An interactive multi-model based composite seeker jamming track recognition method

Abstract

The application discloses a composite seeker jamming track recognition method based on an interactive multi-model, which comprises the following steps: firstly, initializing system parameters, assuming the motion parameters of a target and jamming; secondly, determining a state model used for describing the motion form of the target, and then modeling a multi-model system; thirdly, processing the state model to obtain updated model probability and system state estimation; fourthly, calculating a jamming decision threshold according to the updated model probability, so as to determine the appearing jamming track; fifthly, further identifying the specific jamming; and finally, outputting a jamming track serial number. The application introduces the motion modeling of jamming into the composite seeker, effectively improves the jamming recognition probability of the track gradual change, does not need to introduce an extra high-dimensional feature calculation, removes the jamming track in the track level dimension, and has the advantages of small engineering implementation cost, easy realization and the like.

Description

Technical Field

[0001] This invention relates to the field of guidance and control technology, and in particular to a method for identifying interference tracks of a composite seeker based on interactive multi-model architecture. Background Technology

[0002] With the continuous escalation of battlefield interference offense and defense confrontation, actual battlefield combat is increasingly trending towards combined interference, and the difficulty of interference release measures and countermeasures is spiraling upwards. For seeker detection, interference measures and seeker detection characteristics are usually a process of continuous escalation of confrontation, and single-mode seekers are increasingly unable to meet the increasingly complex interference countermeasures requirements of future operations. Composite seekers employ a multi-sensor composite guidance system, combining two or more modes within a single seeker. By leveraging the characteristics of multiple sensors to compensate for each other's weaknesses and complement each other, the overall anti-jamming performance of the seeker is improved, which has become one of the key measures for anti-jamming in modern warfare. For composite anti-jamming technology, how the seeker correctly eliminates interference sources is of decisive significance for combat strikes. Interference elimination by the seeker can be considered from multiple levels, such as signal level, characteristic level, track level, and decision level. Interference track elimination at the track level has advantages such as low engineering implementation cost and ease of implementation.

[0003] The literature "Research on Anti-jamming Technology of Composite Seeker Target Information Fusion [J]. Flight Control and Detection, 2018" discloses a method that uses the correlation degree of time-domain accumulated measurement values ​​as a criterion for judging interference tracks; the literature "Anti-jamming Tracking Method of Radar / Infrared Composite Seeker [J]. Flight Mechanics, 2016" uses the correlation degree of observation information and the trace value of innovation variance to judge interference. From the perspective of track-level information fusion anti-jamming, based on the existing interference patterns and motion forms, interference tracks can be divided into two types: track abrupt change and track gradual change. Existing composite track-level anti-jamming methods mainly consider the observation innovation. They have a certain recognition rate for track abrupt change interference, but for track gradual change interference, such as centroid interference, the variance decision of innovation for judging interference tracks is greatly reduced during the tracking process of interference tracks and target tracks, which has certain application limitations. Summary of the Invention

[0004] The technical problem solved by this invention is to provide a method for identifying interference tracks of a composite seeker based on interactive multi-model, so as to solve the problems in the background art mentioned above.

[0005] The technical problem solved by this invention is achieved by the following technical solution:

[0006] A method for identifying interference tracks of a composite seeker based on interactive multi-model approaches, comprising the following steps:

[0007] 1) Initialize system parameters

[0008] Assume that the composite seeker is equipped with multiple sensors, and that the multiple sensors simultaneously detect a moving target in the same space, recording the initial target state, total motion time, and system sampling interval T; and assume that the target moves within a specified time, the sensors simultaneously track the target, and then begin to release interference, which moves in an unpredictable manner.

[0009] 2) Multi-model system modeling and interaction estimation

[0010] First, a state model is determined to describe the motion of the target. Then, a multi-model system model is built. Next, the system state transition matrix of the state model is calculated. The transition probabilities of each state model are determined and the state model transition probability matrix is ​​calculated. After the model states are interacted and filtered in turn, the turning rate of each state model is calculated based on the filtering results. Through the interaction process, the updated model probabilities and system state estimates are obtained.

