CN107728121B - Local goodness-of-fit inspection method based on variable window - Google Patents

Local goodness-of-fit inspection method based on variable window Download PDF

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CN107728121B
CN107728121B CN201710762845.8A CN201710762845A CN107728121B CN 107728121 B CN107728121 B CN 107728121B CN 201710762845 A CN201710762845 A CN 201710762845A CN 107728121 B CN107728121 B CN 107728121B
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sea clutter
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范一飞
王伟伟
杨晓超
李财品
黎薇萍
李奇
李渝
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Xian Institute of Space Radio Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The invention discloses a local goodness-of-fit inspection method based on a variable window. The goodness-of-fit test is a quantitative judgment on a sea clutter amplitude distribution model, the problem that amplitude observation intervals are single by mean square error test (MSD) and modified mean square test (MMSD) methods is solved, the weighted result of the goodness-of-fit test of the selected local intervals is calculated by selecting one or more radar-interested local amplitude observation intervals, the method enhances the comprehensiveness of the goodness-of-fit test result of the statistical model, and provides a more reliable basis for the judgment of a sea clutter amplitude sequence statistical model and the design of a sea surface target constant false alarm detection (CFAR) method.

Description

Local goodness-of-fit inspection method based on variable window
Technical Field
The invention relates to a local goodness-of-fit testing method for sea clutter amplitude statistical distribution based on a variable window, and belongs to the technical field of radars.
Background
The sea target detection is an important task of the radar, however, the sea clutter is an important factor influencing the radar target detection, and in order to effectively realize the target detection under the background of the sea clutter, a statistical distribution model of the sea clutter must be analyzed. For actually measured sea clutter data, it is inaccurate to select the best-fitting sea clutter amplitude model from various distribution models by visual observation only, so a statistic for quantitatively describing the fitting degree of the sea clutter amplitude model and the actually measured data, namely, a goodness-of-fit test, is needed. The traditional classical goodness-of-fit inspection method mainly comprises the following steps: MSD method and MMSD method. However, the MSD method only focuses on global statistical fitting of sea clutter amplitude statistics, and neglects the fitting effect of amplitude local intervals; the MMSD method only focuses on the fitting effect of the sea clutter large-amplitude sequence, namely the tailing fitting effect. The two typical goodness-of-fit inspection methods only consider the global or tail fitting result of the sea clutter amplitude singly, and neglect the fitting condition in the sea clutter local amplitude interval under different sea condition conditions. When the radar actually works, complex sea clutter echo signals under different sea conditions can be met, and the model fitting result of analyzing the sea clutter from the whole situation or the tail part only singly is incomplete and inaccurate.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for testing the local goodness of fit based on the variable window overcomes the defects of the prior art, can test the fitting condition in the local amplitude interval of the sea clutter under different sea conditions, enhances the reliability and comprehensiveness of the goodness of fit test, and provides a more reliable basis for target constant false alarm detection.
The technical solution of the invention is as follows: a local goodness-of-fit inspection method based on a variable window comprises the following steps:
(1) extracting a sea clutter amplitude sequence X ═ X from sea clutter echo data measured by radarkAnd equally dividing the sea clutter amplitude sequence into L intervals to obtain the actual probability density distribution p of the sea clutter amplitude statisticse(xl) Wherein N is the length of the sea clutter amplitude sequence, L is 1,2,3, …, L;
(2) according to the sea clutter amplitude sequence, calculating the amplitude statistical distribution model parameter of the sequence by adopting a moment estimation method, and fitting the sea clutter theoretical probability distribution function p of the statistical model by utilizing a common fitting methodt(xl)；
(3) Determining the number, position and length of local observation windows;
(4) sea clutter theoretical probability distribution function p fitted by aiming at each fitting methodt(xl) Calculating the local goodness-of-fit test result of each observation window, and obtaining the sea clutter theory fitted by each fitting method through weighting processingProbability distribution function pt(xl) And the actual probability density distribution pe(xl) The final fitting result of (1);
(5) the minimum value of the final fitting result corresponds to the theoretical probability distribution function p of the sea cluttert(xl) Namely the statistical distribution model of the amplitude sequence of the sea clutter with the best fitting.
