A Statistical Modeling Method for the Peak Characteristics of the Echo Envelope in Missile-Target Interception

Abstract

A statistical modeling method for the peak characteristics of the echo envelope in projectile-target encounter, which extracts multiple peak amplitudes and the number of peaks of the envelope of the Doppler echo signal in projectile-target encounter, takes the median of the multiple peak amplitudes of each echo, establishes a joint statistical distribution model of the median of the peak amplitudes and the number of peaks of the envelopes of multiple Doppler echo signals in projectile-target encounter, realizes model parameter estimation, and realizes the statistical analysis and evaluation of the near-field characteristics of the target under projectile-target encounter conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of radar target near-field characteristic modeling, and in particular to a statistical modeling method for the peak characteristics of the echo envelope in a missile-target encounter. Background Art

[0002] At present, for the feature analysis and modeling of the missile-target encounter echo signal, on the one hand, the electromagnetic scattering calculation method is used to perform forward modeling on the missile-target encounter echo, and on the other hand, the signal processing method is used to extract and analyze the features of the missile-target encounter echo signal. Neither of them involves the statistical modeling content of the peak characteristics of the near-field echo envelope in a missile-target encounter. Summary of the Invention

[0003] The purpose of the present invention is to provide a statistical modeling method for the peak characteristics of the echo envelope in a missile-target encounter, establish a joint probability distribution model of the median and the number change of the peak amplitude for the echo signal envelope under different missile-target encounter states of the same target, and realize the statistical analysis and evaluation of the near-field characteristics of the target under missile-target encounter conditions.

[0004] To achieve the above purpose, the present invention provides a statistical modeling method for the peak characteristics of the echo envelope in a missile-target encounter, extracts multiple peak amplitudes and the number of peaks of the envelope of the missile-target encounter Doppler echo signal, takes the median of the multiple peak amplitudes of each echo, and establishes a joint probability density distribution model of the median of the peak amplitude and the number of peaks of the envelope of the missile-target encounter Doppler echo signal to realize model parameter estimation.

[0005] The joint probability density distribution model of the median of the peak amplitude and the number of peaks is as follows:

[0006]

[0007] where v is the Poisson distribution parameter, α is the shape parameter, β is the inverse scale parameter. Assume that an echo envelope in a missile-target encounter contains N peaks, N is odd, and the peak amplitudes are A1, A2,..., A N , let the number of peaks N follow a Poisson distribution with parameter v, and its probability density function is: The peak amplitude A i follows a gamma distribution, and its probability density function is: The median of the N peak amplitudes of the echo envelope is: A M = median[A1, A2,..., A N , and the probability density function of the median of the peak amplitude A M is: The statistical probability τ of the median of the peak amplitude A M follows a beta distribution,

[0008] The moment estimation method is used to calculate the Poisson distribution parameter v, shape parameter α, and inverse scale parameter β:

[0009] For L pieces of echo data of missile-target intersection, the numbers of peaks of their envelopes are N1, N2, ..., N L , and the corresponding peak amplitudes are respectively

[0010]

[0011]

[0012]

[0013] Among them, and respectively represent the first-order moment and second-order moment estimations of the echo peak amplitude, expressed as:

[0014]

[0015] The Kullback-Leibler distance is used to evaluate the modeling accuracy of the joint probability density distribution model of the median of the peak amplitude and the number of peaks of the missile-target intersection Doppler echo signal envelope:

[0016] Let represent the empirical probability density distribution of the median and the number of the peak amplitudes of the L missile-target intersection echo envelopes, and evaluate the K-L distance between f(A M , N) and is expressed as:

[0017]

[0018] The present invention establishes a joint probability distribution model of the changes in the median of the peak amplitude and the number for the peak characteristics of the echo signal envelope in different missile-target intersection states of the same target, and realizes the statistical analysis and evaluation of the near-field characteristics of the target under missile-target intersection conditions. Brief Description of the Drawings

[0019] Figure 1a is the missile-target intersection echo Doppler signal.

[0020] Figure 1b is the peak envelope of the missile-target intersection echo signal.

[0021] Figure 2a is the median filtering of the missile-target intersection echo amplitude.

[0022] Figure 2b is the matching of the missile-target intersection echo signal and the amplitude envelope.

[0023] Figure 3aIt is the statistical distribution function of the median and number probability of echo multi-peaks.

[0024] Figure 3b It is the empirical distribution function of the median and number probability of echo multi-peaks. Specific implementation mode

[0025] The following specifically describes the preferred embodiments of the present invention with reference to FIGS. 1 to 3.

