阅读说明：本技术 基于极值理论的弱小目标检测前跟踪技术性能分析方法 (Tracking technology performance analysis method before detection of weak and small targets based on extreme value theory ) 是由 赵玉丽 翟海涛 鉴福升 罗军 徐勇 商凯 朱伟 陈硕 刘�文 于 2021-08-04 设计创作，主要内容包括：本发明提供了基于极值理论的弱小目标检测前跟踪技术性能分析方法,包括：步骤1：采集或仿真获取雷达数据；步骤2：对所采集的雷达数据进行弱小目标检测前跟踪(TBD)处理,获取最终值函数,通过提取极大值点检测目标位置；步骤3：采集有目标的雷达数据,重复步骤1和2获取目标样本数据；采集无目标雷达数据,重复步骤1和2获取虚警样本数据；步骤4：TBD算法性能分析,对获取的目标样本通过蒙特卡罗算法分析检测概率；对获取的虚警样本通过极值理论分析虚警概率。(The invention provides a performance analysis method for a tracking technology before detection of a small and weak target based on an extreme value theory, which comprises the following steps: step 1: acquiring or simulating to obtain radar data; step 2: tracking (TBD) processing is carried out on the acquired radar data before the detection of the small and weak targets, a final value function is obtained, and the target position is detected by extracting a maximum value point; and step 3: collecting radar data with a target, and repeating the steps 1 and 2 to obtain target sample data; collecting target-free radar data, and repeating the steps 1 and 2 to obtain false alarm sample data; and 4, step 4: TBD algorithm performance analysis, namely analyzing the detection probability of the obtained target sample through a Monte Carlo algorithm; and analyzing the false alarm probability of the obtained false alarm sample through an extreme value theory.)

1. The method for analyzing the performance of the tracking technology before the detection of the weak and small target based on the extreme value theory is characterized by comprising the following steps of:

step 1, radar data is obtained;

step 2, performing tracking algorithm TBD processing on radar data before detection to obtain a final value function, and detecting a target position by extracting a maximum value point;

step 3, collecting radar data with a target, and repeating the step 1 and the step 2 to obtain target sample data; collecting target-free radar data, and repeating the step 1 and the step 2 to obtain false alarm sample data;

step 4, analyzing the performance of a tracking algorithm TBD before detection, and analyzing the detection probability of the obtained target sample through a Monte Carlo algorithm; and analyzing the false alarm probability of the obtained false alarm sample through an extreme value theory.

2. The method of claim 1, wherein step 1 comprises: acquiring K frames of radar echo data, wherein the size of each frame of data is L multiplied by L, the position of sampling data is represented by a resolution unit (i, j), and data received by the radar at the kth frame time is represented by a matrix as Z_k＝{z_k(i,j)},i,j∈[1,L]，k∈[1，K]；z_k(i, j) is a measured value recorded by the k-th frame time resolution unit (i, j), and is specifically expressed as:

wherein A is_kRepresenting the amplitude, w, of the object at the time of the k-th frame_k(i, j) represents the noise at the k-th frame time resolution unit (i, j), and x is used_kRepresenting the state value of each resolution cell at the time of the k-th frame; one track of the target is defined as a series of continuous states x from time 1 to time K_kSet X (K):

X(K)＝{x₁,x₂...,x_K} (2)。

3. the method of claim 2, wherein step 2 comprises:

step 2-1:initialization value function: dynamic programming is applied to a track-before-detect algorithm TBD, the amplitude value of a signal is selected as a value function, and a 1 st frame value function I (x) is initialized₁) State value phi of 1 st frame₁(x₁)：

I(x₁)＝z₁(i,j)，i,j∈[1,L] (3)

Φ₁(x₁)＝0 (4)

In the formula phi_k(x_k) Saving the state value of the optimal value function in the k-1 stage, and initializing phi of the first frame₁(x₁) Is 0;

step 2-2: and (3) recursive calculation: all resolution cell states x for the k-th frame instant_kK is more than or equal to 2 and less than or equal to K, and a value function I of K moment is obtained in a recursion mode_k(x_k)：

(6)

In the formula, arg { } means the state value of the resolution unit where the evaluation function is located;representing the function I (x) of the value of the time instant k-1_k-1) The extreme point of (a);

step 2-3: obtaining a detection sample: at the end state, i.e. when K equals K, the state value at which the extreme point of the value function is located is found

WhereinFunction of value I (x) at the time of the K-th frame of the function of representation values_K) The extreme point of (c).

