Distributed Radar Signal Sorting Method Based on Binary Hypothesis Testing

Abstract

This invention provides a distributed radar signal sorting method based on binary hypothesis testing. It establishes constraint equations using the geographical coordinates of multiple receiving stations and the observed TDOA (Total Distance Aspect Ratio), then calculates the distance difference between the radiation source and the main station. A binary hypothesis testing model is established for different distance difference values; the decision formula for the binary hypothesis testing model under different conditions is obtained; the variance of the distance difference value is solved; the variance of the distance difference value is substituted into the decision formula to obtain a threshold for filtering out distance difference values ​​that meet the conditions; and the observations corresponding to the distance difference values ​​that meet the conditions are retained. In this invention, when multiple receiving stations simultaneously receive pulse TOA parameters, only the TDOA parameters related only to the radiation source location need to be extracted. The TDOA parameters determined by the radiation source location are more stable than the conventional characteristic parameters of the pulse. Therefore, this invention is more reliable than traditional algorithms and less prone to batch additions or omissions.

Description

Technical Field

[0001] This invention belongs to the field of electronic reconnaissance technology, specifically relating to a distributed radar signal sorting method based on binary hypothesis testing. Background Technology

[0002] Signal sorting can separate the sequence of radar pulses from the interleaved signals of multiple radar pulses and estimate and distinguish the radar parameters. Based on radar characteristic parameters such as arrival time, time difference of arrival, carrier frequency, pulse width, and intra-pulse modulation information, proposed signal sorting algorithms include traditional radar sorting algorithms such as the PRI transform method, CDIF histogram algorithm, and SDIF histogram algorithm.

[0003] Traditional signal sorting algorithms are based on single-signal receiving station processing and analysis. However, due to the increasingly complex electromagnetic environment, tight time requirements for signal processing, large computational load, and the tendency for signals to be added to or missed in batches, these algorithms are prone to errors. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a distributed radar signal sorting method based on binary hypothesis testing. The technical problem to be solved by this invention is achieved through the following technical solution:

[0005] This invention provides a distributed radar signal sorting method based on binary hypothesis testing, comprising:

[0006] Step 1: Obtain the geographic coordinates of multiple distributed receiving stations and the TDOA (Total Distance Availability) of the observations received by the multiple receiving stations for observing interference sources;

[0007] Among them, multiple receiving stations include one main station and several auxiliary stations;

[0008] Step 2: Based on the geographical coordinates of multiple receiving stations and the observed TDOA, use a passive positioning algorithm to establish constraint equations between multiple receiving stations and interference sources, and use the constraint equations to calculate the distance difference between the radiation source and the main station.

[0009] Step 3: Establish a binary hypothesis testing model for distance difference values ​​with and without interference sources;

[0010] Step 4: Using the Neyman-Pearson criterion, obtain the decision formula for the binary hypothesis testing model under different conditions;

[0011] Step 5: Calculate the variance of the distance difference values;

[0012] Step 6: Substitute the variance of the distance difference value into the decision formula to obtain the threshold for filtering out the distance difference values ​​that meet the conditions;

[0013] Step 7: Retain the observations corresponding to the distance difference values ​​that meet the conditions.

[0014] The beneficial effects of this invention are:

[0015] This invention provides a distributed radar signal sorting method based on binary hypothesis testing. It establishes constraint equations using the geographical coordinates of multiple receiving stations and the observed Total Time Amount of Origin (TDOA), then calculates the distance difference between the radiation source and the main station. A binary hypothesis testing model is established for different distance difference values; the decision formula for the binary hypothesis testing model under different conditions is obtained; the variance of the distance difference value is solved; the variance of the distance difference value is substituted into the decision formula to obtain a threshold for filtering out distance difference values ​​that meet the conditions; and the observations corresponding to the distance difference values ​​that meet the conditions are retained. In this invention, when multiple receiving stations simultaneously receive pulse TOA parameters, only the TDOA parameters related only to the radiation source location need to be extracted. The TDOA parameters determined by the radiation source location are more stable than the conventional characteristic parameters of the pulse. Therefore, this invention is more reliable than traditional algorithms and is less prone to batch additions or omissions.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This invention provides a flowchart of a distributed radar signal sorting method based on binary hypothesis testing.

