Distributed multi-pulse detection method based on local sequence statistics

Abstract

The invention discloses a distributed multi-pulse detection method based on local sequence statistics. The method comprises the following steps: initializing a distributed radar target detection system; performing square law and DMOS-CFAR processing on each radar station to obtain local statistics; each radar station takes the maximum value of the data of the Doppler channel and calculates the probability density function of the data; each radar station uses a probability density function of a Doppler channel data maximum value to calculate test statistics according to likelihood ratio test, and sends the test statistics to the fusion center through a communication link; and the fusion center obtains a global optimal statistical magnitude through the local test statistical magnitude, calculates a global judgment threshold through the global optimal statistical magnitude and the false alarm rate, and finally obtains a target detection result in the spatial resolution unit according to the threshold. According to the invention, the anti-interference capability of a distributed pulse Doppler radar system is greatly improved, and the detection capability and false alarm control capability of a radar target detection algorithm under non-uniform backgrounds such as multi-false target interference and clutter edge are enhanced.

Description

Technical Field

[0001] The invention belongs to the technical field of radar target detection, and in particular relates to a distributed multi-pulse detection method based on local order statistics. Background Art

[0002] Radar target detection refers to the process in which the radar detects targets according to the echo signal in the resolution unit of interest according to a predetermined procedure. In order to improve the probability of detecting the target, multiple spatially dispersed radars are usually used to illuminate the target together. This is the typical distributed radar system framework. In a distributed radar system, in order to obtain better detection results, the radar station transmits the processed local test statistics to the fusion center through a link and makes a global decision. In order to prevent the problem of computational overload caused by excessive calculation of the tracking unit, the radar system is usually designed with a fixed false alarm rate during the target detection stage. Since the noise level in practical applications is usually unknown, the existing methods for estimating the noise level of adjacent distance units in the reference window have major defects.

[0003] The patent document with publication number CN118330601A discloses a "distributed radar target detection method based on Doppler channel maximum quantization". This method improves the signal-to-noise ratio and suppresses clutter through pulse accumulation. In the process of local statistical processing, the DMCA-CFAR (unit average constant false alarm) detection algorithm is adopted. The noise power is estimated by averaging adjacent distance units and a threshold value is set. Although its detection performance is good under uniform background, it is very susceptible to interference from multiple false targets and clutter edges, and its anti-interference ability is poor.

[0004] The patent document with publication number CN116106845A discloses "a target detection method based on square root detection and CA-CFAR". This method performs CA-CFAR (unit average) detection after matched filtering and square root detection transformation. It can significantly improve the ability to suppress the shielding effect caused by interfering targets without causing additional detection losses, and the calculation amount is small and easy to implement in engineering. However, this method only optimizes the CA-CFAR algorithm for the case of multi-target interference, does not take into account the clutter edge environment, and does not verify the performance in non-uniform scenes. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a distributed multi-pulse detection method based on local order statistics. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0006] The present invention provides a distributed multi-pulse detection method based on local order statistics, the method comprising:

[0007] Initialize the distributed radar target detection system; the distributed radar target detection system includes: a fusion center and M radar stations distributed in three-dimensional space, each radar station S m N pulses are emitted within a coherent processing time, and the false alarm probability of the fusion center is P fa , each radar station S m Set the same reference window number n; where M≥2, N≥2, n≥2;

[0008] Each radar station S m The signal amplitude in the spatial resolution unit is sampled, and the data is sorted according to the gradient and the order value to obtain sorted data. The sorted data is processed based on the square law and the DMOS-CFAR detection algorithm to obtain the local statistics t of each Doppler channel. m ;

[0009] Each radar station S m The local statistics of the Doppler channel t m Take the maximum value to get η m , through t m The cumulative distribution function of and Get η m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists right and Derived separately, we get η under two assumptions m The probability density function of and

[0010] Each radar station S m based on and Calculate the corresponding local test statistic L(η) according to the likelihood ratio test, and transmit L(η) to the fusion center;

[0011] The fusion center obtains the global optimal statistic T according to the local test statistic L(η) opt ; Based on the global optimal statistic T opt and false alarm probability P fa Get the global decision threshold g of the distributed radar target detection system; based on the global optimal statistics T opt And the global decision threshold g determines whether there is a target in the spatial resolution unit.

