CN114646935A - Sea clutter distribution parameter estimation method - Google Patents

Sea clutter distribution parameter estimation method Download PDF

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CN114646935A
CN114646935A CN202210181604.5A CN202210181604A CN114646935A CN 114646935 A CN114646935 A CN 114646935A CN 202210181604 A CN202210181604 A CN 202210181604A CN 114646935 A CN114646935 A CN 114646935A
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sea clutter
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范一飞
陈铎
宫延云
陶明亮
粟嘉
王伶
张兆林
李滔
谢坚
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Northwestern Polytechnical University
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Abstract

The invention provides a sea clutter distribution parameter estimation method, which improves the accuracy of distribution parameter estimation by windowing a sea clutter echo sample, thereby improving the target detection performance under the background of sea clutter. The method overcomes the defect that parameter estimation is carried out on generalized Pareto distribution based on a traditional moment estimation method, combines a traditional moment estimation theory with local characteristics of sea clutter, carries out windowing processing on a sea clutter sequence, and provides the sea clutter Pareto distribution parameter estimation method based on a variable interval, so that a result of goodness-of-fit inspection is improved, and target detection under a sea clutter background is facilitated to be improved. The method carries out parameter estimation by utilizing the second moment and the zero moment of the data in the interval, wherein the calculation of the zero moment is the percentage of the data in the total data, and compared with the traditional high moment, the method can improve the accuracy of parameter estimation.