In the step (1), the sea clutter amplitude sequence is equally divided into L intervals to obtain the actual probability density distribution p of sea clutter amplitude statisticse(xl) The method comprises the following steps:
equally dividing the sea clutter amplitude sequence into L intervals according to the maximum value and the minimum value in the sea clutter amplitude sequence, counting the number of the sea clutter amplitudes falling into each interval, and obtaining the actual probability density distribution function p of sea clutter amplitude statisticse(xl)，pe(xl) The number of sea clutter amplitudes falling into the ith interval/N. Wherein, the interval L>20。
In the step (2), the number of the local observation windows is equal to the number of the radar-interested local amplitude sequence areas, and the position [ N ] of the ith local observation windowi1，Ni2]Coinciding with the i-th local amplitude sequence region of interest of the radar, Ni1,Ni2Respectively represents the starting position and the ending position of the ith local observation window, and the length len of the ith local observation windowi＝Ni2-Ni1≥4，Ni2、Ni1Are all positive integers.
In the step (4), the goodness-of-fit test result of the ith local observation window is calculated by using the following formula:
Figure BDA0001393505210000021
in the step (4), the final fitting result D of the j fitting method is calculated by using the following formulalmsd：
Dlmsd＝α1Dlmsd,1+α2Dlmsd,2+…+αiDlmsd,i+…+αMDlmsd,M
0<αi<1, and α1+α2+…+αi+…+αM<And 1 and M are the total number of the local observation windows.
αiIs proportional to the sea state grade.
Compared with the prior art, the invention has the following beneficial effects:
the method solves the problem that the amplitude observation interval is single in the traditional method, provides the idea of windowing, can select the number, the position and the length of the local observation windows according to the actual observation requirement of the radar, matches the most suitable distribution model by calculating the inspection result of goodness of fit after windowing, and can inspect the fitting condition in the sea clutter local amplitude observation interval under different sea conditions. When the radar needs to take the fitting results of multiple groups of different intervals (multiple local intervals or multiple local intervals and the whole amplitude interval) into consideration, the combined fitting results of the multiple groups of intervals can be weighted and evaluated, the comprehensiveness of the test results of the fitting goodness of the statistical model is enhanced, and a powerful support is provided for the design of the sea surface target constant false alarm detection algorithm.
Drawings
FIG. 1 is a flow chart of a method for goodness of fit of variable window based local statistics;
FIG. 2 is a statistical fit result of an actually measured sea clutter amplitude sequence;
fig. 3 shows the goodness-of-fit test results of the actually measured sea clutter data, (a) shows MSD test results of four common distributions, (b) shows MMSD test results of four common distributions, and (c) shows local goodness-of-fit test results of four common distributions.
Detailed Description
In consideration of model fitting conditions under different sea conditions, the invention provides a variable window-based local goodness of fit (LMSD) method, which overcomes the problem that the existing method is single in amplitude observation area, and can calculate the goodness of fit inspection result of a local amplitude observation interval through windowing according to the observation requirement of a radar; when a plurality of observation intervals with different amplitudes are interested, the amplitude statistical goodness-of-fit test result under the combined action of the plurality of intervals can be calculated through weighting processing of the plurality of observation intervals, so that the reliability and the comprehensiveness of the goodness-of-fit test are enhanced, and a more reliable basis is provided for judgment of a sea clutter amplitude statistical model and design of a sea surface target constant false alarm detection method.
As shown in fig. 1, the main implementation steps of the present invention are as follows:
step 1, extracting a sea clutter amplitude sequence X ═ X from sea clutter echo data actually measured by a radarkAnd k is 1,2,3,.. N }, and N is the length of the sea clutter amplitude sequence. Equally dividing the sea clutter amplitude sequence into L intervals according to the maximum value and the minimum value in the sea clutter amplitude sequence, counting the occurrence frequency of the sea clutter amplitude in each interval, and obtaining the actual probability density distribution function p of sea clutter amplitude statisticse(xl). Wherein, L is not selected too small, and L is small, which may result in inaccurate fitting result of the amplitude distribution function, therefore, L is generally selected>20。l＝1,2,3,…,L。
The interval between two adjacent intervals is (maximum value-minimum value in amplitude sequence)/L, pe(xl) Dividing the number of the sea clutter amplitudes falling into the ith interval by the total number N of the sea clutter amplitudes.
Step 2, sea clutter amplitude statistical fitting:
according to the sea clutter amplitude sequence, calculating the amplitude statistical distribution model parameter of the sequence by adopting a moment estimation method, and fitting the sea clutter theoretical probability distribution function p of the statistical model by utilizing a common fitting methodt(xl)。
Step 3, determining the number, position and length of the local observation windows:
3.1 select the number M of observation windows. If the radar is only interested in a single local region of the sea clutter amplitude statistics, then a single rectangular window is selected, i.e. M is 1. If the radar is interested in a plurality of local areas of sea clutter amplitude statistics, a rectangular window is selected for each area, namely M >1, and then weighting processing is carried out on a plurality of local area fitting results. The invention mainly takes the fitting result of one group or two groups of observation intervals as an example for analysis, if more observation intervals are interested, M can also be selected to be a larger value, and the analysis method is similar to the case that M is 2.
