Single radiation source tracking method under far and near field change based on Bernoulli filter

Abstract

The invention provides a single radiation source tracking method based on a Bernoulli filter under far and near field changes, in the aspects of detection and tracking, likelihood is constructed by using a fuzzy function, a likelihood function of a Bernoulli filter adopting intensity as measurement is designed, centralized implementation is adopted, and the performance of the method is superior to that of a distributed likelihood function. According to the direct tracking method, intermediate errors of two-step tracking and hard decision in a traditional detection and tracking algorithm are avoided, the adaptability of the algorithm to complex scenes and the robustness under the low signal-to-noise ratio can be improved, and the target tracking performance is improved. According to the method, the problem of single radiation source detection and tracking under the conditions of unknown target appearance time and unknown target far and near fields is solved directly from receiving data, and the method has good performance, has adaptability and robustness to the environment and can meet design requirements in engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to a single radiation source tracking method under far-field and near-field variations based on a Bernoulli filter. Background Art

[0002] With the advancement of network, communication, and computer technologies, emitter tracking methods have gradually evolved from the data level to the signal level. Direct tracking of moving emitters based on raw signal echoes has garnered increasing attention. Traditional emitter tracking is a two-step approach. First, the parameters of the target to be tracked are estimated from the received signal. Then, using the estimated intermediate parameters as input, appropriate filters are selected to process these parameters to estimate the number and state of targets within the detection area. This approach results in estimation errors that cannot be corrected in the next stage, leading to error accumulation and making it difficult to effectively track targets in real time in complex scenarios. Compared to the traditional two-step tracking method, direct tracking algorithms utilize the entire information of the received signal at the receiving station, thereby reducing the error accumulation inherent in the two-step method.

[0003] In the problem of single-radiator tracking, unlike traditional signal modeling methods, this invention introduces signal modeling in both far-field and near-field conditions. Based on the different positional relationships between the radiation source and the receiving station, a more precise signal modeling method is adopted, making the invented method more accurate than traditional methods. In terms of likelihood functions, compared to the traditional single likelihood function, due to the introduction of far-field and near-field conditions, the likelihood functions in this paper are transformed into far-field and near-field likelihood functions. By comparing these two likelihood functions, the target's true far-field and near-field conditions can be determined, thereby achieving more accurate target state estimation. Summary of the Invention

[0004] In response to the above problems, the present invention proposes a single radiation source tracking method under the variation of near and far fields based on Bernoulli filter. In terms of detection and tracking, the likelihood is constructed using fuzzy functions, and a likelihood function of a type of Bernoulli filter that uses intensity as measurement is designed. It is implemented in a centralized manner, and its performance is better than the distributed likelihood function. This direct tracking method avoids the intermediate errors of two-step tracking and the hard decisions in traditional detection and tracking algorithms, and can improve the algorithm's adaptability to complex scenes and robustness under low signal-to-noise ratios, thereby improving the target tracking performance. The present invention directly starts from receiving data to realize the detection and tracking problem of single radiation sources under unknown target appearance time and unknown target near and far fields. It has good performance, adaptability and robustness to the environment, and can meet the design requirements in engineering.

[0005] The technical solution adopted in the present invention is:

[0006] The present invention uses signals containing time delay and Doppler shift, discretizing the received signal as input to a Bernoulli filter. Compared to traditional two-step tracking methods, the direct tracking algorithm effectively reduces the resulting intermediate errors. Furthermore, the entire system is Bernoulli, and information is transmitted in a probabilistic manner, making the proposed scheme highly robust and scalable. Furthermore, because the likelihood function utilizes all relevant information from each receiving station, it can achieve target tracking at lower signal-to-noise ratios.