Description

Sea clutter distribution parameter estimation method
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a sea clutter amplitude distribution model parameter estimation method. The method can be used for giving up to sea police or searching radar, fully considers the local distribution characteristics of the sea clutter samples by analyzing the statistical characteristics of the radar sea clutter units, improves the parameter estimation precision of the sea clutter distribution model, and provides technical support for the accurate design of the radar target detection method.
Background
In the application of radar target detection of sea surface background, the sea radar is usually subjected to interference of large-area sea clutter, and the detection performance of weak targets on the sea is severely restricted. The sea clutter characteristics are complex and changeable, wherein the sea clutter amplitude statistical characteristics are the basis of radar target detection algorithm design, and accurate judgment of a sea clutter statistical model is a key factor for improving target detection performance. Therefore, the development of accurate modeling and parameter estimation of the sea clutter amplitude distribution model is of great significance.
The sea clutter is not only influenced by natural environment factors such as wind speed, wind direction and sea condition, but also influenced by parameters such as radar working frequency, incidence angle and working bandwidth, so that the sea clutter has strong characteristics such as space-time correlation, instability, non-Gaussian and the like. The generalized Pareto distribution fully considers the time-space correlation and trailing characteristics of the sea clutter, can be accurately matched with a sea clutter amplitude distribution model, has a relatively simple probability density function expression, and is widely applied to the field of sea clutter modeling and target detection, so that the generalized Pareto distribution parameter estimation method mainly aims at the generalized Pareto distribution parameter estimation. However, the traditional generalized Pareto distribution parameter estimation adopts a moment estimation method, only the amplitude sequence of the whole sea clutter is considered, and the local characteristics of the sea clutter in different amplitude intervals under different sea conditions are ignored; meanwhile, the actually measured sea clutter data usually include abnormal scattering units, and the amplitude of the abnormal scattering units is high, so that the effect of parameter estimation is affected, and the effect of the moment estimation method is poor.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for estimating sea clutter distribution parameters. The invention aims to provide a variable interval-based sea clutter amplitude distribution model parameter estimation method aiming at the defect of poor robustness of the existing sea clutter amplitude distribution model parameter estimation method.
The method overcomes the defect of parameter estimation on generalized Pareto distribution based on the traditional moment estimation method, combines the traditional moment estimation theory with the local characteristics of the sea clutter, performs windowing processing on the sea clutter sequence, provides the sea clutter Pareto distribution parameter estimation method based on the variable interval, improves the result of goodness-of-fit inspection, and is beneficial to improving target detection under the sea clutter background.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
(1) sequencing a radar echo sequence;
transmitting pulse signals by using a radar transmitter, and setting a time domain echo signal X received by a radar receiver to be { X }kAnd k is 1,2,3, N as an amplitude sample sequence of the sea clutter data, and the obtained original amplitude sample sequence X is subjected to increasing ordering to obtain an increasing order sample sequence X' ═ { X }(k)N, where x is 1,2,3(k)Represents the kth sample element in the increasing sample sequence X ', and N represents the length of the sea clutter sequence X';
(2) calculating an amplitude histogram of the sea clutter sequence;
according to the increasing order sea clutter sample data X' ═ X(k),k＝1,2,3..N, calculating a sea clutter amplitude histogram;
(3) calculating generalized Pareto distribution parameters;
(3.1) selecting a sea clutter sequence, and determining a selection criterion of the sea clutter sequence;
and (3) under the condition of high sea, the sea clutter sequence with larger amplitude in the sea clutter sequence is dominant, when parameter estimation is carried out, part of the sea clutter sequence with smaller amplitude is abandoned, and the sequence with larger amplitude is selected for parameter estimation. Similarly, in the low sea condition, the sea clutter sequence with smaller amplitude in the sea clutter sequence is dominant, when parameter estimation is carried out, part of the sea clutter sequence with larger amplitude is abandoned, and the sea clutter sequence with smaller amplitude is selected for parameter estimation;
(3.2) calculating interval second moment;
selecting an interval according to a probability density function of generalized Pareto distribution and the sequence X' of the sequence increasing sample obtained in the step (1) in combination with a selection criterion of the sea clutter sequence in the step (3.1)
Figure BDA0003522335830000021
The echo data in the interval is integrated to obtain the interval
Figure BDA0003522335830000022
The interval second moment within;
(3.3) calculating interval zero-order moment;
integrating to obtain an interval (x) according to a probability density function of generalized Pareto distribution and the radar echo sequence sequenced in the step (2)(L1),x(L2)) Zero order moments of the inner data;
(3.4) calculating parameters;
according to the steps (3.1) and (3.2), the solved interval second moment and the result of the data in the interval accounting for the percentage of the total data are combined, parameters lambda and a of generalized pareto distribution are solved, and the equation is as follows:
