too high, resulting in being recognized by the radar anti-jamming module or the jamming signal deviating from the tracking gate due to excessive speed.

[0163] S4. Use the mutation point detection result to conduct a qualitative assessment of the jamming effect and obtain the specific success / failure time: The result shows that the jamming fails, and the failure time is Figure 9 2.4 s in

[0164] S5. Use the evaluation result to improve the jamming strategy: As Figure 10 shown, the towing speed of the range towing jammer at the start of the simulation is 500 m / s. When the time t = 1 s, the range towing jammer enters the towing period. From the upper figure in Figure 10 , it can be seen that affected by the jamming, the radar range tracking error gradually increases. At this time, the center of the radar range tracking gate gradually deviates from the true target echo. Around 2.4 s, the radar range tracking error suddenly starts to decrease, indicating that the towing speed is too fast, resulting in the towing jammer signal deviating from the radar range tracking gate. According to the mutation point detection method described in 4.2, after selecting the candidate sudden drop point, it is necessary to continuously judge Δk t times. In this simulation experiment, Δk t = 10. Then at 2.5 s, the sudden drop point is successfully detected. We judge that the jamming fails and immediately turn off the jammer. After a 1-s shutdown period, the jamming ends. According to Figure 10The distance towing jamming strategy adjustment method shown above adjusts the towing speed among the towing jamming parameters. After a 1s towing stop period, it enters the towing period at 4.5s. As can be seen from the figure above, after re-implementing the jamming after the towing jamming strategy adjustment, the jamming is successful at 8.16s, indicating that the distance towing jamming strategy adjustment method in this paper is effective.

[0165] In summary, the method of the present invention mainly has the following advantages

[0166] 1) By using the inverse filtering processing algorithm, it is possible to estimate and perceive the internal processing state of the target radar system under non-cooperative conditions without the need for too much prior knowledge and expert experience.

[0167] 2) Specifically designed the inverse Kalman filtering algorithm applicable to clutter-free scenarios and the inverse PDA filtering algorithm applicable to clutter scenarios, which can better estimate the tracking error of the radar system.

[0168] 3) Based on the estimation of the radar tracking error results implemented by the inverse filtering algorithm, it is possible to realize the real-time online evaluation of the specific jamming effect of the jamming pattern whose design goal is to disrupt the radar tracking system.

[0169] 4) Aiming at the working principle of distance towing jamming, based on the real-time jamming effect evaluation results of inverse filtering processing, the jamming implementation process and parameters can be optimized and adjusted online to realize the real-time improvement of the jamming strategy.

[0170] Therefore, the online jamming effect evaluation method based on inverse filtering processing given by the present invention can provide theoretical and technical support for the design and implementation of an autonomous cognitive countermeasure system.

[0171] In summary, the above is only an implementation example of the jamming effect evaluation of distance towing jamming in the air-to-air countermeasure scenario constructed by the present invention, and is not used to limit the protection scope of the present invention. The inverse PDA filtering algorithm under clutter background, estimating the radar tracking error based on the inverse filtering algorithm, the non-cooperative jamming effect evaluation based on inverse filtering processing, and the jamming strategy adjustment based on the evaluation results are the core points of the present invention. Any online jamming effect evaluation algorithm based on inverse filtering processing formed by corresponding modifications, replacements, improvements, etc. within the above design principles and implementation key points of the present invention should be included in the protection scope of the present invention.