[0012] In one embodiment of the present invention, the false alarm probability P of the fusion center is fa =10 -4 .

[0013] In one embodiment of the present invention, each radar station S m The signal amplitude in the spatial resolution unit is sampled, and the data is sorted according to the gradient and the order value to obtain sorted data. The sorted data is processed based on the square law and the DMOS-CFAR detection algorithm to obtain the local statistics t of each Doppler channel. m ,include:

[0014] Each radar station S m The signal amplitude in the spatial resolution unit is sampled to obtain S m The output signal r of a coherent processing time m and S m The observation values ​​of the reference window; sort the obtained observation values ​​according to the increment size and sequence value j to obtain the sorted data Y (m,j) , j=1,2,…,n; the sorting is as follows:

[0015] Y (m,1) ≤Y (m,2) ≤…≤Y (m,n) ;

[0016] Among them, Y (m,1) is the minimum value, Y (m,n) is the maximum value;

[0017] According to S m The output signal r m And the sorted data Y (m,j) , use the first formula to calculate each radar station S m The local statistics of the Doppler channel t m ;

[0018] The first formula is as follows:

[0019]

[0020] Among them, t m =[t m,1 ,…,t m,i ,…,t m,N ], i=1,2,…,N.

[0021] In one embodiment of the present invention, t m The cumulative distribution function of and The expression is as follows:

[0022]

[0023] Where S represents the signal-to-noise ratio of the radar station, j represents the selected order value, and t m,i ∈tm , i=1,2,…,N.

[0024] In one embodiment of the present invention, n m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists The expression is as follows:

[0025]

[0026] Among them, η m =t m,l , l is the index of the unit where the maximum value of the Doppler channel is located, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding distribution function is represents t under the target existence hypothesis H1 m Medium m,i The corresponding distribution function.

[0027] In one embodiment of the present invention, under two assumptions, n m The probability density function of and The expression is as follows:

[0028]

[0029] in, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding probability density function is, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding distribution function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding probability density function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding distribution function.

[0030] In one embodiment of the present invention, each radar station S m based on and The corresponding local test statistic L(η) is calculated based on the likelihood ratio test, including:

[0031] Each radar station S m based on and The corresponding local test statistic L(η) is calculated using the second formula according to the likelihood ratio test;

[0032] The second formula is as follows:

[0033]

[0034] Among them, t m,i ∈t m , S represents the signal-to-noise ratio of the radar station, j represents the selected order value, and η represents the maximum value of the Doppler channel.

[0035] In one embodiment of the present invention, the global optimal statistic T opt The expression is as follows:

[0036]

[0037] Wherein, ln{·} represents the natural number logarithm operation.

[0038] In one embodiment of the present invention, based on the global optimal statistic T opt and false alarm probability P fa The global decision threshold g of the distributed radar target detection system is obtained, including:

[0039] Based on the global optimal statistics T opt and false alarm probability P fa , the global decision threshold g of the distributed radar target detection system under the assumption that the target does not exist is calculated using the third formula;

[0040] The third formula is as follows:

[0041] g=T opt (H0) -1 (1-P fa );

[0042] in,(·) -1 represents the inverse function of (·).

[0043] In one embodiment of the present invention, based on the global optimal statistic T opt And the global decision threshold g determines whether there is a target in the spatial resolution unit, including:

[0044] Determine the global optimal statistic T opt ≥Whether the global decision threshold g holds:

[0045] If so, there is a target in the spatial resolution unit.

[0046] Otherwise, there is no target in the spatial resolution unit.