[0007] In the radiation source tracking scenario, there are receiving stations Each receiving station has receiving antennas, each antenna element is located at point The receiving antennas are arranged in a uniform linear array. The first unit in the antenna array is used as the reference unit. The adjacent antennas are spaced , the maximum geometric size of the antenna is recorded as , which can be calculated under uniform linear array conditions . Receiving stations Axis and The position vector composed of the axes is , the receiving stations are all stationary, there is a single radiation source, and the position of the radiation source is ,in Representatives in Position in direction, Representatives in The position in the direction and the speed are ,in Representatives in Speed ​​in direction, Representatives in Speed ​​in the direction, the target state is the concatenation of the position and velocity vectors , define the observation time as , reference unit in the receiving station Received signal at the moment for:

[0008]

[0009] in, is a constant, Indicates distance The signal amplitude at (the distance between the radiation source and the reference antenna unit) is It is the signal emitted by the radiation source. is the angular frequency of the signal, is the wavelength of the signal, it can be seen It not only affects the phase of the received signal, but also the amplitude of the signal. The amplitude of the received signal is inversely proportional to the distance. Assuming that the narrowband signal emitted by the radiation source is received by the receiving antenna array, the propagation delay can be converted into phase. Then the first The signal received by each antenna unit is:

[0010]

[0011] in, is additive Gaussian noise, The radiation source and The distance between antenna elements.

[0012]

[0013] It is the angle between the line connecting the radiation source and the reference unit and the plane where the antenna unit is located. At this time, the antenna array The signal received at time can be expressed as

[0014]

[0015] in is additive Gaussian noise, For array flow type, it can be calculated by the following formula

[0016]

[0017] The above formula can be used for signal modeling, but the calculation is too complicated to obtain an analytical solution. Therefore, the Taylor expansion method is used to obtain different approximate solutions under far-field and near-field conditions.

[0018] The conditions for far and near field division are as follows:

[0019]

[0020] From the formula, we can see that the signal amplitude received by different antenna units will vary depending on the distance between the antenna unit and the target. When the radiation source is in the near field, the signal amplitude received by all antenna units is roughly the same, that is, , at this time there is only a phase difference. Performing Taylor expansion and retaining the second-order quantity, we can obtain:

[0021]

[0022] If the radiation source is further away from the receiving antenna array until it is in the far field, then the signal reaching each element of the antenna is approximately a plane wave, that is, At the same time, the propagation distance is much greater than the distance between the receiving antenna units, so we can get .right Perform Taylor expansion and retain the first-order quantity to obtain the following formula:

[0023]

[0024] It can be seen that unlike the near-field case, the phase term in the far-field case is no longer related to the distance related, but only depends on the direction angle of the signal .

[0025] The joint detection and direct tracking method includes:

[0026] S1. Obtain measurement data and The Bernoulli distribution parameter of the moment target, where the measurement data is obtained by Sampling obtained, The measurement matrix at time is expressed as ; The Bernoulli distribution parameter is ,express The existence probability of the target at each moment, the particle weight and the particle state, It is the spatial probability density function used to approximate the Bernoulli distribution The weighted particles, To predict the number of particles;

[0027] S2, yes The existence probability of the target at the moment is predicted, and the spatial probability density function is obtained, which is specifically:

[0028] The predicted probability of existence at the moment for:

[0029]

[0030] in, 、 and Respectively The existence probability, particle weight and particle state at the moment, is the probability of new birth, is the survival probability, , is the number of newly generated particles;

[0031] Spatial probability density function Particles By the prediction part and freshmen section composition:

[0032]

[0033] in, is the predicted probability density of the state, The mean is , the variance is Gaussian function, is the process noise covariance matrix, is the density of newborn particles whose states are known, and the predicted particle weight for:

[0034]

[0035] S3. State function according to the target Construct the likelihood function:

[0036]

[0037]

[0038] in,

[0039]

[0040] and is the likelihood function with and without a target, and are the noise variance and signal variance respectively, is the M-dimensional identity matrix, Points for the snap, Represents the probability density function of the complex Wishart distribution matrix. As mentioned above, The formulas are different in the far-field and near-field cases, so the likelihood functions are also different in the far-field and near-field cases;

[0041] S4. Calculate the parameters related to the likelihood of each particle, including:

[0042] Assuming far field and near field respectively, when calculating without target and with target, the The likelihood function of the receiving station is:

[0043]

[0044]

[0045] The obtained multiple likelihood functions are fused to obtain the likelihood of no target and target in the near and far field respectively:

[0046]

[0047]

[0048] Calculate the likelihood ratio for the far and near field cases:

[0049]

[0050] By comparing the likelihood ratio in the far and near fields, it is determined whether the target is in the far field or the near field.