[0018] Figure 2 This is a schematic diagram of a simulation experiment scenario;

[0019] Figure 3 This is a probability distribution diagram of the distance difference values;

[0020] Figure 4 A diagram showing the time difference of arrival between the main station and the three auxiliary stations;

[0021] Figure 5 It was selected -TDOA serial number correspondence diagram. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0023] Before introducing this invention, the technical concept of this invention will first be described. Given that when multiple distributed receiving stations simultaneously receive pulse TOA parameters, TDOA parameters that are only related to the radiation source location can be extracted. TDOA parameters determined by the radiation source location are more stable than conventional pulse characteristic parameters; therefore, signal sorting algorithms based on time difference TDOA are more reliable than traditional algorithms.

[0024] The technical concept of this invention is as follows: using the Time of Arrival (TOA) of multiple receiving stations to form multiple time difference pairs, and based on the multi-station passive positioning algorithm, a set of constraint equations can be obtained. Through the set of constraint equations, a certain statistic can be obtained. For this statistic, the threshold of the statistic needs to be derived. After obtaining the threshold, the statistic within the error range is selected based on the binary hypothesis testing theory. Finally, the time difference pairs corresponding to the statistic are selected.

[0025] The technical solution of the present invention will be described in detail below.

[0026] refer to Figure 1 The present invention provides a distributed radar signal sorting method based on binary hypothesis testing, comprising:

[0027] Step 1: Obtain the geographic coordinates of multiple distributed receiving stations and the TDOA (Total Distance Availability) of the observations received by the multiple receiving stations for observing interference sources;

[0028] Among them, multiple receiving stations include one main station and several auxiliary stations;

[0029] Step 2: Based on the geographical coordinates of multiple receiving stations and the observed TDOA, use a passive positioning algorithm to establish constraint equations between multiple receiving stations and interference sources, and use the constraint equations to calculate the distance difference between the radiation source and the main station.

[0030] Specifically, step 2 includes:

[0031] Step 21: Based on the geographical coordinates and observations of multiple receiving stations, establish a mathematical model for the location of the interference source and the multiple receiving stations;

[0032] The positioning mathematical model is as follows:

[0033] (1)

[0034] in

[0035] (2)

[0036] (3)

[0037] (4)

[0038] (5)

[0039] Among them, in formulas (1) to (5) The coordinates representing the radiation source, The x and y coordinates of the four stations are given; the left side of equation (1) represents the TDOA observation of the main station relative to the three auxiliary stations. The right side is The theoretical value is composed of the sum of equation (4) and equation (3), where equation (3) is Gaussian white noise; equation (5) is the distance from the radiation source to the main station. .

[0040] Step 22: Solve the positioning mathematical model using the linear least squares method to estimate the distance from the main station to the radiation source;

[0041] Specifically, step 22 includes:

[0042] Transforming equation (1), we get:

[0043] (6)

[0044] in:

[0045] (7)

[0046] (8)

[0047] (9)

[0048] (10)

[0049] (11)

[0050] Solving equation (6) using the linear least squares method yields the estimated result:

[0051] (12)

[0052] (13)

[0053] in The first result of the estimation of equation (6) item ;

[0054] Step 23: Subtract the estimated distance from the main station to the radiation source from the theoretical value to obtain the distance difference value between the main station and the radiation source.

[0055] This step will and The difference is obtained by taking the absolute value of the subtraction:

[0056] (14)

[0057] Substituting formula (12) into (5) yields the following result. .

[0058] Step 3: Establish a binary hypothesis testing model for distance difference values ​​with and without interference sources;

[0059] For distance difference value Establish a binary hypothesis testing model

[0060] (15)

[0061] against There are two cases for binary hypothesis testing: if For noise or If the value exceeds the error range by too much, then it is... Situation; if If the value fluctuates within the error range, then it is... Condition;

[0062] (16)

[0063] in, for The correct theoretical value, where n is Gaussian noise. The situation contains interference sources. It contains no interference sources.