[0047] Beneficial effects of the present invention:

[0048] In the solution provided by the present invention, the local statistics of each radar station are processed by the DMOS-CFAR detection algorithm, thereby avoiding the problem of poor noise estimation by averaging adjacent distance units in the existing DMCA-CFAR detection algorithm under non-uniform background, and eliminating the influence of multiple false target interference and clutter edge environment by selecting appropriate sequence values, thereby greatly improving the anti-interference capability of the distributed pulse radar system, and enhancing the detection capability and false alarm control capability of the radar target detection algorithm under non-uniform backgrounds such as multiple false target interference and clutter edge. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A schematic flow chart of a distributed multi-pulse detection method based on local order statistics provided by an embodiment of the present invention;

[0050] Figure 2 It is a curve diagram showing the variation of detection performance of different detection algorithms with signal-to-noise ratio under the interference of multiple false targets;

[0051] Figure 3 This is a curve diagram showing the detection performance of different detection algorithms changing with the signal-to-noise ratio when the target is in a weak clutter area at the edge of the clutter;

[0052] Figure 4 This is a curve diagram of false alarm probability of different detection algorithms changing with clutter power when the detection unit is a strong clutter area at the edge of the clutter. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0054] In a distributed radar system, in order to obtain better detection results, the radar station transmits the processed local test statistics to the fusion center through a link and makes a global decision. Distributed radar systems often use constant false alarm detection to process local statistics. By setting a fixed false alarm rate, the problem of excessive computational complexity of the tracking unit is avoided, and the noise level of adjacent distance units in the reference window is estimated. However, in engineering practice, the existing technology represented by distributed multi-pulse unit average constant false alarm detection (DMCA-CFAR for short) faces detection performance loss in non-uniform scenarios such as multiple false target interference and clutter edges, and cannot meet the requirements of modern radar anti-interference capabilities. To address this pain point, an embodiment of the present invention provides a distributed multi-pulse detection method based on local order statistics, such as Figure 1 As shown, it may include:

[0055] S1, initialize the distributed radar target detection system.

[0056] Specifically, the distributed radar target detection system includes: a fusion center and M radar stations distributed in three-dimensional space, each radar station S m N pulses are emitted within a coherent processing time, and the false alarm probability of the fusion center is P fa , each radar station S m Set the same reference window number n; where M≥2, N≥2, n≥2. In the embodiment of the present invention, the false alarm probability P of the fusion center fa Can be set to P fa =10 -4 , M can be set to 3, N can be set to 4, and the reference window is the window used to estimate the noise power.

[0057] S2, each radar station S m The signal amplitude in the spatial resolution unit is sampled, and the sorted data is obtained by sorting according to the gradient and sequence value. The sorted data is processed based on the square law and DMOS-CFAR detection algorithm to obtain the local statistics t of each Doppler channel. m .

[0058] For S2, this may include:

[0059] S21, each radar station S m The signal amplitude in the spatial resolution unit is sampled to obtain S m The output signal r of a coherent processing time m and S m The observation values ​​of the reference window; sort the obtained observation values ​​according to the increment size and sequence value j to obtain the sorted data Y (m,j) , j=1,2,…,n; the sorting is as follows:

[0060] Y (m,1) ≤Y (m,2) ≤…≤Y (m,n) ;

[0061] Among them, Y (m,1) is the minimum value, Y (m,n) is the maximum value, and m represents the serial number of the mth radar station.

[0062] S22, according to S m The output signal r m And the sorted data Y (m,j) , use the first formula to calculate each radar station S m The local statistics of the Doppler channel t m ;

[0063] The first formula is as follows:

[0064]

[0065] Among them, t m =[t m,1 ,…,t m,i ,…,t m,N ], i=1,2,…,N.

[0066] It is understandable that the output signal r m and the local statistic t m All are vectors.

