CN111398928B - Method for calculating detection threshold of synthetic ultra-narrow pulse radar based on resampling algorithm - Google Patents

Abstract

The invention provides a method for calculating a detection threshold of a synthetic ultra-narrow pulse radar based on a resampling algorithm.

Description

Method for calculating detection threshold of synthetic ultra-narrow pulse radar based on resampling algorithm

Technical Field

The invention relates to the technical field of target detection, in particular to a method for calculating a detection threshold of a synthetic ultra-narrow pulse radar based on a resampling algorithm.

Background

In synthetic very narrow pulse radar, the target no longer has the characteristics of an ideal point target, but rather behaves as an extended target containing multiple scattering points. At present, radar detection algorithms such as an integral detector, an MN detector, an SSD-GLRT (Spatial Scattering Density-Generalized Likelihood Ratio Test) detector, a sequential detector and the like are available, but detectors such as the SSD-GLRT and the sequential detector are difficult to calculate a detector threshold by an analytical method because the distribution of Test statistic obeys is difficult to obtain.

To obtain the threshold of such detectors, it is conventional to generate enough ambient noise signals, input them to the detector to obtain test statistics, and sort the samples from small to large to determine the detector threshold corresponding to the false alarm rate. The method needs to store a large amount of random numbers, has the defects of high memory occupation and low threshold calculation speed of the detector.

Disclosure of Invention

The invention provides a method for calculating a detection threshold of a synthetic ultra-narrow pulse radar based on a resampling algorithm, which aims to overcome the defect that a large number of random numbers need to be stored and occupy a memory in the traditional method and improve the calculation speed of the detector threshold.

In order to solve the technical problem, the invention provides a method for calculating a detection threshold of a synthetic extremely-narrow pulse radar based on a resampling algorithm, which comprises the following steps:

step one, inputting the number N of test statistics and arranging the false alarm rate into p in the order from large to small₁，p₂，...，p_MThe detector window length is L;

step two, the resampling random sample generator generates N windows with the length of L and the probability density function of f₁Of the noise signal x_n＝{x¹，x²，...，x^L}，n＝1，2，...，N；；

Step three, calculating the weight corresponding to the nth noise sample;

assuming that the probability density function of the ambient noise is f₀；

Step four, generating N test statistics T according to the judgment rule of the detector_n(x)，n＝1，2，...，N；

Step five, initializing a quantile generator, setting (2M +3) quantiles, and sequencing the first (2M +3) test statistics in a sequence from small to large to obtain a sequence statistic T⁽ⁱ⁾I 1, 2., (2M +3), calculated to yield T⁽ⁱ⁾Corresponding sample weight w_iFor the size q of the ith quantile value_iRepresents the number n of accumulated samples corresponding to the ith quantile_iSample increment Δ n corresponding to time-division bit points when the algorithm executes sequentially_iAnd represents the desired number of samples n 'for the ith quantile'_iThe following assignment operations are performed:

q_i＝T⁽ⁱ⁾，i＝1，2，...，(2M+3)；

n′_i＝1+2(M+1)Δn_i；

step six, inputting the jth test statistic T_j(x) Performing iterative update of a threshold, wherein j > (2M + 3);

step seven, outputting q_2m+1As false alarm rate p_m(M1, 2.. times.m) corresponds to an estimate of the threshold.

Further, the sixth step includes:

a) will T_j(x) And q is_iI 1, 2., (2M +3) are compared and T is determined_j(x) Returning to the intermediate variable k when the interval is T_j(x)＜q₁Or T_j(x)＞q_2M+3When q is updated₁Or q_2M+3；

b) Updating n_iAnd n'_i：

n_i＝n_i+w_i，i＝k，...，2M+3；

n′i＝n′_i+Δn′_i，i＝1，...，2M+3；

c) Adjusting the threshold corresponding to the (2M +2) th component site:

d＝n′_i-n_i，i＝2，...，2M+2；

d_l＝n_i-1-n_i；d_r＝n_i+1-n_i；

if (d is not less than 1 and d_rGreater than 1) or (d is less than or equal to-1 and d is_r< -1 >), then order

d′＝sign(d)；

If q is_i-1＜q′_i＜q _i+1, let the ith threshold and the number of samples be:

q_i＝q′_i；

n_i＝n′_i；

otherwise

n_i＝n′_i。

Further, the step a) comprises:

at T_j(x) In the interval of T_j(x)＜q₁Then, the intermediate variable k is returned to 1, and q is updated₁＝T_j(x)；