Claims

1. A non-cooperative online interference effect evaluation method based on inverse filtering processing, characterized in that It includes the following steps: S1. Establish an inverse filtering model based on the presence or absence of clutter, that is, determine the state equation and measurement equation of the inverse filtering model. Specifically: Our radar generates the motion state x according to its own motion mode k , where k = 1, 2,... represents the discretized time, and x k represents the motion state at time k; the opponent's radar obtains the noisy observation value y k of the true motion state x of our radar k , performs tracking filtering to obtain the estimated value of our motion state and takes the adaptive action u k ; we observe the adaptive action u of the opponent's radar in the noise k , and observe that the radar action is a k ; S11. When there is no clutter in the background, the radar uses the Kalman filtering algorithm to obtain the inverse filtering state equation and measurement equation at time k, which are the following two formulas respectively: When there is clutter in the background, the radar uses the PDA filtering algorithm to obtain the inverse filtering state equation and measurement equation, which are the following two formulas respectively: Among them, represents the estimated value of our motion state at time k-1, v k is the measurement noise of the opponent's radar at the current time k, which is Gaussian white noise with a mean of zero, R k is the covariance of the measurement noise at the current time k; μ k is the measurement noise of our side at the current time k; K k is the filtering gain at the current time k, C is the radar filtering measurement matrix, A is the radar state matrix, is the radar action matrix at the current time k, that is, our inverse filtering measurement matrix; P D 、P G are the radar detection probability and the probability that the measurement falls into the associated gate in the radar PDA filtering respectively; S12. Initialize the opponent radar filtering parameters and our inverse filtering parameters, including: the initial covariance of radar filtering ∑0, the initial estimated value of radar filtering The state matrix A of radar filtering, the state noise covariance Q of radar filtering, the measurement matrix C of radar filtering, the measurement noise covariance R of radar, and the inverse filtering measurement noise covariance S13. Simulate the filtering parameters of the opponent's radar according to the initialization parameters, including: Predicted covariance at time K: Σ k|k-1 = AΣ k-1 A T + Q; Innovation covariance at time K: S k = CΣ k|k-1 C T + R; Filter gain at time K: Among them, Σ k-1 represents the radar filtering covariance at time k-1. When k = 1, it is taken as the initial value ∑0; When K > 1, if there is no clutter in the background, the filtering covariance of the opponent's radar: Σ k-1 =(I - K k-1 C)Σ k-1|k-2 ; If there is clutter in the background, use the modified Riccati to calculate the filtering covariance: In the above formula, ∑ k-1|k-2 , S k-1 , K k-1 , V k-1 are respectively the predicted covariance, innovation covariance, filtering gain and associated gate area at time k-1; λ is the clutter density, and a, b, c are coefficients obtained by looking up a table from expert experience; S14. Calculate the inverse filtering model parameters at the current moment according to the filtering parameters of the other party's radar, including: State matrix: No clutter; There is clutter; State equation control matrix: No clutter; There is clutter; State noise: No clutter; There is clutter; S15. Observe the opponent's radar actions a in real time in noise k , record the true state x of our radar k , and use the observation set and our state to obtain the estimated value of the radar tracking filtering result, which is divided into the following two steps: (1) One-step prediction of inverse filtering, predicting the opponent's estimation of the state of our radar at time k: One-step prediction of the optimal estimate of the opponent's radar at time K: Predict the inverse filter error covariance at time instant K: Among them, represents the estimation of the enemy by our side at time k-1; represents the error covariance of the inverse filtering of our radar at time k-1; (2) Using the measurement a of the radar action in noise k Correct the one-step prediction result in (1); Innovation covariance: Filter gain: Use the observed value to correct the one-step prediction result to obtain our estimation of the opponent's estimation: Update the error covariance of our radar inverse filtering: S2. Real-time estimate the tracking error of the radar in the corresponding dimension through inverse filtering. Specifically: Based on the estimation of the opponent's radar by our side at time k For each parameter information, assuming that the true value of a certain parameter at time k is r k , after the opponent's radar performs tracking filtering, the estimated value of this parameter is After our side's inverse filtering process, the estimation of is Then the radar range tracking error can be estimated as S3. Use the tracking error of the opponent's radar obtained in S2 to detect the mutation points of the tracking error, including the detection of sudden increase points and sudden decrease points: S4. Use the detection result of the mutation point to conduct a qualitative evaluation of the success or failure of the interference effect.

2. The non - cooperative online interference effect evaluation method based on inverse filtering processing according to claim 1, characterized in that, In S3, the method for detecting sudden increase points is: Continuously memorize the slope of the estimated tracking error curve and calculate the mean value of the error slope up to the current k-th moment After entering the towing period, when the growth of the mean error slope before a certain moment compared to the mean error slope of the previous moment is greater than the set threshold γ e1 at that time, this moment is recorded as a candidate sudden increase point; if the growth of the mean error slope within the set time after this moment is also greater than the set threshold γ e1 , then this moment is recorded as a sudden increase point.

3. The non-cooperative online interference effect evaluation method based on inverse filtering processing according to claim 2, characterized in that, In S3, the method for detecting sudden decrease points is: Continuously memorize the slope of the estimated tracking error curve and calculate the mean value of the error slope up to the current k-th moment After entering the towing period, when the decrease in the mean error slope before a certain moment compared to the mean error slope of the previous moment is greater than the set threshold γ e2 at that time, mark this moment as a candidate sudden drop point; if the decrease in the mean error slope within the set time after this moment is also greater than the set threshold γ e2 , then mark this moment as a sudden drop point.

4. The non-cooperative online interference effect evaluation method based on inverse filtering processing according to claim 3, characterized in that, In S4, the method for conducting a qualitative evaluation of the success or failure of the interference effect using the detection result of the mutation point is: Case 1). If two consecutive sudden increase points are detected before the end of the towing period, it is determined that the interference is successful, and the successful moment is the moment of the second sudden increase point; Case 2). If a sudden decrease point is detected before the end of the towing, it is determined that the interference fails, and the failure moment is the moment of the sudden decrease point; Case 3). If only one sudden increase point is detected during the entire towing period, it is also determined that the interference fails, and the failure moment is the end moment of the towing period; Case 4). If no sudden increase point is detected until the middle of the towing period, it is determined that the interference fails, and the failure moment is the middle moment of the towing period.

5. The non-cooperative online interference effect evaluation method based on inverse filtering processing according to claim 4, wherein In S4, when it is Case 1), end the interference at the successful moment until the next towing cycle arrives.

6. The non-cooperative online interference effect evaluation method based on inverse filtering processing according to claim 4, characterized in that In S4, when it is Case 2), immediately stop towing at the failure moment and reduce the towing speed in the next towing cycle.

7. The non-cooperative online interference effect evaluation method based on inverse filtering processing according to claim 4, wherein In S4, when it is Case 3), start the next interference cycle at the failure moment and increase the towing speed.

8. The non - cooperative online interference effect evaluation method based on inverse filtering processing according to claim 4, characterized in that, In S4, when it is Case 4), stop towing and start the next interference cycle, reducing the towing speed.

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