[0064] Step 4: Using the Neyman-Pearson criterion, obtain the decision formula for the binary hypothesis testing model under different conditions;

[0065] Specifically, step 4 includes:

[0066] Step 41: Establish the probability density function for the distance difference value under different conditions, including and without interference sources;

[0067] exist In this situation, The probability density function PDF is:

[0068] (17)

[0069] exist In this situation, The probability density function PDF is:

[0070] (18)

[0071] Step 42: Calculate the log-likelihood ratio of the distance difference values ​​based on the probability density function under the given conditions;

[0072] Then the log-likelihood ratio of the distance difference values ​​in step 42 is:

[0073] (19)

[0074] Step 43: Establish constraints on the probability of missed detection based on the Neyman-Pearson criterion;

[0075] With a certain false alarm probability Lowering the false negative probability Minimal or make detection The probability is extremely high, and step 43 satisfies the following constraints:

[0076] (20)

[0077] Step 44: Derive the objective function using Lagrange multipliers and constraints;

[0078] Step 45: Solve the objective function to obtain the decision formula of the binary hypothesis testing model.

[0079] To solve the decision equation under this criterion, we set... At the same time, using Lagrange multipliers To derive the objective function :

[0080]

[0081] (twenty one)

[0082]

[0083] When the integration region Includes all When the value is positive, the objective function in step 44 has a maximum value. All points within the interior satisfy:

[0084] (twenty two)

[0085] That is, equation (19) satisfies:

[0086] (twenty three)

[0087] Therefore, the decision item in step 45 is:

[0088] (twenty four)

[0089] Simplifying equation (24), we get the following equation:

[0090] (25)

[0091] Wherein, the threshold is ,in for The variance.

[0092] Step 5: Calculate the variance of the distance difference values;

[0093] Step 5 includes:

[0094] Step 51: Based on observations probability density function and observations obey Based on the distribution properties, the constraint equations are transformed;

[0095] because If it follows a Gaussian distribution with a mean of 0, then The probability density function (PDF) is:

[0096] (26)

[0097] The constrained equations after deformation are:

[0098] (27)

[0099] in, It follows a Gaussian distribution with a mean of 0. for The covariance matrix is ​​not a diagonal matrix. obey The distribution, ;

[0100] Step 52: Observe the measurements Considered as an unbiased estimate of the parameters Distribution , for observation The probability density function is transformed as follows:

[0101] (28)

[0102] Step 53: Based on the observed deformation The probability density function, when transformed into the constraint equation, is:

[0103] (29)

[0104] in, It is a parameter that carries noise, and it is related to... A linear relationship exists. and Carrying noise with the same distribution;

[0105] Step 54: Based on the deformed constraint equations, through... The derivation of the Cramer-Leyborg boundary (CRLB) is obtained. variance Thus, the threshold is obtained. .

[0106] Can It can be considered as a parameter carrying noise, and it is related to A linear relationship exists; theoretically, this can be called... and Carrying noise with the same distribution, therefore variance It is possible The Cramer-Leod boundary (CRLB) was derived.

[0107] Step 6: Substitute the variance of the distance difference values ​​into the decision formula to filter out the distance difference values ​​that meet the conditions;

[0108] Using thresholds ,Will The corresponding observations Perform discriminative screening to obtain those that meet the criteria. Hypothetical data.

[0109] Step 7: Retain the observations corresponding to the distance difference values ​​that meet the conditions.

[0110] After filtering Corresponding observations Retain and discard the remaining false observations. .

[0111] Because radar receivers have reception errors during signal reception, Gaussian white noise is present in the received TDOA. The distributed passive localization algorithm creates a constraint relationship between the TDOA and the coordinates of the radiation source. Based on these two characteristics, this invention proposes a method to obtain the threshold value of a certain statistic in the localization algorithm using a binary hypothesis test, then filter out the data with the statistic within the error range, and finally filter out the TDOA time difference pairs corresponding to the statistic.

[0112] The effects of the present invention will be further illustrated below with simulation experiments.