[0011] 3) Calculate the interference decision threshold

[0012] The interference decision threshold is calculated based on the updated model probability obtained in step 2). After determining the interference track based on the calculated interference decision threshold, the specific sensor that is interfered with is further identified.

[0013] 4) Output interference track number

[0014] Repeat steps 2) to 3) until interference is found, then the iteration ends and the interference track number is output.

[0015] In this invention, the state equation for the multi-sensor multi-model system is:

[0016]

[0017] in, This represents the target motion state vector of the m-th model at time k, where the superscript T represents matrix transpose. These represent the target's position and velocity along the x-axis, respectively. This represents the target's position and velocity along the y-axis, where T is the sampling interval and F is the velocity. k-1,m This represents the state transition equation for the m-th model at time k-1. Considering that the target / disturbance motion model is not fixed throughout the entire motion process, therefore F... k-1,m Represents the state transition equations at different times, v k This indicates process noise.

[0018] In this invention, the state models include a uniform velocity model (CV), a cooperative turning model (CT), and a uniform acceleration model (CA), denoted as F, respectively. k,CV F k,CT F k,CAThe system state transition matrix F of the model k,CV F k,CT F k,CA They are represented as follows:

[0019] The system state transition matrix F of the uniform velocity model k,CV for

[0020]

[0021] Cooperative turning model system state transition matrix F k,CT for

[0022]

[0023] Among them, w k The turning rate w represents the target's motion state at time k. k Since the number of turns is usually unknown, the cooperative turning model is extended by adding w. k Incorporate into the state vector, i.e. The state transition matrix of the cooperative turning model under unknown turning rate is:

[0024]

[0025] Where β represents the turning rate state coefficient;

[0026] The state transition matrix F of the uniformly accelerated model system k,CA for

[0027]

[0028] In the uniform acceleration model, the state vector is: These represent the target's acceleration along the x-axis.

[0029] In this invention, the measurement equation is established as follows:

[0030]

[0031] Among them, z k n represents the sensor's measurement value at time k. k The measurement noise is represented by h(.), and the measurement equation is represented by h(.). It is worth noting that the measurement equation is generally determined by the sensing characteristics of the sensor. Different forms of measurement equations are modeled according to the detection characteristics of different sensors.

[0032] In this invention, the transition probabilities of each model are calculated as follows:

[0033] Assuming there are M models in total, each model can describe any possible target motion state, and the transition probabilities between the system models are represented by Markov chains:

[0034] P{m(k+1)=j|m(k=i}=p ij i,j=1,2,...,M

[0035] Where, p ij This represents the transition probability from model i to model j in the system. During the tracking process of the seeker, the probability value is selected a priori based on the scenario settings, and the transition probability generally remains unchanged during the tracking process.

[0036] In this invention, particle filtering is used to facilitate the state interaction of each model, specifically as follows:

[0037] a: Obtain particle sample swarms for each model

[0038] If k = 1

[0039] The initial particle state and its corresponding weights are generated based on known priors or the results of detection and tracking preprocessing. In practical applications, Gaussian approximation is performed based on the track header output at the start of the track to obtain the initialized particle state. Initialize particle weights as Where N represents the number of sampled particles;

[0040] If k>1

[0041] Based on the known state variables and covariance at time k-1 Generate particle sample swarms for each model A Gaussian approximation strategy is adopted to approximate each model particle sample as a Gaussian distribution, that is, Gaussian fitting is performed on the particles after each iteration.

[0042]

[0043] Where N(.) denotes the Gaussian distribution marker;

[0044] b: Particle interactions between models

[0045] Based on the given model transition probability p ij Known model probability State variables and covariance individual particles The particles obtained through interaction with other models are represented as follows:

[0046]

[0047] in, This represents the update probability of each model at time k-1. The probability that the model is m at time k and i at time k-1 is calculated as follows:

[0048]

[0049] Among them, c m (k-1) is the normalization constant.