4. The method of claim 3, wherein step 3 comprises:

step 3-1: collecting radar echo data containing a specific target, repeating the step 1 and the step 2 for M times, and obtaining M target echo samples;

step 3-2: and (3) acquiring the echo data of the non-target radar, repeating the step 1 and the step 2 for N times, and acquiring N false alarm extreme point samples.

5. The method of claim 4, wherein step 4 comprises:

step 4-1: analyzing the detection probability by using a Monte Carlo algorithm;

step 4-2: and analyzing the false alarm probability by an extreme method.

6. The method of claim 5, wherein step 4-1 comprises: defining a detection probability P_D：

Wherein x is_KThe state value of the target signal exists at the moment K;for the Kth frame value function I (x)_K) Is less than the threshold V_TProbability of (F)_n(x) Is an extreme valueDistribution function of F_n(V_T) To an extreme value of V_TThe value of time; the statistical test times N satisfy:

in the formula, p is the probability of occurrence of an event in each test, alpha represents confidence coefficient, and epsilon represents precision;

statistics of M obtained by step 3-1_sThe number of the target positions correctly detected in each sample is set as V_sS, S is the number of set thresholds, m is 1,2_sFor M sample values being greater than threshold V_sThe number of the TBD is estimated as the detection probability distribution function P of the pre-detection tracking algorithm TBD_D(V_s) Comprises the following steps:

7. the method of claim 6, wherein step 4-2 comprises: defining false alarm probability P_FA：

In the formula V_TTo detect the threshold, F_n(x) Is an extreme valueA distribution function of (a);

let the extremum sample be denoted x, taking the following two forms of Gumbel extremum distribution:

in the formula a_n，b_nV is a constant, formula (12) is called an extreme value theory EVT, formula (13) is called a generalized extreme value theory GEVT, and when v in formula (13) is 0, the formula is the extreme value theory EVT formula;

least Squares (LS) estimation of extremum theoretical EVT parameters:

sample sequence is notedX₁,X₂,...,X_NFor the N extreme value samples collected, the sample sequence is arranged in ascending order to obtain a set

WhereinIs an ascending order of extreme samples, from which a distribution function is counted

The equation (12) is transformed into:

-ln{-ln[F_n(x)]}＝(x-a_n)/b_n (16)

let the intermediate parameter u_i,z_iInstead of the following formula:

z_i＝-ln{-ln[F_n(x)]}＝-ln{-ln[u_i]},i＝1,2,...,N (18)

the minimum variance estimation is to minimize the value of the following formula:

as a sequence of samplesMinimum variance from EVT distribution;

respectively to the parameter a_n,b_nThe derivative is obtained and is made to be 0, and the estimated values of the two parameters are obtained

In the formulaAs a sequence of samplesThe average value of (a) of (b),is a sequence (z)₁,z₂,...,z_N) The mean value of (a);

minimum variance estimation of generalized extremum theory GEVT parameters:

transforming equation (13) to obtain:

z_i,u_iare set as formula (17) and formula (18), and the minimum variance estimates the three parameters v, a_n,c_nThat is, the following equation is minimized:

L(ν,a_n,c_nx) is the minimum variance of the sample sequence and the GEVT distribution; wherein the value of v is takenAndthe value of the correlation is the largest, and the correlation coefficient r (ν) is expressed as follows:

in the formulaIs sequence (X)₁ ^v,X₂ ^v,...,X_N ^v) The average value of (a) of (b),is a sequence (z)₁,z₂,...,z_N) The mean value of (a); the value of v when the value of r (v) is maximum is taken as the optimal estimation value;

respectively to the parameter a_n,c_nCalculating the derivative, making the derivative be 0, and solving two parameters a_n,c_nIs estimated value of

Further, a distribution function of the sample data is obtained through the estimated parameters:

the false alarm probability function is estimated as P_FA≈1-F_n(V_s)，V_sIs the detection threshold.

Technical Field

The invention relates to the field of radar signal detection, in particular to a performance analysis method for a tracking technology before detection of a small and weak target based on an extreme value theory.

Background

The tracking-before-detection technology is firstly applied to the infrared and optical image processing fields, and in recent years, a tracking-before-detection algorithm (TBD) has been applied to the field of weak signal detection of radar. Two methods are commonly adopted for analyzing the detection performance, one method is a Monte Carlo statistical method, a large number of samples are collected, the detection performance is analyzed through statistics, and the statistical accuracy is influenced by the number of the samples; the second is a theoretical analysis performance method, which calculates the detection performance by deducing a distribution function analytical expression of the detection data. Monte Carlo statistics require a large number of samples to estimate an accurate value, such as the false alarm probability 10^-6At least 10 is required⁸The large number of samples is a limitation of the Monte Carlo statistical method. The theoretical analysis algorithm needs to accurately derive the distribution function of the sample data, but the distribution characteristic of the data after TBD processing becomes very complex, and the analysis of the expression cannot be started.