Figure BDA0003522335830000023
(4) testing and calculating the goodness of fit;
(4.1) calculating a mean square error (Msd);
the mean square error is one of the most commonly used methods used as a goodness-of-fit test, and the mean square error function is defined as:
Figure BDA0003522335830000031
wherein f isr(. and f)k(. -) represents a sample data probability density function and a fitting model probability density function, k represents the sequence number of the sea clutter sequence, and N represents the length of the sea clutter sequence;
(4.2) calculating a modified mean square error (Mmsd);
and correcting the mean square error, and mainly checking the fitting effect of the tailing part, wherein the effect is expressed on the sea clutter echo sequence and is the description effect on sea spikes, and the sea spikes seriously influence the detection of the marine radar on the target. In view of this, the improved mean square error is defined as:
Figure BDA0003522335830000032
Figure BDA0003522335830000033
wherein f isr(. represents a probability density function of sample data, ft(. cndot.) represents a fitted model probability density function,
Figure BDA0003522335830000034
set of trailing samples, taken to be minimal
Figure BDA0003522335830000035
To detect threshold values, functions
Figure BDA0003522335830000036
For constant false alarm detection, PfIs a false alarmRate;
msd and Mmsd are used for measuring the accuracy of parameter estimation, and the smaller the result values of Msd and Mmsd are, the smaller the error between the sample data probability density function and the fitting model probability density function is, and the more accurate the parameter estimation is.
In the step 3.2, the interval second order moment is defined according to the upper and lower boundaries of the interval as follows:
Figure BDA0003522335830000037
Figure BDA0003522335830000038
Figure BDA0003522335830000039
wherein L is1And L2Are respectively two quantiles, and 0 is more than L1＜L2＜1，
Figure BDA00035223358300000310
And
Figure BDA00035223358300000311
respectively represent quantiles L1And L2The amplitude value of the sea clutter sequence is obtained,
Figure BDA00035223358300000312
representing the calculation result of the interval second moment;
the significance of the interval estimation in the actual clutter sequence is as follows: echo sequence x with length N1,x2...xNAnd (3) performing increasing sequencing, and combining the selection criterion of the sea clutter sequence in 3.1 according to the difference of the sea clutter echo data of different sea conditions and different distance units, and calculating the second-order origin moment of the data in the interval according to the following formula:
Figure BDA0003522335830000041
in the step 3.3, the interval zero order moment is a percentage of the data in the calculation interval in the total data, and the zero order moment of the data in the interval is defined as follows according to the upper and lower boundaries of the interval:
Figure BDA0003522335830000042
wherein
Figure BDA0003522335830000043
Representing the calculation result of the interval zero order moment.
The sea clutter Pareto distribution parameter estimation method based on the variable interval has the advantages that the sea clutter Pareto distribution parameter estimation method based on the variable interval is provided according to the difference of sea clutter echo data of different sea conditions and different distance units, interval parameter estimation is completed through windowing, the fitting effect of a generalized Pareto distribution probability density function is improved, and target detection under the sea clutter background is facilitated to be improved.
The method utilizes the second moment and the zero moment of the data in the interval to carry out parameter estimation, wherein the calculation of the zero moment is the percentage of the data in the total data, and compared with the traditional high moment, the method can improve the accuracy of parameter estimation.
Drawings
FIG. 1 is a flow chart of an algorithm implementation of the present invention.
FIG. 2 is a graph of the probability density function of sample data and the probability density function of a fitted model.
Figure 3 is a graph of the results of the mean square error between the sample data probability density function and the fitted model probability density function.
Figure 4 is a graph of the results of improving the mean square error between the sample data probability density function and the fitted model probability density function.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Referring to fig. 1, the specific implementation process of the present invention is as follows:
step 1: and sequencing the radar echo sequence. Transmitting pulse signals by using a radar transmitter, and converting time domain sample echo signals X received by a radar receiver into { X }kAnd k is 1,2,3, N and is used as a sample sequence of the sea clutter data, and the sample echo sequence is subjected to increasing sequencing to obtain an increasing sample sequence X' ═ { X ═(k),k＝1,2,3...N}。
And 2, step: and (5) carrying out amplitude histogram statistics on the sea clutter sequence. According to the echo sequence X of the increasing sequence sea clutter samples, X is { X ═ X(k)And k is 1,2,3.
And 3, step 3: calculating generalized Pareto distribution parameters;
3.1) calculating the probability density function expression of the generalized Pareto distribution.
The received vector of the generalized Pareto distribution is represented as:
Figure BDA0003522335830000051
wherein c is a radar receiver receiving vector, tau is a slowly-varying texture component, u is a rapidly-varying speckle component, the texture component is a random variable subject to inverse gamma distribution, and a probability density expression of the texture component is as follows:
Figure BDA0003522335830000052
wherein a is a scale parameter; λ is a shape parameter; Γ (·) is a gamma function;
the speckle component is subject to a complex gaussian random variable with a mean value of 0. The magnitude of the clutter vector is expressed as:
Figure BDA0003522335830000053
wherein (c) (i) represents the ith component of the clutter vector, and according to the expression of the clutter vector x, under the condition that the texture component tau is known, the clutter amplitude x is a mode of two Gaussian distributions with the same mean and variance, and obeys Rayleigh distribution. The conditional probability density function expression of clutter amplitude x is:
Figure BDA0003522335830000054
and (3) according to a total probability formula, deducing a probability density expression of the sea clutter amplitude x:
Figure BDA0003522335830000055
order to
Figure BDA0003522335830000056
Substituting the formula to obtain:
Figure BDA0003522335830000057
wherein x is clutter amplitude; λ is a shape parameter; a is a scale parameter. Lambda determines the non-gaussian nature of the sea clutter, lambda → ∞, the generalized Pareto distribution degenerates to a rayleigh distribution; λ → 0, the generalized Pareto distribution tails slightly heavier.
3.2) calculating an expression of interval second moment estimation aiming at the sequence increasing echo sequence obtained in the step 3.1), and obtaining an equation:
Figure BDA0003522335830000061
3.3) aiming at the sequence increasing echo sequence obtained in the step 3.1), calculating the zeroth order moment of the data in the interval, and obtaining an equation:
(1+aλ-1x(L1) 2)-λ-(1+aλ-1x(L2) 2)-λ＝L2-L1
3.4) solving for the parameters a and λ for the equations listed in 3.2) and 3.3), a system of simultaneous equations.
Step 4, testing the goodness of fit;
4.1) drawing a sample data probability density function graph and a curve chart of a fitting model probability density function according to parameters lambda and a of the Pareto distribution estimated in the step 3 to obtain a graph 2.
4.2) carrying out goodness-of-fit test on the curve chart drawn in the step 4.1), and calculating the mean square error (msd) between the probability density function of the sample data and the probability density function of the fitting model, wherein the calculation formula is as follows:
Figure BDA0003522335830000062
wherein f isr(. and f)tAnd (t) the sample data probability density function and the fitting model probability density function are represented, k represents the sequence number of the sea clutter sequence, and N represents the length of the sea clutter sequence.
4.2) carrying out goodness-of-fit test on the curve chart drawn in the step 4.1), and calculating a corrected mean square error (mmsd) between the probability density function of the sample data and the probability density function of the fitting model, wherein the calculation formula is as follows:
Figure BDA0003522335830000063
Figure BDA0003522335830000064
fr(. and f)k(. cndot.) is defined as in mean square error, fr(. represents a probability density function of sample data, fk(. cndot.) represents a fitted model probability density function,
Figure BDA0003522335830000065
representing a set of trailing samples. Get the smallest
Figure BDA0003522335830000066
In order to detect the threshold value(s),function(s)
Figure BDA0003522335830000067
For constant false alarm detection, PfIs the false alarm probability.
The effect of the invention can be further illustrated by the following measured data experiment:
experimental data: the file name of the actually measured sea clutter data set selected in the experiment is 19980126_222936_ ANTSTEP.CDF, the number of distance cells is 28, the number of pulses of each distance cell is 60000, and 28 data are 60000 in total, and the detailed radar parameters are shown in Table 1:
table 1X-band radar parameter index table
Parameter index Parameter value
Intermediate frequency 150MHz
Radar resolution 30m
Height of antenna 30m
Pulse width 200us
Antenna gain 45.7dB
Polarization mode HH、HV、VH、VV
The experimental conditions are as follows: in the experiment, the sea clutter data of the distance units 1,2,3, 4, 6, 7, 8, 9, 12 and 13 are selected. The experiment uses generalized pareto distribution to model the actually measured sea clutter data, and adopts a double-quantile estimation method, a truncation moment estimation method and an interval moment estimation method to estimate parameters.
Test contents and results:
figure 3 is a graph of the results of the mean square error between the sample data probability density function and the fitted model probability density function. It can be seen from fig. 3 that the mean square error value (msd) between the fitted model probability density function derived using interval moment estimation and the sample data probability density function is minimal.
Figure 4 is a graph of the results of improving the mean square error between the sample data probability density function and the fitted model probability density function. It can be seen from fig. 4 that the modified mean square error value (mmsd) between the fitted model probability density function estimated using interval moments and the sample data probability density function is the smallest.
And (3) testing the performance of goodness of fit: in this section, the results of averaging the mean square error (msd) and the modified mean square error (mmsd) between the ten distance unit fitting model probability density functions obtained by the present invention and the sample data probability density function were analyzed. Table 2 shows the error value comparison for different parameter estimation methods.
TABLE 2 comparison of goodness of fit test Performance for different methods
Parameter estimation method msd mmsd
The proposed method 4.3952×10-4 1.0352×10-9
Truncation moment estimation 4.7805×10-4 2.4614×10-9
Dual split-site estimation 1.2×10-3 2.3783×10-9
It can be found intuitively from table 2: the parameter estimation method can emphatically improve the fitting effect of the trailing part of the probability density function on the basis of integrally improving the fitting effect of the probability density function of the fitting model, is favorable for inhibiting the interference of clutter with larger amplitude on target detection, and improves the performance of the target detection.