[0067] S3, each radar station S m The local statistics of the Doppler channel t m Take the maximum value to get η m , through t m The cumulative distribution function of and Get η m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists right and Derived separately, we get η under two assumptions m The probability density function of and

[0068] For S3, the following may be included:

[0069] S31, each radar station S m The local statistics of the Doppler channel t m Take the maximum value to get η m , through t m The cumulative distribution function of and Get η m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists

[0070] Specifically, in the embodiment of the present invention, the fluctuation characteristics of the target amplitude can be assumed to be a Swerling I model, t m The probability density function of and The expression is as follows:

[0071]

[0072] Where n is the total number of reference windows, S is the signal-to-noise ratio of the radar station, j is the selected order value, and t m,i ∈t m, i=1,2,…,N.

[0073] t m The cumulative distribution function of and The expression is as follows:

[0074]

[0075] Among them, S represents the signal-to-noise ratio of the radar station, and j represents the selected order value.

[0076] Doppler channel maximum value η m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists The expression is as follows:

[0077]

[0078] in, for In the Doppler channel data t m The cumulative distribution function at the maximum value, η m =t m,l , l is the index of the unit where the maximum value of the Doppler channel is located, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding distribution function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding distribution function.

[0079] S32, yes and Derived separately, we get η under two assumptions m The probability density function of and

[0080] Specifically, under the two assumptions, η m The probability density function of and The expression is as follows:

[0081]

[0082] in, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding probability density function is, represents t under the hypothesis H0 that the target does not exist m Medium m,iThe corresponding distribution function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding probability density function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding distribution function.

[0083] It can be understood that the embodiment of the present invention adopts a distributed multi-pulse detection method (DMOS-CFAR) based on local order statistics for local statistics, eliminates the interference of multiple false targets and the influence of clutter edges by selecting appropriate order values, and sets up a comparative simulation experiment below to verify the anti-interference ability of the method proposed in the embodiment of the present invention.

[0084] S4, each radar station S m based on and The corresponding local test statistic L(η) is calculated based on the likelihood ratio test and transmitted to the fusion center.

[0085] For S4, this may include:

[0086] Each radar station S m based on and The corresponding local test statistic L(η) is calculated using the second formula according to the likelihood ratio test;

[0087] The second formula is as follows:

[0088]

[0089] Among them, t m,i ∈t m , S represents the signal-to-noise ratio of the radar station, j represents the selected order value, and η represents the maximum value of the Doppler channel.

[0090] S5, the fusion center obtains the global optimal statistic T according to the local test statistic L(η) opt ; Based on the global optimal statistic T opt and false alarm probability P fa Get the global decision threshold g of the distributed radar target detection system; based on the global optimal statistics T opt And the global decision threshold g determines whether there is a target in the spatial resolution unit.

[0091] For S5, this may include:

[0092] S51, the fusion center obtains the global optimal statistic T according to the local test statistic L(η) opt .

[0093] Specifically, the fusion center calculates the global optimal statistic T according to m local test statistics L(η) opt , the global optimal statistic T opt The expression is as follows:

[0094]

[0095] Wherein, ln{·} represents the natural number logarithm operation.

[0096] It can be understood that the embodiment of the present invention designs an optimal fusion algorithm based on the Neyman-Pearson criterion (Neyman-person) in the fusion center to calculate the global optimal statistics, so as to make a global decision to determine whether there is a target.

[0097] S52, based on the global optimal statistic T opt and false alarm probability P fa Obtaining the global decision threshold g of the distributed radar target detection system may include:

[0098] Based on the global optimal statistics T opt and false alarm probability P fa , the global decision threshold g of the distributed radar target detection system under the assumption that the target does not exist is calculated using the third formula;

[0099] The third formula is as follows:

[0100] g=T opt (H0) -1 (1-P fa );

[0101] in,(·) -1 represents the inverse function of (·).

[0102] S53, based on the global optimal statistic T opt The global decision threshold g is used to determine whether there is a target in the spatial resolution unit, which may include:

[0103] Determine the global optimal statistic T opt ≥Whether the global decision threshold g holds:

[0104] If so, there is a target in the spatial resolution unit.

[0105] Otherwise, there is no target in the spatial resolution unit.