[0050]

[0051] In this invention, particle filtering is used to filter the states of each model, specifically as follows:

[0052] i: Based on the state equation, the particles after interaction To make a prediction

[0053]

[0054] ii: Calculate the weights of each particle

[0055]

[0056] Where ∝ represents proportionality to the symbol, Let represent the likelihood function, used to describe the measured density of predicted particles. Its distribution model is specific to the actual scenario, assuming it follows a Rayleigh distribution, denoted as .

[0057]

[0058] iii: Resample the predicted particles to obtain

[0059] To avoid particle decay, the sampled particles are resampled. This involves normalizing the weights of all particles n = 1, 2, ..., N, and then resampling the normalized particle set. The resampling uses a system resampling algorithm, which includes the following steps:

[0060] ①: Initially a1 = 0, u1 ~ U[0,N -1 ], where U[.,.] represents a uniform distribution within the interval;

[0061] ②: Calculation

[0062] ③: Calculate u j =u1+N -1 (j-1),j=1:N

[0063] If a i <u j If n = n + 1, return to step ②; otherwise, record the position of the nth particle at the jth position.

[0064] iv: Use resampled particles to perform state estimation for each model

[0065]

[0066] The covariance matrix of the target state of each model is estimated using the least mean square criterion.

[0067]

[0068] In this invention, the turning rate estimation for each model is as follows:

[0069] Based on the filtering results, the turning rate of each state model is calculated. For the uniform velocity (CV) model, the ratio of acceleration to velocity output at each step is used as the turning rate.

[0070]

[0071]

[0072]

[0073] For the cooperative turning model (CT), it is obtained by weighting the sampled particles, i.e.

[0074]

[0075] In this invention, the probability updates of each model and the system state estimation are as follows:

[0076] Updating the model probabilities, we get:

[0077]

[0078] in, The likelihood function of each model filter is generally assumed to be Gaussian distributed and is calculated using the following formula.

[0079]

[0080] Where exp[.] denotes an exponential function with base e. Indicates information, used to describe the difference between the predicted and measured values ​​of a measurement:

[0081]

[0082] The covariance matrix representing the new information is used to measure the uncertainty of the new information.

[0083]

[0084] Calculate the probability model of each model being correct. Then, by weighting the state estimates when each model is correct, the system state estimate is obtained:

[0085]

[0086] Similarly, turning rate estimation

[0087]

[0088] In this invention, the interference decision threshold Δ is calculated.

[0089]

[0090] in, This represents the probability of state model m in sensor i.

[0091] Beneficial effects:

[0092] 1) The method of the present invention is based on interactive multi-model, which introduces motion modeling of interference into the composite seeker, effectively improving the probability of interference recognition for gradual track changes;

[0093] 2) This invention does not require the introduction of additional high-dimensional feature calculations, and performs interference track removal at the track level, which has the advantages of low engineering implementation cost and ease of implementation;

[0094] 3) This invention has wide applicability and can be extended to other application fields such as collaborative detection and decoy identification. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of an interactive multi-model algorithm based on particle filtering in a preferred embodiment of the present invention.

[0096] Figure 2 This is a flowchart of a preferred embodiment of the present invention.

[0097] Figure 3 This is a schematic diagram of the target and interference motion scene in a preferred embodiment of the present invention.

[0098] Figure 4 This is a schematic diagram of multi-model probabilities in a preferred embodiment of the present invention.

[0099] Figure 5 This is a schematic diagram of interference track threshold decision in a preferred embodiment of the present invention.

[0100] Figure 6 This is a schematic diagram of the target and the turning speed of the interference in a preferred embodiment of the present invention. Detailed Implementation

[0101] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific illustrations.