At T_j(x) In the interval q₁≤T_j(x)＜q₂If yes, returning an intermediate variable k to be 1;

at T_j(x) In the interval q₂≤T_j(x)＜q₃If yes, returning an intermediate variable k to be 2; ...;

at T_j(x) In the interval q_2M+2≤T_j(x)＜q_2M+3If yes, returning an intermediate variable k which is 2M + 2;

at T_j(x) In the interval q_2M+3＜T_j(x) Then, the intermediate variable k is returned to 2M +2, and q is updated_2M+3＝T_j(x)。

The invention has the beneficial effects that:

according to the method for calculating the detection threshold of the synthetic ultra-narrow pulse radar based on the resampling algorithm, random samples are generated through resampling, and the threshold corresponding to each false alarm rate of the detector is determined simultaneously by using the quantile interpolation algorithm, so that the defect that a large amount of random numbers need to be stored to occupy an internal memory in the traditional method is overcome, and the calculation speed of the threshold of the detector is improved.

Drawings

Fig. 1 is a schematic flow chart of a synthetic ultra-narrow pulse radar detection threshold calculation method based on a resampling algorithm according to an embodiment of the present invention;

FIG. 2 is a schematic view of an iterative update process according to a first embodiment of the present invention;

fig. 3 is a schematic diagram of threshold updating of the SSD-GLRT detector according to the first embodiment of the invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following detailed description and accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The first embodiment is as follows:

in order to solve the problems that a large number of random numbers need to be stored, the memory occupation is high and the threshold calculation speed of the detector is low in the traditional threshold determination mode, a quantile point interpolation algorithm is utilized. By setting the quantiles corresponding to the false alarm rate and calling an interpolation algorithm to iteratively update the corresponding thresholds of the quantiles according to the input test statistic, the defect that the traditional method for determining the quantiles by sequencing needs to store a large number of random numbers to occupy a memory is overcome.

The re-sampling enables the sampling algorithm to generate more samples contributing to the calculation of the false alarm rate by changing the probability distribution of the generated random numbers, further reduces the number of the generated samples required for accurately counting the false alarm probability, and improves the threshold acquisition speed of the detector.

The invention assumes that the environmental noise is additive complex Gaussian white noise and the noise power is sigma²With a probability density function of f₀The method provided by the invention is shown in figure 1 and mainly comprises the steps of resampling to generate random samples, calculating sample weight, generating test statistic, initializing a dynamic quantile generator, updating a threshold and outputting the threshold. The method comprises the following specific steps:

step one, inputting the number N of test statistics and arranging the false alarm rate into p in the order from large to small₁，p₂，...，p_MThe detector window length is L;

step two, the resampling random sample generator generates N windows with the length of L and the probability density function of f₁Of the noise signal x_n＝{x¹，x²，...，x^L}，n＝1，2，...，N

Step three, calculating the weight corresponding to the nth noise sample;

assuming that the probability density function of the ambient noise is f₀；

Step four, generating N test statistics T according to the judgment rule of the detector_n(x)，n＝1，2，...，N；

Step five, initializing a quantile generator, setting (2M +3) quantiles, and sequencing the first (2M +3) test statistics in a sequence from small to large to obtain a sequence statistic T⁽ⁱ⁾I 1, 2., (2M +3), calculated to yield T⁽ⁱ⁾Corresponding sample weight w_iFor the size q of the ith quantile value_iRepresents the number n of accumulated samples corresponding to the ith quantile_iSample increment Δ n corresponding to time-division bit points when the algorithm executes sequentially_iAnd represents the desired number of samples n 'for the ith quantile'_iThe following assignment operations are performed:

q_i＝T⁽ⁱ⁾，i＝1，2，...，(2M+3)；

n′_i＝1+2(M+1)Δn_i；

step six, inputting the jth test statistic T_j(x) Performing iterative update of a threshold, wherein j > (2M + 3);

step seven, outputting q_2m+1As false alarm rate p_m(M1, 2.. times.m) corresponds to an estimate of the threshold.