[0106] It can be understood that the embodiment of the present invention designs an optimal fusion algorithm based on the Neyman-Pearson criterion (Neyman-person) in the fusion center to calculate the global optimal statistics, so as to make a global decision to determine whether the target exists. Compared with the existing DMCA-CFAR that averages the noise of adjacent distance units, under the interference of multiple false targets, the distributed multi-pulse detection method (DMOS-CFAR) based on local order statistics provided by the embodiment of the present invention determines the threshold value by selecting the order value. On the one hand, it solves the problem that the traditional detection algorithm is interfered by false targets and the background noise is poorly estimated. On the other hand, selecting the optimal order value can effectively avoid the order value being too high to include the false target into the background noise power estimation value and raise the threshold, or the order value being too low to ignore the high amplitude noise and underestimate the threshold. And it has been proved by simulation experiments that under the condition of maintaining a certain global constant false alarm rate, the correct detection probability of DMOS-CFAR that selects the optimal order value is higher than that of DMCA-CFAR. Compared with the existing DMCA-CFAR which averages the noise of adjacent distance units, in the clutter edge environment, the DMOS-CFAR detection algorithm determines the threshold value by selecting the optimal sequence value, avoiding the contamination of the detection unit by high-energy clutter to raise the threshold, or the low-energy clutter to lower the threshold. The simulation experiment proves that the correct detection probability of DMOS-CFAR under the optimal sequence value condition is higher than that of DMCA-CFAR, and the ability to control false alarms is also better than DMCA-CFAR.

[0107] The embodiment of the present invention adopts the DMOS-CFAR detection algorithm to process the local statistics of each radar station respectively, thereby avoiding the problem of poor noise estimation by averaging adjacent distance units in the existing DMCA-CFAR detection algorithm under non-uniform background, eliminating the influence of multiple false target interference and clutter edge environment by selecting appropriate sequence values, thereby greatly improving the anti-interference capability of the distributed pulse radar system, and enhancing the detection capability and false alarm control capability of the radar target detection algorithm under non-uniform backgrounds such as multiple false target interference and clutter edge.

[0108] The technical effects of the present invention are further described in detail below in conjunction with simulation experiments.

[0109] Simulation conditions:

[0110] In the distributed radar system, three radar stations and one fusion center are set, the number of pulses is 4, and the false alarm probability is set to 10 -4 The signal-to-noise ratio of local radar stations is set to S, and the total signal-to-noise ratio ranges from 0dB to 25dB. The selection order value is set to j = 6, 12, 18, 24, and two control experiments are set: Neyman-person optimal detection and DMCA-CFAR.

[0111] Simulated hardware environment: CPU is AMD Ryzen 5 5625U with Radeon Graphics, main frequency is 2.3Ghz, main memory is 16GB. Software environment: Windows 11 Home Chinese version, MATLAB R2023a simulation software.

[0112] Simulation content:

[0113] a. Multiple false target interference

[0114] The false target interference is set at the 90th, 95th, 105th and 110th distance units, with an interference-to-noise ratio of 10dB, and the real target is located at the 100th distance unit, with a signal-to-noise ratio of 14dB. Figure 2 The curves of detection performance of different detection algorithms with signal-to-noise ratio under the interference of multiple false targets are shown in Figure 2. Figure 2 It can be seen that when the order value j is 24 (the maximum value of the order statistic), the detection performance is the lowest. This is because the interference amplitude of the false target is large. After sorting, the interference target has a higher probability of becoming the maximum value of the order statistic. At this time, if it is still used as the estimated value of the background noise power, it will greatly raise the detection threshold, resulting in a loss of detection performance. When j = 12, 18, from a statistical point of view, the interference target is unlikely to affect the estimation of the noise power, that is, j = 18 has a higher threshold value than j = 12, effectively controlling false alarms and having better detection performance. j = 6 has worse detection performance than j = 12, 18, but is better than j = 24. Under the interference of multiple false targets, the detection performance of DMCA-CFAR is worse than that of DMOS-CFAR when j=12,18, which proves the superiority of the proposed DMOS-CFAR algorithm in multi-target scenarios. Under the condition of maintaining a constant false alarm rate, by selecting appropriate sequence values ​​(such as j=12,18), the correct detection probability of DMOS-CFAR is significantly higher than that of DMCA-CFAR.