Disclosure of Invention

The purpose of the invention is as follows: the invention aims to solve the technical problem of providing a performance analysis method based on an extreme value theory aiming at the defects of the existing TBD performance analysis method.

The extreme value theory considers that the distribution of the extreme values of the random variable is independent of the distribution itself. The theory is mainly applied to statistical data with serious deviation from distribution mean, and is generally used for predicting the occurrence of tsunami, earthquake and other extreme events. In a statistical sense, the extrema refer to the maxima and minima of some random process, usually at the tail of the distribution. The detection result of the TBD is an extreme point in the data sample, which can be regarded as the maximum of a random process, and the distribution characteristic of the TBD can be analyzed by adopting an extreme value theory.

Radar target detection requires very low false alarm probability (e.g.<10^-6) While requiring a higher detection probability (e.g., higher detection probability)>0.9). The Monte Carlo statistical method can quickly and accurately estimate the performance curve by analyzing and detecting the probability performance curve. For analyzing the false alarm probability performance curve, the Monte Carlo statistical method needs huge number of samples, and in order to accurately estimate the value, the extreme value theory is adopted to solve the problem.

The invention specifically comprises the following steps:

step 1, radar data is acquired or simulated.

Step 2, performing tracking algorithm TBD processing on radar data before detection to obtain a final value function, and detecting a target position by extracting a maximum value point;

step 3, collecting radar data with a target, and repeating the step 1 and the step 2 to obtain target sample data; collecting target-free radar data, and repeating the step 1 and the step 2 to obtain false alarm sample data;

step 4, analyzing the performance of a tracking algorithm TBD before detection, and analyzing the detection probability of the obtained target sample through a Monte Carlo algorithm; and analyzing the false alarm probability of the obtained false alarm sample through an extreme value theory.

Further, in one implementation, the step 1 includes:

acquiring K frames of radar echo data through collection or simulation, wherein the size of each frame of data is L multiplied by L, the position of sampling data is represented by (i, j), and data received by the radar at the kth frame time is represented by Z through a matrix_k＝{z_k(i,j)},i,j∈[1,L]，k∈[1，K]；z_k(i, j) is a measured value recorded by the k-th frame time resolution unit (i, j), and is specifically expressed as:

wherein A is_kRepresenting the amplitude, w, of the object at the time of the k-th frame_k(i, j) represents the noise at the k-th frame time resolution unit (i, j), and x is used_kThe state value (including the information of spatial position, amplitude and the like) of each resolution unit at the moment of the kth frame is represented; one track of the target is defined as a series of continuous states x from time 1 to time K_kSet X (K):

X(K)＝{x₁,x₂...,x_K} (2)。

further, in one implementation, the step 2 includes:

step 2-1: initialization value function: dynamic programming is applied to a track-before-detect algorithm TBD, the amplitude value of a signal is selected as a value function, and a 1 st frame value function I (x) is initialized₁) State value phi of 1 st frame₁(x₁)：

I(x₁)＝z₁(i,j)，i,j∈[1,L] (3)

Φ₁(x₁)＝0 (4)

In the formula phi_k(x_k) Saving the state value of the optimal value function of the last stage, namely the k-1 stage, and initializing phi of the first frame₁(x₁) The value of (d) is 0.

Step 2-2: and (3) recursive calculation: all resolution cell states x for the k-th frame instant_kK is more than or equal to 2 and less than or equal to K, and a value function I of K moment is obtained in a recursion mode_k(x_k)：

In the formula, arg { } means the state value of the resolution unit where the evaluation function is located;representing the function I (x) of the value of the time instant k-1_k-1) The extreme point of (a);

step 2-3: obtaining a detection sample: at the end state, i.e. when K equals K, the state value at which the extreme point of the value function is located is found

WhereinFunction of value I (x) at the time of the K-th frame of the function of representation values_K) The extreme point of (c).

Further, in one implementation, the step 3 includes:

step 3-1: and (3) collecting radar echo data containing a specific target, repeating the step 1 and the step 2M times, and acquiring M target echo samples.