3.2 after the number of the observation windows is determined according to the number 3.1, the position of the observation windows can be selected according to the interested area of the radar. When the radar is interested in the statistical distribution of the local amplitude of a certain part of the sea clutter, a rectangular window can be added to any observation interval; a rectangular window may be added over the entire observation interval when the radar is interested in a global fitting statistical distribution of sea clutter.
3.3 selection of the local observation window length. Let the ith local observation window be at [ N ]i1，Ni2]，Ni1,Ni2Respectively representing the start and end positions, N, of the ith local observation windowi2、Ni1Are all positive integers, and the length len of the ith local observation windowi＝Ni2-Ni1And the amplitude range of the windowed sequence is more than 4N/L of the amplitude of the whole sequence, so that enough amplitude samples can participate in operation, and the random error influence caused by too few noise and samples is reduced.
Step 4, calculating the local goodness of fit (LMSD) result of each observation window
For the jth fitting method, the result D of goodness-of-fit test of the ith local observation windowlmsd,i：
Figure BDA0001393505210000051
The final fitting result D of the jth fitting method is calculated by using the following formulalmsd：
Dlmsd＝α1Dlmsd,1+α2Dlmsd,2+…+αiDlmsd,i+…+αMDlmsd,M
0<αi<1, and α1+α2+…+αi+…+αM<And 1 and M are the total number of the local observation windows.
αiIs proportional to the level of the sea state, α is selected according to the actual observation requirementiThe higher the sea state grade is, the higher the weight of the large-amplitude sequence can be increased; sea stateThe lower the rank, the more equally the weight of the amplitude sequence can be reduced.
The choice of M weights is analyzed by taking M ═ 2 as an example, and so on for the case of M >2, that is:
Dlmsd＝α1Dlmsd,1+α2Dlmsd,2,0<α1<1,0<α2<1
α therein1,α2Respectively represents the weight values of the two groups of goodness-of-fit results, and satisfies α1+α2＝1。
Pair weight α1,α2Can be selected according to the actual radar observation needs. Under the condition of high sea, the weight of the large-amplitude observation interval can be increased; under the condition of low sea, the weight of the small-amplitude observation interval can be increased.
Suppose Dlmsd,1And Dlmsd,2Respectively representing the fitting test result of the global amplitude and the fitting test result of the local amplitude, and if the radar focuses on the result of the statistical combined action of the amplitude of the sea clutter and the fitting test result of the global amplitude and the fitting test result of the local amplitude, α can be selected1＝α20.5, α may be selected if the radar is more focused on global fit test results1＝0.7,α20.3, and α may be selected if the radar is more focused on local fit test results1＝0.3,α20.7, wherein, α1,α2The proportion of (A) can be properly adjusted according to actual needs.
Step 5, judging a statistical distribution model:
obtaining a local goodness-of-fit test result D of the sea clutter amplitude according to the step 4lmsdSimilar to conventional MSD and MMSD, DlmsdA smaller value of (a) indicates a better fit over this interval. By comparing different statistical distribution modelslmsdAs a result, the set of sea clutter data can be determined to fit the best statistical distribution model.
The effect of the invention is demonstrated by the test of measured data:
simulation conditions
Extracting sea clutter echo from sea clutter echo data actually measured by certain shore-based S-band radarWave amplitude sequence X ═ { X ═ Xk,k＝1,2,3,...,N}。
(II) simulation content
FIG. 2 is a statistical fit result of the actually measured sea clutter amplitude sequence. The test divides the sea clutter amplitude sequence into L (L is 50) observation intervals, and the histogram is the actual probability density distribution p of the sea clutter amplitude statisticse(xl) The four curves respectively correspond to the sea clutter theoretical probability distribution function p obtained by fitting the four fitting methodst(xl)。
Aiming at the fitting result of the measured data in fig. 2, the MSD test, the MMSD test and the LMSD test proposed by the present invention are respectively adopted to evaluate the goodness and badness of the fitting result.
Fig. 3 (a) shows the results of four common MSD tests, and it can be seen that: for the global statistical fitting of the sea clutter amplitude, the fitting effect of the K distribution is the best, the Weibull distribution and the Rayleigh distribution are followed, and the fitting effect of the log-normal distribution is the worst.