[0115] b. Clutter edge environment

[0116] The ratio of the number of reference cells in the low-energy clutter area to the high-energy clutter area is set to 2:1. Figure 3 The curves of detection performance of different detection algorithms versus signal-to-noise ratio when the target is in the weak clutter area at the edge of the clutter are shown in Figure 2. Figure 3It can be seen that the detection performance when j=18 is lower than that when j=12. This is because after sorting, the high-energy clutter is located in the order statistics of 2n / 3 (the ratio of the number of reference units in the low-energy clutter area to the high-energy clutter area is 2:1) and above. j=18 is a reference unit contaminated by high-energy clutter. If it is still used as an estimated value of the background noise power, the detection threshold will be raised, resulting in a loss of detection performance. If the order value j is 24, the pollution is more serious, and the detection performance loss is the greatest. When j=6, from a statistical point of view, the high-energy clutter at this time is unlikely to affect the estimation of the noise power, so it is consistent with the simulation results of the uniform background, that is, the detection performance of j=6 is worse than that of j=12, but better than that of j=24. It should be noted that in the clutter edge environment, the detection performance of DMCA-CFAR is worse than that of DMOS-CFAR when j = 6, 12, and 18. This proves the superiority of the proposed DMOS-CFAR algorithm in the clutter edge environment. Under the condition of maintaining a constant false alarm rate, by selecting appropriate sequence values ​​(j = 6, 12, 18), the correct detection probability of DMOS-CFAR is significantly higher than that of DMCA-CFAR. Figure 4 The curves of false alarm probability of different detection algorithms changing with clutter power when the detection unit is a strong clutter area at the edge of the clutter. Figure 4 It can be seen that the false alarm control ability of DMOS-CFAR is significantly better than that of DMCA-CFAR.

[0117] In summary, the local DMOS-CFAR detection algorithm proposed in the present invention can greatly enhance the anti-interference capability of the radar system in the environment of multiple false target interference and clutter edge, improve the target detection probability and false alarm control capability, and expand the application ideas of distributed radar systems in non-uniform backgrounds.

[0118] The distributed multi-pulse detection method (DMOS-CFAR) based on local order statistics proposed in the embodiment of the present invention eliminates the interference of multiple false targets and the influence of clutter edges by selecting appropriate order values, thereby improving the anti-interference ability of the distributed pulse Doppler radar system in non-uniform backgrounds such as multiple false target interference and clutter edges. The embodiment of the present invention greatly expands the application of the target detection algorithm of the distributed radar system in non-uniform backgrounds, and provides a new idea for the signal-level fusion detection method, that is, in the face of complex interference and clutter scenes, DMOS-CFAR or improved methods based on it can be tried to suppress clutter and interference and improve the robustness of the radar system. In addition to multiple false targets and clutter edges, the appropriate selection of order values ​​can also effectively suppress or eliminate certain processed atmospheric noise, which means that the present invention greatly enriches the application scenarios of radar systems on the sea and in the air.

[0119] It should be noted that in the description of the present invention, it should be understood that the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0120] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A distributed multi-pulse detection method based on local order statistics, characterized in that: include: Initialize the distributed radar target detection system; The distributed radar target detection system includes: a fusion center and M radar stations distributed in three-dimensional space, each radar station S m N pulses are emitted within a coherent processing time, and the false alarm probability of the fusion center is P fa , each radar station S m Set the same reference window number n; where M≥2, N≥2, n≥2; Each radar station S m The signal amplitude in the spatial resolution unit is sampled, and the data is sorted according to the gradient and the order value to obtain sorted data. The sorted data is processed based on the square law and the DMOS-CFAR detection algorithm to obtain the local statistics t of each Doppler channel. m ; Each radar station S m The local statistics of the Doppler channel t m Take the maximum value to get η m , through t m The cumulative distribution function of and Get η m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists right and Derived separately, we get η under two assumptions m The probability density function of and Each radar station S m based on and Calculate the corresponding local test statistic L(η) according to the likelihood ratio test, and transmit L(η) to the fusion center; The fusion center obtains the global optimal statistic T according to the local test statistic L(η) opt ; Based on the global optimal statistic T opt and false alarm probability P fa Get the global decision threshold g of the distributed radar target detection system; based on the global optimal statistics T opt And the global decision threshold g determines whether there is a target in the spatial resolution unit.