[0102] A method for identifying interference tracks of a composite seeker based on interactive multi-model approaches, comprising the following steps:

[0103] 1) Initialize system parameters

[0104] Assume a composite seeker head has two sensors, S=2, that both sensors simultaneously detect a moving target in a two-dimensional plane. The target starts from [60000m, 40000m] with an initial velocity of [-172m / s, 246m / s], denoted as x0 = [60000m, -172m / s, 40000m, 246m / s]. The total motion time is L=150s, and the system sampling interval is T=1s. The target moves at a constant speed of 300m / s from 0 to 55s, and both sensors track the target simultaneously. Assume interference is released starting at 56s, meaning the interference occurs at a velocity of 1.5g (g=9.8m / s²) from 56 to 150s. 2 The motion acceleration of the target is used for coordinated turning motion. During this stage, considering the scenario where the composite seeker is interfered with and deceived, one sensor continues to track the target motion, while the other sensor starts tracking the interference motion from 56s. Figure 3 As shown;

[0105] 2) Multi-model system modeling and interaction estimation

[0106] A1: State equation modeling

[0107] A1.1: Establishing the state equations for multiple sensors and multiple models

[0108]

[0109] in, The superscript represents the target motion state vector of the m-th model at time k. T Represents matrix transpose. These represent the target's position and velocity along the x-axis, respectively. This represents the target's position and velocity along the y-axis, where T is the sampling interval and F is the velocity. k-1,m This represents the state transition equation for the m-th model at time k-1. Considering that the target / disturbance motion model is not fixed throughout the entire motion process, therefore F... k-1,m Represents the state transition equations at different times, v k Indicates process noise;

[0110] State models used to describe the motion of a target include: uniform velocity model, uniform acceleration model, and uniform turning model.

[0111] In this embodiment, the model set is considered to mainly consist of two types of models: the uniform velocity model (CV) and the cooperative turning model (CT), i.e., M=2, denoted as F respectively. k,CV F k,CTNote that the actual model set can consist of any number of models, depending on the specific application scenario. The system state transition matrix F of the model... k,CV F k,CT They are represented as follows:

[0112] The system state transition matrix F of the uniform velocity model k,CV for

[0113]

[0114] Cooperative turning model system state transition matrix F k,CT for

[0115]

[0116] Among them, w k The turning rate w represents the target's motion state at time k. Since the turning rate w is used to estimate the actual target's motion state... k Since the number of turns is usually unknown, the cooperative turning model is extended by adding w. k Incorporate into the state vector, i.e. The state transition matrix of the cooperative turning model under unknown turning rate is:

[0117]

[0118] Wherein, β represents the turning rate state coefficient, and in this embodiment, β = 1;

[0119] A1.2: Establishing Measurement Equations

[0120]

[0121] Among them, z k n represents the sensor's measurement value at time k. k The measurement noise is represented by h(.), and the measurement equation is represented by h(.). It is worth noting that the measurement equation is generally determined by the sensing characteristics of the sensor. Different forms of measurement equations are modeled according to the detection characteristics of different sensors. In this embodiment, the measurement equation is assumed to be a linear equation.

[0122] A2: Determine the transition probabilities for each model

[0123] Assuming there are M models in total, each model can describe any possible target motion state, and the transition probabilities between the system models are represented by Markov chains:

[0124] P{m(k+1)=j|m(k=i}=p ij i,j=1,2,...,M

[0125] Where, p ijThis represents the transition probability of the system from model i to model j;

[0126] In this embodiment, it is assumed that the initial probabilities of each model are... In general, without any prior knowledge, a uniform distribution is assumed.

[0127] The transition probability matrix between the models is

[0128]

[0129] Where, p ij The transition probability from model i to model j represents the system. During the tracking process of the seeker, the probability value is selected a priori according to the scenario settings. The transition probability generally remains unchanged during the tracking process. The initial probability and transition probability of each model are preset parameters, and the parameters remain unchanged during the calculation process.

[0130] A3: Interaction between Model States

[0131] This embodiment uses particle filtering for state interaction and filtering of each model. In practical applications, Kalman, random set and other filtering algorithms can be selected according to actual needs. Considering the uncertainty of the disturbance release motion form, the particle filtering algorithm can adapt to nonlinear and non-Gaussian scenarios.