[0026] Based on the assumption of the target point scatterer, a statistical modeling method for the peak characteristics of the missile-target echo envelope provided by the present invention includes the following steps:

[0027] Step S1, statistical modeling of the peak characteristics of the missile-target echo;

[0028] For the peak envelope extraction of any missile-target echo Doppler signal, the echo envelope exhibits multi-peak characteristics, and each peak characteristic corresponds to a scatterer of the target. The echo peak amplitude and number change are closely related to factors such as the target miss distance, miss azimuth, missile-target relative velocity, antenna beam width, and scatterer position.

[0029] Use a statistical distribution model to model the change in the number and amplitude of the peaks of a missile-target echo. Assume that a missile-target echo envelope contains N peaks, and the peak amplitudes are A1, A2,..., A N , let the number of peaks N follow a Poisson distribution with parameter v, and its probability density function is:

[0030]

[0031] The peak amplitude A i follows a gamma distribution, and its probability density function is:

[0032]

[0033] where α is the shape parameter and β is the inverse scale parameter,

[0034] Define the median of the N peak amplitudes of the echo envelope as follows:

[0035] A M = median[A1, A2,..., A N , (3)

[0036] where N is odd.

[0037] Sort the peak amplitudes A i in order statistics, and it can be deduced that the statistical probability τ of the peak amplitude median A M follows a beta distribution, and its probability density function is:

[0038]

[0039] Among them,

[0040] Thus, the joint probability density function of the median of the multi-peak amplitude and the number of peaks of the projectile-target encounter echo envelope is established, expressed as:

[0041]

[0042] where v is the Poisson distribution parameter, α is the shape parameter, and β is the inverse scale parameter.

[0043] Step S2, Model parameter estimation;

[0044] For the model parameters v, α, and β of the joint probability density function f(A M , N), the moment estimation method is used for calculation respectively.

[0045] For L pieces of projectile-target encounter echo data, the numbers of peaks of their envelopes are N1, N2,..., N L , and the corresponding peak amplitudes are respectively Using the moment estimation method, the model parameter estimations are respectively

[0046]

[0047]

[0048]

[0049] Among them, and respectively represent the first-order moment and second-order moment estimations of the echo peak amplitude, expressed as:

[0050]

[0051] Substitute equations (6)-(8) into equation (5) to obtain the joint probability density distribution model of the median of the peak amplitude and the number of peaks.

[0052] Step S3, Establish a model modeling accuracy evaluation criterion;

[0053] The Kullback-Leibler (K-L) distance is used to evaluate the modeling accuracy of the statistical distribution model of the median of the multi-peak amplitude and the number of peaks of the projectile-target encounter echo envelope.

[0054] The K-L distance (or information) represents the amount of information about the difference between two probability distribution models, and can also be expressed as the amount of information loss in predicting one probability distribution model from another probability distribution model.

[0055] Let represent the empirical probability density distribution of the median and number of the peak amplitudes of the echo envelopes of L projectile-target encounters, and evaluate the K-L distance between f(A M , N) and be expressed as:

[0056]

[0057] In an embodiment of the present invention, L pieces of projectile-target encounter echo data are selected, and the implementation approach for statistical modeling of its peak characteristics includes three parts: echo data preprocessing, model parameter estimation, and modeling accuracy evaluation.

[0058] 1. Preprocessing of projectile-target encounter echoes.

[0059] Transformation of the real signal of the projectile-target encounter echo into a complex signal. The Doppler signal of the projectile-target encounter echo is in the form of a real signal, generally considered as the echo signal of the in-phase receiving channel of the radar, expressed in the form of a cosine function. The change in the Doppler frequency reflects the periodicity of the signal change during the encounter process, and the change in the echo amplitude reflects the change in the radar target characteristics of the detection of the scatterer by the radar. Select a Doppler signal of a projectile-target encounter echo, as Figure 1a shown, and use the Hilbert transform method to transform it from a real signal to a complex signal to obtain the complex signal amplitude envelope characteristics, as Figure 1b shown. Due to the interference of the self-vibration noise of the detector carrying platform, the measurement noise of the receiver, etc. during the projectile-target encounter test, Figure 1b there are still a large amount of fluctuating noises in the peak envelope of the encounter echo in

[0060] Filtering and denoising of the projectile-target encounter echo envelope. To overcome the influence of noise interference factors in the projectile-target encounter echo data, a median filter is selected to Figure 1a and Figure 1b perform noise smoothing filtering on the encounter echo data in Figure 2a and Figure 2b shown. Figure 2a It shows that the median filter can effectively smooth the noise signal and obtain a relatively smooth amplitude envelope curve. Compare the amplitude envelope after median filtering with the Doppler signal of the near-field encounter echo, as Figure 2b shown, indicating that the echo envelope can accurately reflect the change in the amplitude of the Doppler echo signal.