2. A distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: The false alarm probability P of the fusion center fa =10 -4 .

3. The distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: Each radar station S m The signal amplitude in the spatial resolution unit is sampled, and the data is sorted according to the gradient and the order value to obtain sorted data. The sorted data is processed based on the square law and the DMOS-CFAR detection algorithm to obtain the local statistics t of each Doppler channel. m ,include: Each radar station S m The signal amplitude in the spatial resolution unit is sampled to obtain S m The output signal r of a coherent processing time m and S m The observation values ​​of the reference window are sorted by the increment and sequence value j to obtain the sorted data Y (m,j) , j=1,2,…,n; the sorting is as follows: AND (m,1) ≤And (m,2) ≤…≤And (m,n) ; Among them, Y (m,1) is the minimum value, Y (m,n) is the maximum value; According to S m The output signal r m And the sorted data Y (m,j) , use the first formula to calculate each radar station S m The local statistics of the Doppler channel t m ; The first formula is as follows: where t m = [t m,1 , …, t m,i , …, t m,N , i = 1, 2, …, N.

4. The distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: The m The cumulative distribution function of and The expression is as follows: Where S represents the signal-to-noise ratio of the radar station, j represents the selected order value, and t m,i ∈t m , i=1,2,…,N.

5. The distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: The η m Cumulative distribution function under the target non-existence hypothesis H0 The cumulative distribution function under the hypothesis H1 exists The expression is as follows: Among them, η m =t m,l , l is the index of the unit where the maximum value of the Doppler channel is located, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding distribution function is represents t under the target existence hypothesis H1 m Medium m,i The corresponding distribution function.

6. A distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: Under the two assumptions, η m The probability density function of and The expression is as follows: in, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding probability density function is, represents t under the hypothesis H0 that the target does not exist m Medium m,i The corresponding distribution function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding probability density function is, represents t under the target existence hypothesis H1 m Medium m,i The corresponding distribution function.

7. A distributed multi-pulse detection method based on local order statistics according to claim 6, characterized in that: Each radar station S m based on and The corresponding local test statistic L(η) is calculated based on the likelihood ratio test, including: Each radar station S m based on and The corresponding local test statistic L(η) is calculated using the second formula according to the likelihood ratio test; The second formula is as follows: Among them, t m,i ∈t m , S represents the signal-to-noise ratio of the radar station, j represents the selected order value, and η represents the maximum value of the Doppler channel.

8. The distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: The global optimal statistic T opt The expression is as follows: Wherein, ln{·} represents the natural number logarithm operation.

9. The distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: The global optimal statistic T opt and false alarm probability P fa The global decision threshold g of the distributed radar target detection system is obtained, including: Based on the global optimal statistics T opt and false alarm probability P fa , the global decision threshold g of the distributed radar target detection system under the assumption that the target does not exist is calculated using the third formula; The third formula is as follows: g=T opt (H0) -1 (1-P fa ); in,(·) -1 represents the inverse function of (·).

10. The distributed multi-pulse detection method based on local order statistics according to claim 1, characterized in that: Based on the global optimal statistic T opt And the global decision threshold g determines whether there is a target in the spatial resolution unit, including: Determine the global optimal statistic T opt ≥Whether the global decision threshold g holds: If so, there is a target in the spatial resolution unit. Otherwise, there is no target in the spatial resolution unit.

Images