[0051] S5. Use the obtained likelihood ratio to calculate the integral of the approximate likelihood ratio:

[0052]

[0053] S6. Update the Bernoulli parameters and get Bernoulli parameter at time , where the probability of existence is:

[0054]

[0055] S7. For each particle, update the particle weight according to the calculated likelihood of having a target , and then normalize the particle weights:

[0056]

[0057] S8, resampling, for and ,by The probability of selecting particles is high, and the probability of particles with large weights being selected is high. The particle state after resampling is:

[0058]

[0059] S9. Reset the particle weight to ;

[0060] S10, get The existence probability, particle weight and particle state of the target at the moment, and the state extraction is performed to obtain , Include The estimated values ​​of the target's position, velocity and signal power at the moment; iterative processing, , until all moments are processed.

[0061] The beneficial effects of the present invention are:

[0062] 1) This invention uses a Bernoulli filter to solve the tracking problem using signals as measurements. It also introduces a likelihood function based on fuzzy functions for typical radiation source tracking scenarios and for near- and far-field scenarios. This solves the problem of calculating the likelihood function when the transmitted signal and transmit power are unknown, providing a solution for radiation source tracking in more complex scenarios.

[0063] 2) The present invention can solve the problem of joint detection and direct tracking of radiation sources, avoiding the intermediate errors caused by the traditional two-step tracking method. The method is robust and has good effects under low signal-to-noise ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is the scene graph, including the receiving station location and target motion trajectory;

[0065] Figure 2 for Three likelihood function models are used in Axis and Specific tracking curves for the axis;

[0066] Figure 3 for Below, the average OSPA change curves of the three likelihood models;

[0067] Figure 4 for Next, the target estimates the near and far field situations; DETAILED DESCRIPTION

[0068] The practicability and effectiveness of the present invention are demonstrated below with reference to the accompanying drawings and simulation examples;

[0069] Example

[0070] This example uses MATLAB to verify the above-mentioned radiation source joint detection and tracking algorithm. For simplicity, the following assumptions are made for the algorithm model:

[0071] Simulation conditions and parameters

[0072] Simulation environment: For ease of illustration, consider a representative two-dimensional scenario, assuming two passive receiving stations They are located at [3000,0], [6000,0] respectively, and the target state vector is , the initial position is determined, the speed is unknown, and the total observation time is assumed to be The target moves in a variable speed curve, and the survival probability The measurement equation has been given in the previous article. The carrier frequency of the transmitter is , sampling frequency , The target is born at 0s and disappears at 70s. The target appears from a fixed point, and the target birth model is as follows:

[0073]

[0074] in,

[0075]

[0076] For simulation Natural regeneration near the target (x, y are the initial positions of the target). A total of 3000 particles are used, of which N = 2500 are surviving particles, B = 500 are newborn particles, and the number of Monte Carlo simulations is 100.

[0077] like Figure 2 , Figure 3 As shown, at a lower signal-to-noise ratio ( ), the tracking track of the proposed algorithm is closest to the real track compared to the tracking track using only a likelihood model (near-field model or far-field model). Figure 4 This shows that the proposed algorithm is extremely accurate in estimating the near and far fields of the target. Figure 1-4 From the above analysis, the proposed algorithm is suitable for the joint detection and direct tracking of radiation sources, and has strong robustness to low signal-to-noise ratio and strong adaptability to complex environments with unknown far and near field conditions.