[0061] Extraction of the peak characteristics of the echo envelope. Figure 2b The echo envelope in shows multi-peak characteristics, and each peak characteristic corresponds to a scatterer of the target. The partial overlapping of multiple peak envelopes indicates that there are multiple scatterers within one antenna beam. Set parameters such as the minimum peak height, minimum peak width, and peak spacing to extract the peak characteristics of the echo envelope.

[0062] 2. Statistical Modeling of Echo Envelope Peak Characteristics

[0063] Through the extraction of the peak envelope characteristic parameters of L intersection echoes, the number of peaks is N1, N2, ..., N L , and the corresponding peak amplitudes are respectively According to the moment estimation of the parameters of the statistical distribution model, Equations (6)-(8), the estimated values of the model parameters are respectively

[0064] Substitute into Equation (5) to obtain the joint probability density distribution function of the median A and the number N of multiple peaks of the intersection echo:

[0065]

[0066] where

[0067] Select L = 100 pieces of missile-target intersection echo data, and obtain the following parameter estimates

[0068]

[0069] Thus, calculate the joint probability distribution f(A M , N) of the median of the echo envelope peak amplitude and the number as Figure 3a shown

[0070] 3. Modeling Accuracy Evaluation

[0071] Through the extraction of the peak envelope characteristic parameters of L intersection echoes, the number of peaks is N1, N2, ..., N L , and the corresponding peak amplitudes are respectively

[0072] Take the median of the peak amplitude of each echo envelope:

[0073]

[0074] Through N1, N2, ..., N L and obtain the histogram distribution of the median of the multiple peak amplitudes of the echo envelope and the number of peaks, and thus obtain the empirical probability density distribution

[0075] For L = 100 pieces of missile-target intersection echo data, the distribution is as Figure 3b shown. Evaluate the difference between the probability density distribution model f(A M , N) and the empirical probability density distribution model through the K-L distance criterion, and obtain f(AM , N) The accuracy of modeling the peak characteristics of the cross - echo envelope.

[0076] The present invention establishes a joint probability distribution model of the median value and the number change of the peak amplitude for the peak characteristics of the echo signal envelope in different missile - target encounter states of the same target, and realizes the statistical analysis and evaluation of the near - field characteristics of the target under missile - target encounter conditions.

[0077] It should be noted that in the embodiments of the present invention, the orientation or positional relationship indicated by terms such as "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the embodiments, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0078] Although the content of the present invention has been introduced in detail through the above - mentioned preferred embodiments, it should be recognized that the above description should not be considered as a limitation of the present invention. After those skilled in the art have read the above content, various modifications and substitutions to the present invention will be obvious. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims

1. A statistical modeling method for the peak characteristics of the echo envelope in missile-target encounter, characterized in that Extract the multiple peak amplitudes and the number of peaks of the envelope of the missile-target encounter Doppler echo signal, take the median of the multiple peak amplitudes of each echo, establish a joint probability density distribution model of the median of the peak amplitudes and the number of peaks of the envelope of the missile-target encounter Doppler echo signal, and realize the estimation of the model parameters.

2. The statistical modeling method for the echo envelope peak characteristics of the missile-target encounter according to claim 1, characterized in that The joint probability density distribution model of the median of the peak amplitudes and the number of peaks is as follows: where ν is the Poisson distribution parameter, α is the shape parameter, and β is the inverse scale parameter. Assume that the envelope of the echo of a missile-target encounter contains N peaks, where N is odd, and the peak amplitudes are A1, A2,..., A N , and let the number of peaks N follow a Poisson distribution with parameter ν, and its probability density function is: The peak amplitude A i follows a gamma distribution, and its probability density function is: The median of the N peak amplitudes of the echo envelope is: A M = median[A1, A2,..., A N , and the probability density function of the peak amplitude median A M is: The statistical probability τ of the peak amplitude median A M follows a beta distribution, 3. The statistical modeling method for the echo envelope peak characteristics of missile-target encounter according to claim 2, characterized in that, Use the method of moment estimation to calculate the Poisson distribution parameter ν, the shape parameter α, and the inverse scale parameter β: For the L echo data of projectile-target intersection, the numbers of peak values of their envelopes are N1, N2,..., N L , and the corresponding peak amplitudes are Among them, and respectively represent the first-order moment and the second-order moment estimates of the echo peak amplitude, expressed as:

4. The statistical modeling method for the echo envelope peak characteristics of missile-target encounter according to claim 3, characterized in that Use the Kullback-Leibler distance to evaluate the modeling accuracy of the joint probability density distribution model of the median of the peak amplitudes and the number of peaks of the envelope of the missile-target encounter Doppler echo signal: Let represent the empirical probability density distribution of the median and the number of the peak amplitudes of the echo envelopes of L bar projectile intersections, and evaluate the K-L distance between f(A M , N) and is expressed as:

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