Claims (3)

1. A sea clutter distribution parameter estimation method is characterized by comprising the following steps:
(1) sequencing radar echo sequences;
transmitting pulse signals by using a radar transmitter, and setting a time domain echo signal X received by a radar receiver to be { X }kAnd k is 1,2,3, N as an amplitude sample sequence of the sea clutter data, and the obtained original amplitude sample sequence X is subjected to increasing ordering to obtain an increasing order sample sequence X' ═ { X }(k)N, where x is 1,2,3(k)Represents the kth sample element in the increasing sample sequence X ', and N represents the length of the sea clutter sequence X';
(2) calculating an amplitude histogram of the sea clutter sequence;
according to the increasing order sea clutter sample data X ═ X(k)And k is 1,2,3A degree histogram;
(3) calculating generalized Pareto distribution parameters;
(3.1) selecting a sea clutter sequence, and determining a selection criterion of the sea clutter sequence;
(3.2) calculating interval second moment;
selecting an interval according to a probability density function of generalized Pareto distribution and the sequence X' of the sequence increasing sample obtained in the step (1) in combination with a selection criterion of the sea clutter sequence in the step (3.1)
Figure FDA0003522335820000011
The echo data in the interval are integrated to obtain an interval
Figure FDA0003522335820000012
Interval second moment within;
(3.3) calculating interval zero-order moment;
integrating to obtain an interval (x) according to a probability density function of generalized Pareto distribution and the radar echo sequence sequenced in the step (2)(L1),x(L2)) Zero order moments of the inner data;
(3.4) calculating parameters;
according to the steps (3.1) and (3.2), the solved interval second moment and the result of the data in the interval accounting for the percentage of the total data are combined, parameters lambda and a of generalized pareto distribution are solved, and the equation is as follows:
Figure FDA0003522335820000013
(4) testing and calculating the goodness of fit;
(4.1) calculating mean square error Msd;
the mean square error function is defined as:
Figure FDA0003522335820000014
wherein f isr(. and f)k(. cndot.) represents sample data probabilityA density function and a fitting model probability density function, wherein k represents the sequence number of the sea clutter sequence, and N represents the length of the sea clutter sequence;
(4.2) calculating a corrected mean square error Mmsd;
the improved mean square error is defined as:
Figure FDA0003522335820000021
Figure FDA0003522335820000022
wherein f isr(. represents a probability density function of sample data, ft(. cndot.) represents a fitted model probability density function,
Figure FDA0003522335820000023
set of trailing samples, taken to be minimal
Figure FDA0003522335820000024
To detect threshold values, functions
Figure FDA0003522335820000025
For constant false alarm detection, PfIs the false alarm probability;
msd and Mmsd are used for measuring the accuracy of parameter estimation, and the smaller the result values of Msd and Mmsd are, the smaller the error between the sample data probability density function and the fitting model probability density function is, and the more accurate the parameter estimation is.
2. The sea clutter distribution parameter estimation method according to claim 1, wherein:
in the step 3.2, the interval second order moment is defined according to the upper and lower boundaries of the interval as follows:
Figure FDA0003522335820000026
Figure FDA0003522335820000027
Figure FDA0003522335820000028
wherein L is1And L2Are respectively two quantiles, and 0 is more than L1＜L2＜1，
Figure FDA0003522335820000029
And
Figure FDA00035223358200000210
respectively represent quantiles L1And L2The amplitude value of the sea clutter sequence is obtained,
Figure FDA00035223358200000211
representing the calculation result of the interval second moment;
the significance of the interval estimation in the actual clutter sequence is as follows: echo sequence x with length N1,x2...xNAnd (3) performing increasing sequencing, and combining the selection criterion of the sea clutter sequence in the step (3.1) according to the difference of the sea clutter echo data of different sea conditions and different distance units, and calculating the second-order origin moment of the data in the interval according to the following formula:
Figure FDA00035223358200000212
3. the sea clutter distribution parameter estimation method according to claim 1, wherein:
in the step 3.3, the interval zero order moment is a percentage of the data in the calculation interval in the total data, and the zero order moment of the data in the interval is defined as follows according to the upper and lower boundaries of the interval:
Figure FDA0003522335820000031
wherein
Figure FDA0003522335820000032
Representing the calculation result of the interval zero order moment.
CN202210181604.5A 2022-02-26 2022-02-26 Sea clutter distribution parameter estimation method Pending CN114646935A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115390031A (en) * 2022-07-15 2022-11-25 西北工业大学 High-resolution sea clutter modeling and simulation method
CN117970279A (en) * 2024-04-02 2024-05-03 中国人民解放军火箭军工程大学 Sea clutter-based dual CG-IG distribution model and parameter correction method thereof

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115390031A (en) * 2022-07-15 2022-11-25 西北工业大学 High-resolution sea clutter modeling and simulation method
CN115390031B (en) * 2022-07-15 2024-04-19 西北工业大学 High-resolution sea clutter modeling and simulation method
CN117970279A (en) * 2024-04-02 2024-05-03 中国人民解放军火箭军工程大学 Sea clutter-based dual CG-IG distribution model and parameter correction method thereof

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