Step 3-2: and (3) acquiring the echo data of the non-target radar, repeating the step 1 and the step 2 for N times, and acquiring N false alarm extreme point samples.

Further, in one implementation, the step 4 includes:

step 4-1: the Monte Carlo algorithm analyzes the detection probability:

defining a detection probability P_D：

Wherein x is_KThe state value of the target signal exists at the moment K;for the Kth frame value function I (x)_K) Is less than the threshold V_TProbability of (F)_n(x) Is an extreme valueDistribution function of F_n(V_T) To an extreme value of V_TThe value of time; from the above equation, it can be seen that the distribution F to which the extreme final state values are also to be analyzed_n(x) Then, a relation curve of the detection probability and the threshold can be obtained.

The simulation accuracy of the Monte Carlo method is very important, the number of samples is a very important factor influencing the simulation accuracy, and if the number of samples is too large, the application of the statistical test method sometimes has to be abandoned. Usually, a certain confidence degree alpha is used to satisfy a certain precision epsilon as a basis for selecting the number of statistical tests. The statistical test times N satisfy:

in the formula, N is the number of times of statistical tests, and p is the probability of occurrence of events in each test. For example, the required number of tests for a radar detection probability p of 0.9 is at least 2.4x10, with α being 0.95 and ≦ 0.01³。

Statistics of M obtained by step 3-1_sThe number of the target positions correctly detected in each sample is set as V_sS, S is the number of set thresholds, m is 1,2_sFor M sample values being greater than threshold V_sThe number of the TBD is estimated as the detection probability distribution function P of the pre-detection tracking algorithm TBD_D(V_s) Comprises the following steps:

step 4-2: analyzing false alarm probability by an extreme method:

defining false alarm probability P_FA：

In the formula V_TTo detect the threshold, F_n(x) Is an extreme valueThe distribution function of (2). From the above formula, it can be seen that the distribution F obeyed by the extreme value can be analyzed_n(x) Then the false alarm probability performance curve can be analyzed approximately.

Radar target detection usually requires a very low false alarm probability, such as a false alarm probability p 10^-6If the Monte Carlo statistical method is adopted, the required test times under the accuracy of 0.01 are at least 10⁸The sample size is huge, which becomes a burden of a computer, and especially when a large amount of calculation is needed for a TBD model, the Monte Carlo method is very difficult.

Fisher and Tippet (1928) and Gneenko (1943) studied with the BMM method to derive distribution functions of extreme statistical variables. An extreme sample is set to be denoted x, where the Gumbel distribution has the following two forms:

in the formula a_n，b_nV is a constant, formula (12) is referred to as Extreme Value Theory (EVT), formula (13) is referred to as Generalized Extreme Value Theory (GEVT), and when v is 0 in formula (13), it is the Extreme Value Theory EVT formula. I.e., EVT is a special case of GEVT;

the estimation method of the extreme parameters comprises a least square estimation (LS) method and a maximum likelihood estimation (ML) method, and the invention adopts the least square estimation (LS) method when the extreme value theory is applied.

(1) Least Squares (LS) estimation of extremum theoretical EVT parameters:

sample sequenceIs marked asX₁,X₂,...,X_NFor the N extreme value samples collected, the sample sequence is arranged in ascending order to obtain a set

WhereinIs an ascending order of extreme samples, from which a distribution function is counted

The equation (12) is transformed into:

-ln{-ln[F_n(x)]}＝(x-a_n)/b_n(16) let the intermediate parameter u_i,z_iInstead of the following formula:

z_i＝-ln{-ln[F_n(x)]}＝-ln{-ln[u_i]}(18)

the minimum variance estimation is to minimize the value of the following formula:

as a sequence of samplesMinimum variance from EVT distribution;

respectively to the parameter a_n,b_nThe derivative is obtained and is made to be 0, and the estimated values of the two parameters are obtained

In the formulaAs a sequence of samplesThe average value of (a) of (b),is a sequence (z)₁,z₂,...,z_N) The mean value of (a);

(2) minimum variance estimation of generalized extremum theory GEVT parameters:

transforming equation (13) to obtain:

z_i,u_iare set as formula (17) and formula (18), and the minimum variance estimates the three parameters v, a_n,c_nThat is, the following equation is minimized:

L(ν,a_n,c_nx) is the minimum variance of the sample sequence and the GEVT distribution; wherein the value of v is takenAndthe value of the correlation is the largest, and the correlation coefficient r (ν) is expressed as follows:

in the formulaIs a sequence ofThe average value of (a) of (b),is a sequence (z)₁,z₂,...,z_N) The mean value of (a); the value of v when the value of r (v) is maximum is taken as the optimal estimation value;

respectively to the parameter a_n,c_nCalculating the derivative, making the derivative be 0, and solving two parameters a_n,c_nIs estimated value of

Further, a distribution function of the sample data is obtained through the estimated parameters

The false alarm probability function can be estimated as P_FA≈1-F_n(V_s)，V_sIs the detection threshold.