Wherein, step six includes:

a) will T_j(x) And q is_iI 1, 2., (2M +3) are compared and T is determined_j(x) Returning to the intermediate variable k when the interval is T_j(x)＜q₁Or T_j(x)＞q_2M+3When q is updated₁Or q_2M+3(ii) a See table 1 below:

TABLE 1

At T_j(x) In the interval of T_j(x)＜q₁Then, the intermediate variable k is returned to 1, and q is updated₁＝T_j(x)；

At T_j(x) In the interval q₁≤T_j(x)＜q₂If yes, returning an intermediate variable k to be 1;

at T_j(x) In the interval q₂≤T_j(x)＜q₃If yes, returning an intermediate variable k to be 2; ...;

at T_j(x) In the interval q_2M+2≤T_j(x)＜q_2M+3If yes, returning an intermediate variable k which is 2M + 2;

at T_j(x) In the interval q_2M+3＜T_j(x) Then, the intermediate variable k is returned to 2M +2, and q is updated_2M+3＝T_j(x)。

b) Updating n_iAnd n'_i：

n_i＝n_i+w_i，i＝k，...，2M+3；

n′_i＝n′_i+Δn′_i，i＝1，...，2M+3；

c) Adjusting the threshold corresponding to the (2M +2) th component site:

d＝n′_i-n_i，i＝2，...，2M+2；

d_l＝n_i-1-n_i；d_r＝n_i+1-n_i；

if (d is not less than 1 and d_rGreater than 1) or (d is less than or equal to-1 and d is_r< -1 >), then order

d′＝sign(d)；

If q is_i-1＜q′_i＜q_i+1Let the ith threshold and the number of samples be:

q_i＝q′_i；

n_i＝n′_i；

otherwise

n_i＝n′_i。

The following gives a simulation example to which the present invention is applied, and analyzes and explains the threshold determination process.

SSD-GLRT detector is the energy accumulation detection method based on scattering point space Density weighting (SSD). The SSD-GLRT detector firstly needs to know a priori parameter alpha of the density of target scattering points, and then reduces the influence of range unit echoes containing weak scattering points or non-scattering points on the detection performance of the detector by weighting the echoes of each range unit in a detection window. The method for solving the test statistic of the SSD-GLRT detector comprises the following steps:

x_irepresents the modulo square of the i-th range bin echo data within the detection window, at H₀Let x beⁱObey meanAn exponential distribution of 1, x_n＝{x¹，x²，...，x^L1,2, the probability density function of N can be expressed as:

the SSD-GLRT detector has no threshold calculation formula because it is difficult to find the likelihood function of the SSD-GLRT detector test statistic t (x).

To find the threshold, the conventional method is at H₀Under the assumption that L multiplied by N random numbers are generated, the test statistic T of each simulation is obtained by the judgment rule_i(x) 1,2, N, and mixing T_i(x) Arranged in the order of T from small to large⁽¹⁾，T⁽²⁾，…，T^(N)A decision of H is determined by the false alarm probability₁T of_i(x) The upper limit of the number U, and the sum of the number T^(N-U)The corresponding value is used as the detection threshold.

According to the invention, the threshold solving process comprises the following steps:

step one, determining the number N of input test statistics to be 10⁵The false alarm rate p is 0.1, and the window length L is 10;

step two, the resampling random sample generator generates N groups of data x with the window length of L and obeying the exponential distribution with the mean value of 2_n＝{x¹，x²，...，x^L1,2, N, whose probability distribution can be expressed as:

step three, calculating the weight of each noise sample:

step four, setting prior parameter alpha of scattering point density to be 0.1, and generating N test statistics T according to the judgment rule of the detector_n(x)，n＝1，2，...，N；

Step five, initializing the dynamic quantile generator, and sequencing the test statistics input in the first five times in a sequence from small to large to obtain a sequence statistic T ⁽ⁱ⁾1,2, 5, find the generation T⁽ⁱ⁾Weight w of corresponding sample_iAs shown in table 2 below:

TABLE 2

i	1	2	3	4	5
						T(i)	7.6977	7.7678	7.9533	8.4929	11.0927
wi	0.0843	0.0642	0.9472	0.0334	0.0371

To q is_i，n_i，Δn_i，n′_iPerforming assignment operation, as shown in the following table 3:

TABLE 3

Step six, after the initialization of the dynamic quantile generator is completed, continuously inputting the test statistic to carry out the iterative update of the threshold, wherein the iterative process is shown in figure 2;

in the simulation example, only 1 false alarm corresponding threshold is required, M is 1, 2M +3 is 5 quantiles q, so the 3 rd quantile q is taken₃As a detection threshold. Above table q₃7.9533 is the initial assignment, updating quantile q through six iterations of step₃To obtain q₃The final value is 5.5984, q in the updating process₃See fig. 3 for values of (a).

Step seven, outputting (1-p) -quantile point q₃The final value 5.5984 is taken as the estimate of the false alarm probability p for the threshold.