[0132] A31: Obtain particle sample swarms for each model

[0133] If k = 1

[0134] The initial particle state and its corresponding weights are generated based on known priors or the results of detection and tracking preprocessing. In practical applications, after the seeker detects the initial probe points output by the tracking module and initiates the trajectory, a Gaussian approximation is performed based on the trajectory head output from the trajectory initiation to obtain the initialized particle state. Initialize particle weights as Where N represents the number of sampled particles;

[0135] If k>1

[0136] Based on the known state variables and covariance at time k-1 Generate particle sample swarms for each model In this embodiment, a Gaussian approximation strategy is adopted to approximate each model particle sample as a Gaussian distribution, that is, Gaussian fitting is performed on the particles after each iteration.

[0137]

[0138] Where N(.) denotes the Gaussian distribution marker;

[0139] A32: Particle Interactions Among Various Models

[0140] Based on the given model transition probability p ij Known model probability State variables and covariance individual particles The particles obtained through interaction with other models are represented as follows:

[0141]

[0142] in, This represents the update probability of each model at time k-1. The probability that the model is m at time k and i at time k-1 is calculated as follows:

[0143]

[0144] Among them, c m (k-1) is the normalization constant.

[0145]

[0146] A4: Filtering for Each Model

[0147] After interaction, the particles take into account the factors of mutual influence between models and further filter each model;

[0148] A41: Based on the state equation, the particles after interaction... To make a prediction

[0149]

[0150] A42: Calculate the weights of each particle

[0151]

[0152] Where ∝ represents proportionality to the symbol, Let represent the likelihood function, used to describe the measured density of the predicted particles. Its distribution model is specific to the actual scenario and can generally be assumed to be a Gaussian or Rayleigh distribution. In this embodiment, it is assumed to follow a Rayleigh distribution, denoted as .

[0153]

[0154] A43: Resample the predicted particles to obtain...

[0155] To avoid particle decay, two methods are used: 1) Selecting the optimal importance probability density; 2) Resampling the sampled particles. In this embodiment, resampling is used. The weights of all particles n = 1, 2, ..., N are normalized, and the normalized particle set is resampled.

[0156] Resampling algorithms can be categorized into various types based on their processing methods, such as multinomial resampling, residual resampling, systematic resampling, and hierarchical resampling. In this embodiment, a systematic resampling algorithm is employed, comprising the following steps:

[0157] A431: Initially a1 = 0, u1 ~ U[0,N] -1 ], where U[. ,. ] indicates that the distribution follows a uniform distribution within the interval;

[0158] A432: Calculation

[0159] A433: Calculate u j =u1+N -1 (j-1),j=1:N

[0160] If a i <u j If n = n + 1, return to step A432; otherwise, record the position of the nth particle at the jth position.

[0161] A44: Use resampled particles to perform state estimation for each model.

[0162]

[0163] The covariance matrix of the target state of each model is estimated using the least mean square criterion.

[0164]

[0165] A5: Turning rate estimation for each model

[0166] Based on the filtering results above, the turning rate of each model is calculated. For the uniform velocity (CV) model, the ratio of acceleration to velocity output at each step is taken as the turning rate.

[0167]

[0168]

[0169]

[0170] For the Cooperative Turning (CT) model, since it has already been incorporated into the state vector during state modeling, the turning rate is calculated by weighting the sampled particles, i.e.

[0171]

[0172] A6: Probability Updates for Each Model and System State Estimation

[0173] Updating the model probabilities, we get:

[0174]

[0175] in, The likelihood function of each model filter can generally be assumed to follow a Gaussian distribution and is calculated using the following formula.

[0176]

[0177] Where exp[.] denotes an exponential function with base e. Indicates information, used to describe the difference between the predicted and measured values ​​of a measurement:

[0178]

[0179] The covariance matrix representing the new information is used to measure the uncertainty of the new information.