Claims

1. A single radiation source tracking method based on Bernoulli filter under near-far field changes is characterized by: In the radiation source tracking scenario, there are receiving stations Each receiving station has Each receiving antenna is located at point The receiving antennas are arranged in a uniform linear array. The first unit in the antenna array is used as the reference unit. The adjacent antennas are spaced , the maximum geometric size of the antenna is recorded as , ; Record Receiving stations Axis and The position vector composed of the axes is , the receiving stations are all stationary, there is a single radiation source, and the position of the radiation source is ,in Representatives in Position in direction, Representatives in The position in the direction and the speed are ,in Representatives in Speed ​​in direction, Representatives in Speed ​​in the direction, the target state is the concatenation of the position and velocity vectors , define the observation time as , reference unit in the receiving station Received signal at the moment for: ， in, is a constant, Indicates distance The signal amplitude at It is the signal emitted by the radiation source. is the angular frequency of the signal, is the wavelength of the signal, we can get It not only affects the phase of the received signal, but also the amplitude of the signal. The amplitude of the received signal is inversely proportional to the distance. The narrowband signal emitted by the radiation source is received by the receiving antenna array, and the propagation delay is converted into phase. Then the first The signal received by each antenna unit is: ， in, is additive Gaussian noise, The radiation source and The distance between antenna elements; ， It is the angle between the line connecting the radiation source and the reference unit and the plane where the antenna unit is located. At this time, the antenna array The signal received at the moment is expressed as: ， in is additive Gaussian noise, For array flow type: ， is the direction angle of the signal; the signal amplitude received by different antenna units will vary depending on the distance between the antenna unit and the target; when the radiation source is in the near field, the signal amplitude received by all antenna units is roughly the same, that is, , at this time there is only a phase difference; Performing Taylor expansion and retaining the second-order quantity, we obtain: ， When the radiation source is in the far field, the signal reaching each element of the antenna is approximately a plane wave, that is, ; At the same time, the propagation distance is much greater than the distance between the receiving antenna units, then we get ,right Perform Taylor expansion and retain the first-order quantity to obtain: ， It can be seen that the phase term in the far field is no longer related to the distance, unlike the near field case. related, but only depends on the direction angle of the signal ; The tracking method includes: S1. Obtain measurement data and The Bernoulli distribution parameters of the moment target, where the measurement data is obtained by Sampling obtained, The measurement matrix at time is expressed as ; The Bernoulli distribution parameter is ,express The existence probability of the target at each moment, the particle weight and the particle state, It is the spatial probability density function used to approximate the Bernoulli distribution The weighted particles, To predict the number of particles; S2, yes The existence probability of the target at the moment is predicted, and the spatial probability density function is obtained, which is specifically: The predicted probability of existence at the moment for: ， in, 、 and Respectively The existence probability, particle weight and particle state at the moment, is the probability of new birth, is the survival probability, , is the number of newly generated particles; Spatial probability density function Particles By the prediction part and freshmen section composition: ， in, is the predicted probability density of the state, The mean is , the variance is Gaussian function, is the process noise covariance matrix, is the density of newborn particles whose states are known, and the predicted particle weight for: ， S3. State function according to the target Construct the likelihood function: ， ， in, ， and is the likelihood function with and without a target, and are the noise variance and signal variance respectively, is the M-dimensional identity matrix, Points for the snap, Represents the probability density function of the complex Wishart distribution matrix. As mentioned above, The formulas are different in the far-field and near-field cases, so the likelihood functions are also different in the far-field and near-field cases; S4. Calculate the parameters related to the likelihood of each particle, including: Assuming far field and near field respectively, when calculating without target and with target, the The likelihood function of a receiving station is: ， ， The obtained multiple likelihood functions are fused to obtain the likelihood of no target and target in the near and far field respectively: ， ， Calculate the likelihood ratio for the far and near field cases: ， By comparing the likelihood ratios in the far and near fields, it is determined whether the target is in the far field or the near field. S5. Use the obtained likelihood ratio to calculate the integral of the approximate likelihood ratio: ； S6. Update the Bernoulli parameters and get Bernoulli parameter at time , where the probability of existence is: ； S7. For each particle, update the particle weight according to the calculated likelihood of having a target , and then normalize the particle weights: ； S8, resampling, for and ,by The probability of selecting particles is high, and the probability of particles with large weights being selected is high. The particle state after resampling is: ； S9. Reset the particle weight to ; S10, get The existence probability, particle weight and particle state of the target at the moment, and the state extraction is performed to obtain , Include The estimated values ​​of the target's position, velocity and signal power at the moment; iterative processing, , until all moments are processed.

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