[0113] 1. Simulation conditions:

[0114] This invention was simulated using MATLAB 2021a software on an Intel® Core™ i5-6300 CPU 2.30GHz processor and a Windows 10 operating system.

[0115] Simulation scenario setup: The simulation experiment scenario of this invention is as follows Figure 2As shown, two radiation sources and four receiving stations are set up in space. The receiving stations are arranged in a square pattern. The main station is located at (0,0), and the auxiliary stations SlaSta1,2,3 are located at (2000,0), (2000,2000), and (0,2000) respectively. Radiation source 1 is located at (3000,8000), and radiation source 2 is located at (300,6000).

[0116] Simulation parameters are set as follows: the timing error of the four receiving stations is 20 ns, and the signals emitted by the two radiation sources are fixed repetition frequency signals with a PRI of 160 ns.

[0117] 2. Simulation content and result analysis:

[0118] The simulation experiment of this invention uses the method of this invention to sort the signals of the two radiation sources mentioned above. Figure 4 This diagram shows the arrival time differences grouped between the main station and the three auxiliary stations. The vertical axis represents the arrival time difference in nanoseconds, and the horizontal axis represents the sequence number of the arrival time difference. Figure 4 In the three figures, there are two horizontal solid lines, which represent the theoretical time difference of arrival for the two radiation sources, and the remaining points in the figures represent the measurement time difference. Figure 4 The left figure is a schematic diagram of the arrival time difference grouping between the main station and auxiliary station 1. Figure 4 The middle diagram is a schematic diagram of the arrival time difference grouping of main station 1 and auxiliary station 2. Figure 4 This is a schematic diagram showing the arrival time difference grouping of the main station and auxiliary station 3.

[0119] Figure 3 It means The probability distribution plot is obtained by selecting one data point from each of the three sets of TDOA data and combining them. This yields multiple sets of combined data. The observation data was substituted into the equations, and the LLS method was used to obtain the coordinates of the radiation source. The estimated value and The estimated value ,Will Substituting into equation (5) yields , and then, will and Substituting into equation (14) yields ,Depend on Figure 3 And as can be seen from the law of large numbers, It follows a certain pattern with a mean of 0. The variance is a Gaussian distribution, because and If there is a linear relationship, we can consider it as and The distribution is consistent, thus it can be used The CRLB solution process is obtained variance Substituting into the decision formula yields The threshold for judgment. Figure 5 It was selected -TDOA serial number correspondence diagram.

[0120] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0121] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0122] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A distributed radar signal sorting method based on binary hypothesis testing, characterized in that, The method comprises the following steps: Step 1: obtaining geographical coordinates of a plurality of receiving stations distributed in a distributed manner and observation quantities TDOA for observing an interference source received by the plurality of receiving stations; Wherein, the plurality of receiving stations comprise a main station and a plurality of auxiliary stations; Step 2: according to the geographical coordinates of the plurality of receiving stations and the observation quantities TDOA, a constraint equation between the plurality of receiving stations and the interference source is established by using a passive positioning algorithm, and a distance difference value between the radiation source and the main station is calculated by using the constraint equation; the distance difference value is a difference between a directly estimated distance value and a distance value calculated by using estimated coordinates of the radiation source; Step 3: a binary hypothesis test model under different conditions of containing the interference source and not containing the interference source is established; Step 4: a decision formula of the binary hypothesis test model under different conditions is obtained by using the Neyman-Pearson criterion; Step 5: a variance of the distance difference value is solved; Step 6: the variance of the distance difference value is substituted into the decision formula, so that a threshold is obtained to screen out distance difference values meeting the conditions; Step 7: observation quantities corresponding to the distance difference values meeting the conditions are reserved; Step 3 comprises: For the distance difference value A binary hypothesis testing model is established: （15） For the binary hypothesis test of , there are two cases: if is noise or is out of the error range, it is the case; if is within the error range, it is the case. （16） wherein is the correct theoretical value, n is Gaussian noise, the case is with an interferer, is without an interferer; Step 4 comprises: Step 41: a probability density function under different conditions of containing the interference source and not containing the interference source is established; Step 42: a log-likelihood ratio of the distance difference value is calculated according to the probability density functions under the two conditions; Step 43: a constraint condition of a missed detection probability is established according to the Neyman-Pearson criterion; Step 44: a target function is derived by using a Lagrange multiplier and the constraint condition; Step 45: the target function is solved to obtain a decision formula of the binary hypothesis test model; In step 41 In In the case where The probability density function PDF of the sum （17） In In the case where The probability density function PDF of （18） Then, the log-likelihood ratio of the distance difference value in step 42 is: （19） At a certain false alarm probability The missed detection probability Is minimized or made Probability is maximized, step 43 satisfies the following constraint: （20） To solve the decision formula under this criterion, set , and use the Lagrange multiplier to derive the objective function : （21） When the integral region contains all points for which The objective function of step 44 has a maximum value at the point for which All points within satisfy: （22） That is, formula (19) satisfies: （23） Therefore, the decision term in step 45 is: （24） After simplifying formula (24), the following formula is obtained: （25） wherein the threshold is , is variance of 2. The distributed radar signal sorting method based on binary hypothesis testing according to claim 1, characterized in that, Step 2 comprises: Step 21: a positioning mathematical model of the interference source and the plurality of receiving stations is established according to the geographical coordinates of the plurality of receiving stations and the observation quantities; Step 22: the positioning mathematical model is solved by using a linear least square method to estimate a distance estimation value from the main station to the radiation source and coordinates of the radiation source; Step 23: a distance difference value from the main station to the radiation source is obtained by subtracting a distance value calculated by using the estimated coordinates of the radiation source from the distance estimation value from the main station to the radiation source.