The obtained threshold is verified by Monte Carlo simulation, the SSD _ GLRT detector generates 1e5 test statistics, the comparison with the threshold 5.5984 is carried out, the obtained false alarm rate is 0.1002, and the correctness of the method can be verified.

It will be apparent to those skilled in the art that the steps of the present invention described above may be implemented in a general purpose computing device, centralized on a single computing device or distributed across a network of computing devices, or alternatively, in program code executable by a computing device, such that the steps shown and described may be performed by a computing device stored on a computer storage medium (ROM/RAM, magnetic or optical disk), and in some cases, performed in a different order than that shown and described herein, or separately fabricated into individual integrated circuit modules, or fabricated into a single integrated circuit module from multiple ones of them. Thus, the present invention is not limited to any specific combination of hardware and software.

The foregoing is a more detailed description of the present invention that is presented in conjunction with specific embodiments, and the practice of the invention is not to be considered limited to those descriptions. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (3)

1. The method for calculating the detection threshold of the synthetic extremely-narrow pulse radar based on the resampling algorithm is characterized by comprising the following steps of:

step one, inputting the number N of test statistics and arranging the false alarm rate into p in the order from large to small₁,p₂,…,p_MThe detector window length is L;

step two, the resampling random sample generator generates N windows with the length of L and the probability density function of f₁Of the noise signal x_n＝{x¹,x²,…,x^L},n＝1,2,…,N；

Step three, calculating the weight corresponding to the nth group of noise samples;

assuming that the probability density function of the ambient noise is f₀；

Step four, generating N test statistics T according to the judgment rule of the detector_n(x),n＝1,2,…,N；

Step five, initializing a quantile generator, setting 2M +3 quantiles, sequencing the first 2M +3 test statistics according to the sequence from small to large to obtain a sequence statistic T⁽ⁱ⁾I 1,2, …,2M +3, calculated to yield T⁽ⁱ⁾Corresponding sample weight w_iFor the size q of the ith quantile value_iWatch, watchNumber n of accumulated samples corresponding to ith quantile_iSample increment Δ n corresponding to time-division bit points when the algorithm executes sequentially_iAnd represents the desired number of samples n 'for the ith quantile'_iThe following assignment operations are performed:

q_i＝T⁽ⁱ⁾,i＝1,2,…,2M+3；

n′_i＝1+2(M+1)Δn_i；

step six, inputting the jth test statistic T_j(x) Performing an iterative update of a threshold, said j>(2M+3)；

Step seven, outputting q_2m+1As false alarm rate p_mM is 1,2, …, and M corresponds to an estimate of the threshold.

2. The resampling algorithm based synthetic extremely narrow pulse radar detection threshold calculation method according to claim 1, wherein the sixth step comprises:

a) will T_j(x) And q is_iI-1, 2, …,2M +3, and determining T_j(x) Returning to the intermediate variable k when the interval is T_j(x)<q₁Or T_j(x)>q_2M+3When q is updated₁Or q_2M+3；

b) Updating n_iAnd n'_i：

n_i＝n_i+w_i,i＝k,…,2M+3；

n′_i＝n′_i+Δn′_i,i＝1,…,2M+3；

c) Adjusting the threshold corresponding to the 2 nd, … nd, 2M +2 nd quantile:

d＝n′_i-n_i,i＝2,…,2M+2；

d_l＝n_i-1-n_i；d_r＝n_i+1-n_i；

if d is not less than 1 and d_r>1 or d is less than or equal to-1 and d_l<-1, then order

d′＝sign(d)；

If q is_i-1<q′_i<q_i+1Let the ith threshold and the number of samples be:

q_i＝q′_i；

n_i＝n′_i；

otherwise

n_i＝n′_i。

3. The resampling algorithm based synthetic extremely narrow pulse radar detection threshold calculation method according to claim 2, wherein the step a) comprises:

at T_j(x) In the interval of T_j(x)<q₁Then, the intermediate variable k is returned to 1, and q is updated₁＝T_j(x)；

At T_j(x) In the interval q₁≤T_j(x)<q₂If yes, returning an intermediate variable k to be 1;

at T_j(x) In the interval q₂≤T_j(x)<q₃If yes, returning an intermediate variable k to be 2;

……；

at T_j(x) In the interval q_2M+2≤T_j(x)<q_2M+3If yes, returning an intermediate variable k which is 2M + 2;

at T_j(x) In the interval q_2M+3<T_j(x) Then, the intermediate variable k is returned to 2M +2, and q is updated_2M+3＝T_j(x)。

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