[0180]

[0181] Through the interaction process, the updated model interaction probabilities are obtained, representing the degree of mutual influence between models;

[0182] Calculate the probability model of each model being correct. Then, by weighting the state estimates when each model is correct, the system state estimate is obtained:

[0183]

[0184] Similarly, turning rate estimation

[0185]

[0186] 3) Calculate the interference decision threshold

[0187] B1: Interference Track Identification

[0188] In this embodiment, the number of sensors S=2, and the two sensors in the composite seeker track the target and the interference motion respectively;

[0189] Sensor s undergoes interactive multi-model estimation, i.e., step 2), to obtain the updated model probability of sensor s at time k. In this embodiment, two models are used: uniform motion and cooperative turning. Therefore, the updated model probability is denoted as follows: and

[0190] B11: Interference detected in flight path

[0191] First, calculate the interference decision threshold Δ

[0192]

[0193] in, This represents the probability of the uniform velocity (CV) model in sensor i at time k. The constant velocity (CV) model probability in sensor j at time k represents the probability of the motion model. The interference decision threshold characterizes the difference in target / interference tracking motion models between different sensors. Based on the difference in motion models, it serves as a criterion for determining whether interference has occurred. For example, if two sensors track the target and interference respectively, their... and The difference must be significant;

[0194] Set a threshold ε. If the interference threshold Δ exceeds the threshold ε, it indicates that the seeker tracking is being interfered with, and an interference track is identified.

[0195] It is worth noting that the value of the threshold ε directly affects the performance of the decision result. The threshold setting affects both the decision accuracy and the false alarm rate P. fa The two are often mutually restrictive, so the Neyman-Pearson criterion is adopted to optimize decision performance while ensuring that the false alarm rate does not exceed the tolerable range.

[0196]

[0197] Where erf(.) represents the error function, and the superscript... -1 Represents the reciprocal, σ 2 Δ represents the variance, which is calculated using the formula for sample variance. The threshold value is calculated using the above formula to ensure a certain false alarm rate.

[0198] Furthermore, the actual combat scenario also has a significant impact on the threshold. In engineering, for specific combat scenarios, statistical methods are typically used to determine the threshold. A parameter that guarantees performance is fitted through debugging experimental data. In this embodiment, the false alarm probability P is taken as... fa =10 -6 , σ 2 =0.8, then ε =1.5;

[0199] B12: Identify interference tracks

[0200] After determining the presence of an interfering track based on the interference decision threshold calculated in step B11), the specific sensor that is being interfered with is further identified.

[0201] First, determine the prior of interference release. and the prior knowledge of target mobility It is worth noting that, in actual combat scenarios, the strategies and forms of jamming release in the current main battlefield environment can be obtained through intelligence departments. For typical targets, such as ships on the sea surface, their maneuverability can also be obtained through certain modeling. If the intelligence department can guarantee the jamming movement prior... Or target motion prior The acquisition of this information can provide a basis for the next step of the judgment; in this embodiment, it is assumed that the target is a ship moving at sea, and the ship's maneuverability is generally weak, so the prior motion of the target is taken. Disruption of motion priors

[0202] Model probabilities after updating the model for sensors s, s = 1, 2, ..., S Perform differentiation and find the absolute value

[0203]

[0204] Further determine the rate of change Δμ of the sensor s model. k,s

[0205]

[0206] B121: Initialization: s = 1, interference track number I = s

[0207] B122: Interference track determination

[0208] Combined with the turning rate of sensor s, s=1,2,…S The interference trajectory is determined based on the target maneuver's prior conformity and the model's rate of change, using the following criteria:

[0209] I. If Δμ k,s >η·Δμ k,s+1 ,or

[0210] I = s

[0211] s = s + 1;

[0212] II. If Δμ k,s <η·Δμ k,s+1 ,or

[0213] I = s + 1;

[0214] s = s + 1;

[0215] Repeat steps I to II until s = S-1;

[0216] Where η is the decision coefficient, which is related to the actual application scenario. The actual combat scenario has an impact on the threshold that cannot be ignored. In engineering, it is common to use statistical methods to determine the threshold for specific combat scenarios, and then fit a parameter that can guarantee performance by debugging the experimental data. In this embodiment, η = 1 is taken.

[0217] 4) Iterative repetition

[0218] Iterate k = k + 1; repeat steps 2) to 3) until k = L, the iteration ends, and the interference track number is output.