The invention has the following beneficial effects:

(1) the method can analyze the false alarm probability performance of the DP-TBD by a small sample;

(2) the method can accurately predict the detection threshold under the specific false alarm.

Drawings

The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.

FIG. 1 is a graph of Monte Carlo statistical detection probability in the method of the present invention;

FIG. 2 is a graph of the probability of false alarm for the extreme value theory analysis in the method of the present invention;

fig. 3 is a logarithmic curve of false alarm probability for extremum theory analysis in the method of the present invention.

Detailed Description

The invention discloses a weak and small target tracking before detection technical performance analysis method based on an extreme value theory, which comprises the following steps of:

step 1: and acquiring or simulating radar data.

Step 2: and TBD processing is carried out on the acquired radar data to obtain a final value function, and the target position is detected by extracting the maximum value point.

And step 3: collecting radar data with a target, and repeating the steps 1 and 2 to obtain target sample data; and (3) collecting non-target radar data, and repeating the steps 1 and 2 to obtain the number of false alarm samples.

And 4, step 4: TBD algorithm performance analysis, namely analyzing the detection probability of the obtained target sample through a Monte Carlo algorithm; and analyzing the false alarm probability of the obtained false alarm sample through an extreme value theory.

In this embodiment, the method for analyzing performance of tracking technology before detection of small and weak targets based on the extremum theory includes:

step 1-1: target echo data simulation

The noise parameter is rayleigh distribution with sigma being 0.5, the target signal amplitude is constant value, the signal-to-noise ratio is 7, the frame number of data is K16, and each frame of data contains L²＝32²A resolution unit for simulating the generation of radar data with target echo

In the formula A_k＝2σ²×10^SNR/10，w_k(i, j) is noise whose σ is 0.5. One track of the target is defined as a series of continuous states x from time 1 to time K_kSet X (K):

X(K)＝{x₁,x₂...,x_K} (2)

step 1-2: targetless data simulation

Rayleigh distribution with noise parameter σ of 0.5, frame number of data K of 16, each frame of data including L²＝32²A resolution unit for simulating the generation of radar data with or without target echo

z_k(i,j)＝w_k(i,j),i,j∈[1,L]In the formula w_k(i, j) is noise whose σ is 0.5.

The step 2 comprises the following steps:

step 2-1: initialization value function:

applying dynamic programming in a TBD algorithm, selecting an amplitude value of a signal as a value function, and initializing a 1 st frame value function:

I(x₁)＝z₁(i,j)，i,j∈[1,L] (3)

Φ₁(x₁)＝0 (4)

in the formula phi_k(x_k) Saving the state value of the optimal value function in the last stage (the k-1 stage), and initializing phi of the first frame₁(x₁) The value of (d) is 0.

Step 2-2: recursive computation

All resolution cell states x for time k_kK is more than or equal to 2 and less than or equal to K, and a value function I of K moment is obtained in a recursion mode_k(x_k)，

In the formula q_ijThe echo state values are echo state values of 3x3 around (i, j). arg means the state value of the resolution cell in which the evaluation function is located.

Step 2-3: obtaining a test sample

In the final state, i.e. at the moment when K equals K, the extreme point of the value function is found

Further, in one implementation, the step 3 includes:

step 3-1: repeating the step 1-1 and the step 2 10000 times, and acquiring 10000 target echo samples M.

Step 3-2: repeating the step 1-2 and the step 2 10000 times, collecting and obtaining the no-target radar echo data, and obtaining 10000 false alarm extreme point samples N.

Further, in one implementation, the step 4 includes:

step 4-1: analyzing the detection probability by using a Monte Carlo algorithm;

the detection probability is defined as follows:

note: x is the number of_KFor the state with signal at time K, the states within two cells around the true position of the target are both considered to be the state with signal. From the above equation, it can be seen that the distribution F to which the extreme final state values are also to be analyzed_n(x) Then, a relation curve of the detection probability and the threshold can be obtained.