3. The distributed radar signal sorting method based on binary hypothesis testing according to claim 2, characterized in that, The positioning mathematical model is: （1） Wherein, （2） （3） （4） （5） wherein the formulas (1) to (5) are representing the coordinates of the radiation source, are the horizontal and vertical coordinates of the 4 stations; the left side of the equation of formula (1) represents the observation of the TDOA of the main station relative to the 3 auxiliary stations , and the right side is the theoretical value of , which is composed of the sum of formula (4) and formula (3), wherein formula (3) is the Gaussian white noise; formula (5) is the distance of the radiation source to the main station .

4. The distributed radar signal sorting method based on binary hypothesis testing according to claim 3, characterized in that, Step 22 comprises: After transforming formula (1), the following formula is obtained: （6） Wherein: （7） （8） （9） （10） （11） The estimated result is obtained by solving formula (6) by using the linear least square method: （12） （13） wherein the first estimate of the result of formula (6) term ; Step 23 comprises: calculating a distance value from the estimated coordinates of the radiation source and the directly estimated distance value Subtracting and taking the absolute value gives a distance difference value: （14）。 5. The distributed radar signal sorting method based on binary hypothesis testing according to claim 3, characterized in that, Step 5 comprises: Step 51 : Transform the constraint equation based on the probability density function of the observation and the distribution properties of the observation subject to​​ where the observation is the probability density function of （26） The transformed constraint equation is: （27） wherein, is a Gaussian distribution with 0 mean, is a covariance matrix of and is not a diagonal matrix, obeys a distribution of ;​ Step 52: Form the observation Consider the distribution of the unbiased estimator parameter The probability density function of the observation is transformed to:​ （28） Step 53: Deformation of the observation The constraint equation is deformed as follows: （29）； wherein is a parameter carrying a noise term which is in linear relationship with , and carries a noise with the same distribution; Step 54: Based on the deformed constraint equations, through... The derivation of the Cramer-Leyborg boundary (CRLB) is obtained. variance Thus, the threshold is obtained. .

6. The distributed radar signal sorting method based on binary hypothesis testing according to claim 5, characterized in that, Step 6 comprises: Utilizing a threshold , the corresponding of the observation quantity is obtained , the discriminant is screened, and the data conforming to the hypothesis is obtained.

7. The distributed radar signal sorting method based on binary hypothesis testing according to claim 6, characterized in that, Step 7 comprises: The filtered corresponding observations retained, the rest of the false observations discarded .

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