[0219] from Figure 4 As can be seen, when the interference is released, the model probability updated by the sensor tracking the interference will change, while the model probability of the sensor tracking the target remains basically unchanged. By using the target maneuver prior conformity and the model change rate, the interference track can be accurately identified and eliminated. Figure 5 As can be seen, by setting an appropriate threshold through the judgment threshold, it can be determined that interference has occurred in the composite seeker tracking, and one of the sensors is experiencing interference.

Claims

1. A method for identifying interference tracks of a composite seeker based on interactive multi-model architecture, characterized in that, The specific steps are as follows: 1) Initialize system parameters Assume that the composite seeker is equipped with multiple sensors, and these sensors simultaneously detect a moving target in the same space, recording the target's initial state and the total motion time L. 、 System sampling interval T； It is assumed that the target moves within a specified time, the sensor tracks the target simultaneously, and then begins to release interference, which moves in an unpredictable manner. 2) Multi-model system modeling and interaction estimation First, a state model is determined to describe the motion of the target. Then, a multi-model system model is built. Next, the system state transition matrix of the state model is calculated. Then, the transition probability of each state model is determined and the transition probability matrix between the state models is calculated. After the model states are interacted and filtered in sequence, the turning rate of each state model is calculated based on the filtering results. Through the interaction process, the updated model probability and system state estimate are obtained. The state equations for a multi-sensor, multi-model system are as follows: ， in, express k Time of the first m The target motion state vector of the model, superscript T Represents matrix transpose. These represent the target's position and velocity along the x-axis, respectively. This indicates the target's position and velocity along the y-axis. T The sampling interval is... express k -1 moment m The state transition equations of the model This represents the target motion state vector of the m-th model at time k-1. Indicates process noise; State models include uniform velocity (CV), cooperative turning (CT), and uniform acceleration (CA) models, and the system state transition matrix of the models. , , They are represented as follows: The system state transition matrix of the uniform velocity model for ， Cooperative turning model system state transition matrix for ， in, This represents the turning rate of the target's motion state at time k. T Given a sampling interval, the state transition matrix of the cooperative turning model under unknown turning rates is: ， in, Indicates the turning rate state coefficient; State transition matrix of uniformly accelerated model system for ， The measurement equation is ,in, This represents the sensor's measurement value at time k. Represents measurement noise. Represent the measurement equation; 3) Calculate the interference decision threshold Based on the updated model probabilities obtained in step 2), the interference decision threshold is calculated. Then, after determining the interfering trajectory based on the calculated interference decision threshold, the specific sensor affected by the interference is further identified, as follows: Sensor s undergoes interactive multi-model estimation (i.e., step 2) to obtain the updated model probability of sensor s at time k. Two models are used: uniform motion and cooperative turning. Therefore, the updated model probability is denoted as... and ; B11: Interference detected in flight path First, calculate the interference decision threshold. : ， in, This represents the CV probability of the uniform velocity model in sensor i at time k. This represents the CV probability of the uniform velocity model in sensor j at time k; Set threshold If the interference threshold Exceeding the threshold This indicates that the seeker's tracking is being interfered with, and it is determined that an interference track has appeared. threshold The value of is determined using the Neyman-Pearson criterion, ensuring that the false alarm rate does not exceed the tolerable range, thereby achieving optimal decision performance. ， in, Represents the error function, superscript -1 Represents the reciprocal count. represent variance; In addition, take the false alarm probability , Then we can obtain B12: Identify interference tracks After determining the interfering track based on the interference decision threshold calculated in step B11), the specific sensor that is being interfered with is further identified. First, determine the prior of interference release. and the prior knowledge of target mobility Assuming the target is a ship moving at sea, we take the target's maneuverability as a priori. Interference release prior ; For sensors s , s=1,2,…S Model probabilities after update Perform differentiation and find the absolute value : ， Further determine the rate of change of the sensor model s : ， B121: Initialization: s=1, interference track number I=s; B122: Interference track determination Combined with sensors s , s=1,2,…S Turning rate The interference trajectory is determined based on the target maneuver's prior conformity and the model's rate of change, using the following criteria: I. If ,or , , I=s; s = s + 1; II. If ,or , , I = s + 1; s = s + 1; Repeat steps I to II until s = S-1; in, Let be the decision coefficient, and take . ; 4) Output interference track number Iteration Repeat steps 2) to 3) until... The iteration ends, and the interference track number is output.