FIG. 3 (b) shows the results of MMSD test for four common distributions, which can be seen: for the statistical fitting (trailing fitting result) of the sea clutter large amplitude sequence, the fitting effect of the Weibull distribution is the best, and the fitting effect of the K distribution, the Rayleigh distribution and the log-normal distribution is the worst.
FIG. 3(c) shows the local goodness-of-fit test results for four common distributions, where two observation windows are selected, the first window being [1, 50 ], taking the weighted fit result as an example]Calculating a global fitting test result of the amplitude; the second observation window is [40, 50 ]]In addition, the weight of the two groups of fitting test results is selected as α1＝α20.5. As can be seen in fig. 3 (c): for the statistical fitting of the overall sea clutter amplitude and the combined action of the tail, the fitting effect of K distribution is the best, and then Weibull distribution and Rayleigh distribution are carried out, and the fitting effect of log-normal distribution is the worst.
MSD and MMSD only consider partial information of sea clutter amplitude, however, the local goodness-of-fit inspection method provided by the invention integrates global and local information, and is more comprehensive than the number of samples adopted from the whole and tail part intervals and other partial intervals, so that the conclusion obtained is more accurate and reliable.
Those skilled in the art will appreciate that the details of the invention not described in detail in the specification are within the skill of those skilled in the art.

Claims (5)

1. A local goodness-of-fit inspection method based on a variable window is characterized by comprising the following steps:
(1) extracting a sea clutter amplitude sequence X ═ X from sea clutter echo data measured by radarkAnd equally dividing the sea clutter amplitude sequence into L intervals to obtain the actual probability density distribution p of the sea clutter amplitude statisticse(xl) Wherein N is the length of the sea clutter amplitude sequence, L is 1,2,3, …, L;
equally dividing the sea clutter amplitude sequence into L intervals to obtain the actual probability density distribution p of sea clutter amplitude statisticse(xl) The method comprises the following steps:
equally dividing the sea clutter amplitude sequence into L intervals according to the maximum value and the minimum value in the sea clutter amplitude sequence, counting the number of the sea clutter amplitudes falling into each interval, and obtaining the actual probability density distribution function p of sea clutter amplitude statisticse(xl)，pe(xl) Number of sea clutter amplitudes/N falling into the L-th interval, wherein the interval L>20；
(2) According to the sea clutter amplitude sequence, calculating the amplitude statistical distribution model parameter of the sequence by adopting a moment estimation method, and fitting the sea clutter theoretical probability distribution function p of the statistical model by utilizing a common fitting methodt(xl)；
(3) Determining the number, position and length of local observation windows;
(4) sea clutter theoretical probability distribution function p fitted by aiming at each fitting methodt(xl) Calculating the local goodness-of-fit test result of each observation window, and obtaining the sea clutter theoretical probability distribution function p fitted by each fitting method through weighting processingt(xl) And the actual probability density distribution pe(xl) The final fitting result of (1);
(5) the minimum value of the final fitting result corresponds to the theoretical probability distribution function p of the sea cluttert(xl) Namely the statistical distribution model of the amplitude sequence of the sea clutter with the best fitting.
2. The method of claim 1, wherein the local goodness-of-fit test based on the variable window is as follows: in the step (2), the number of the local observation windows is equal to the number of the radar-interested local amplitude sequence areas, and the position [ N ] of the ith local observation windowi1，Ni2]Coinciding with the i-th local amplitude sequence region of interest of the radar, Ni1,Ni2Respectively represents the starting position and the ending position of the ith local observation window, and the length len of the ith local observation windowi＝Ni2-Ni1≥4，Ni2、Ni1Are all positive integers.
3. The method of claim 2, wherein the local goodness-of-fit test based on the variable window is as follows: in the step (4), the goodness-of-fit test result of the ith local observation window is calculated by using the following formula:
Figure FDA0002166784820000021
4. the method of claim 3, wherein the local goodness-of-fit test based on the variable window is as follows: in the step (4), the final fitting result D of the j fitting method is calculated by using the following formulalmsd：
Dlmsd＝α1Dlmsd,1+α2Dlmsd,2+…+αiDlmsd,i+…+αMDlmsd,M
0<αi<1, and α1+α2+…+αi+…+αM<And 1 and M are the total number of the local observation windows.
5. According toThe method of claim 4, wherein α is a method for testing local goodness-of-fit based on variable windowiIs proportional to the sea state grade.
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