The simulation accuracy of the Monte Carlo method is very important, the number of samples is a very important factor influencing the simulation accuracy, and if the number of samples is too large, the application of the statistical test method sometimes has to be abandoned. Usually, a certain confidence degree alpha is used to satisfy a certain precision epsilon as a basis for selecting the number of statistical tests.

Wherein N is the number of statistical tests, p is the probability of occurrence of the event A in each test, and q is 1-p. For example, the required number of tests for a radar detection probability p of 0.9 is at least 2.4x10, with α being 0.95 and ≦ 0.01³。

Traversing threshold V_sFirst, counting the number of samples with a threshold larger than Vs among M samples, assuming that M is equal to 0.1:70_sThen, the detection probability distribution function of the predicted TBD algorithm is:

p obtained by Monte Carlo method statistics_D(V_s) The graph is shown by a solid line in fig. 1, and a dotted line and a dashed line are respectively estimated detection probability curves of the EVT and the GEVT, so that the goodness of fit is high.

Step 4-2: and analyzing the false alarm probability by an extreme method.

False alarm probability definition:

in the formula V_TTo detect the threshold, F_n(x) Is an extreme valueThe distribution function of (2). From the above formula, it can be seen that the distribution F obeyed by the extreme value can be analyzed_n(x) Then the false alarm probability performance curve can be analyzed approximately.

Radar target detection usually requires a very low false alarm probability, such as a false alarm probability p 10^-6If Monte card is adoptedRow statistical method, the number of tests required is at least 10 at an accuracy of 0.01⁸The sample size is huge, which becomes a burden of a computer, and especially when a large amount of calculation is needed for a TBD model, the Monte Carlo method is very difficult.

Fisher and Tippet (1928) and Gneenko (1943) studied with the BMM method to derive distribution functions of extreme statistical variables. Wherein the Gumbel distribution has the following two forms:

equation (12) is referred to as Extreme Value Theory (EVT), equation (13) is referred to as Generalized Extreme Value Theory (GEVT), and when ν is 0 in equation (13), it is referred to as EVT equation. I.e., EVT is a special case of GEVT;

the estimation method of the extreme parameters comprises a least square estimation (LS) method and a maximum likelihood estimation (ML) method, and the invention adopts the least square estimation (LS) method when the extreme value theory is applied.

(1) Least Squares (LS) estimation of EVT parameters:

sample sequence is notedThe sample sequences were arranged in ascending order:

whereinThe distribution function is thus counted:

by transforming formula (12)

-ln{-ln[F_n(x)]}＝(x-a_n)/b_n(16) Order:

z_i＝-ln{-ln[F_n(x)]}＝-ln{-ln[u_i]}

(18) the minimum variance estimation is to minimize the value of the following formula:

respectively to the parameter a_n,b_nAnd (3) obtaining the estimated values of two parameters by taking the derivative as 0:

(2) LS estimation of GEVT parameters

Transforming equation (13) to obtain:

z_i,u_iare set as formula (17) and formula (18), and the minimum variance estimates the three parameters v, a_n,c_nThat is, the following equation is minimized:

wherein the value of v is takenAndthe value of the correlation is the largest, and the correlation coefficient r (ν) is expressed as follows:

and v is taken as the best estimated value when the value of r (v) is maximum.

For the parameter a in the equation (23)_n,c_nThe derivative is found and is made 0, and the estimated values of the two parameters are solved:

further, a distribution function of the sample data is obtained through the estimated parameters

The false alarm probability function can be estimated as P_FA≈1-F_n(V_s)，V_sIs the detection threshold. The curve is shown in FIG. 2, it can be seen that the GEVT estimated curve is more consistent with the Monte Carlo statistical curve, and the false alarm probability requirement is 10^-6The logarithmic curve shown in FIG. 3 can be obtained by taking the logarithm of the curve, and it can be seen that the Monte Carlo samples are not enough, and 10 statistics cannot be carried out^-6The lower detection threshold, and the GEVT function curve can be accurately estimated. Thereby solving the problem of accurate prediction of 10 under 10000 samples^-6A detection threshold at a false alarm rate.

The invention provides a performance analysis method for a tracking technology before detection of weak and small targets based on an extreme value theory, and a plurality of methods and ways for specifically implementing the technical scheme, and the above description is only a preferred embodiment of the invention, and it should be noted that, for a person skilled in the art, a plurality of improvements and embellishments can be made without departing from the principle of the invention, and the improvements and embellishments should also be regarded as the protection scope of the invention. All the components not specified in the present embodiment can be realized by the prior art.