2. The method for identifying interference tracks of a composite seeker based on an interactive multi-model approach according to claim 1, characterized in that, Calculation of transition probabilities for each model: Assuming a total of M There are 10 models, each capable of describing any possible target motion state. The transition probabilities between the system models are represented using Markov chains. ， in, The representation system consists of a model i To model j The transition probability.

3. The method for identifying interference tracks of a composite seeker based on an interactive multi-model approach according to claim 1, characterized in that, Particle filtering is used to handle the state interactions between different models, specifically as follows: a: Obtain particle sample swarms for each model If k=1 The initial particle state and its corresponding weights are generated based on known priors or the results of detection and tracking preprocessing. In practical applications, Gaussian approximation is performed based on the track header output at the start of the track to obtain the initialized particle state. Initialize particle weights as ,in N Indicates the number of sampled particles; If k>1 Based on the known state variables at time k-1 and covariance Generate particle sample swarms for each model The Gaussian approximation strategy is adopted to approximate the particle samples of each model as a Gaussian distribution, that is, Gaussian fitting is performed on the particles after each iteration. ， Where N(.) denotes the Gaussian distribution marker; b: Particle interactions between models Based on the given model transition probability Known model probability State variables and covariance Each particle The particles obtained through interaction with other models are represented as follows: ， in, This represents the update probability of each model at time k-1. The probability that the model is m at time k and i at time k-1 is calculated as follows: ， in, Normalization constant 。 4. The method for identifying interference tracks of a composite seeker based on an interactive multi-model approach according to claim 1, characterized in that, Particle filtering is used to filter the states of each model, specifically as follows: i: Based on the state equation, the particles after interaction To make a prediction ， ii: Calculate the weights of each particle ， in, Indicates proportionality by the sign. Let represent the likelihood function, used to describe the measured density of predicted particles. Its distribution model is specific to the actual scenario, assuming it follows a Rayleigh distribution, denoted as . ， The measurement equation is as follows: ， This represents the sensor's measurement value at time k. Represents measurement noise. Represent the measurement equation; iii: Resample the predicted particles to obtain ; To avoid particle decay, the sampled particles are resampled, that is, all particles are resampled. The weights are normalized, and then the normalized particle set is resampled. The resampling uses a system resampling algorithm, which includes the following steps: ①: Initial , , where U[.,.] represents a uniform distribution within the interval; ②: Calculation ; ③: Calculation ; like ,but Return to step ②; otherwise, record the first step. n The particle is at position j; iv: Use resampled particles to perform state estimation for each model ， The covariance matrix of the target state of each model is estimated using the least mean square criterion. Based on the filtering results, the turning rate of each model is estimated.

5. The method for identifying interference tracks of a composite seeker based on an interactive multi-model approach according to claim 4, characterized in that, The turning rate estimates for each model are as follows: Based on the filtering results Calculate the turning rate of each state model. : For the uniform velocity model, the filtering result is: The estimated turning components of the x-axis and y-axis are denoted as: ， The turning rate of the uniform velocity model is estimated as follows: ， For the cooperative turning model, it is obtained by weighting the sampled particles, i.e. ， in, This represents the turning rate of each sampled particle.

6. The method for identifying interference tracks of a composite seeker based on an interactive multi-model approach according to claim 1, characterized in that, The probability updates and system state estimates for each model are as follows: Updating the model probabilities, we get: ， in, The likelihood function of each model filter is generally assumed to be Gaussian distributed and is calculated using the following formula. ， Where exp[.] denotes an exponential function with base e. Indicates information, used to describe the difference between the predicted and measured values ​​of a measurement: ， in, This represents the sensor's measurement value at time k. Indicates the predicted measurement value; The covariance matrix representing the new information is used to measure the uncertainty of the new information. ， Calculate the probability model of each model being correct. Then, by weighting the state estimates when each model is correct, the system state estimate is obtained: ， Similarly, turning rate estimation: 。

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