CN111830481A - Radar echo single-component amplitude distribution model parameter estimation method and device - Google Patents

Radar echo single-component amplitude distribution model parameter estimation method and device Download PDF

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CN111830481A
CN111830481A CN202010657861.2A CN202010657861A CN111830481A CN 111830481 A CN111830481 A CN 111830481A CN 202010657861 A CN202010657861 A CN 202010657861A CN 111830481 A CN111830481 A CN 111830481A
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ccdf
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radar echo
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CN111830481B (en
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丁昊
董云龙
刘宁波
周伟
黄勇
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Naval Aeronautical University
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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
    • G01S7/41—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
    • G01S7/414—Discriminating targets with respect to background clutter
    • 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
    • G01S7/417—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 involving the use of neural networks
    • 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
    • G01S7/418—Theoretical aspects

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  • Radar Systems Or Details Thereof (AREA)

Abstract

The embodiment of the invention provides a method and a device for estimating parameters of a radar echo single-component amplitude distribution model, wherein the method comprises the following steps: based on radar echo data, determining experience CCDF, an experience CCDF interval range and corresponding experience quantile points; determining an initial theoretical CCDF (complementary continuous function) based on initial parameters of a radar echo single-component amplitude distribution model; determining a theoretical quantile corresponding to each empirical quantile in the range of the empirical CCDF interval; and (3) performing iterative optimization on model parameters of the radar echo single-component amplitude distribution model by taking the minimum error of the empirical quantile and the theoretical quantile in the CCDF interval as a target function to obtain a parameter estimation value of the radar echo single-component amplitude distribution model. The method and the device provided by the embodiment of the invention have general applicability to parameter estimation of a radar echo single-component amplitude distribution model, have robustness to abnormal samples, and can be used for radar target detection under a clutter background.

Description

Radar echo single-component amplitude distribution model parameter estimation method and device
Technical Field
The invention relates to the technical field of signal processing, in particular to a method and a device for estimating parameters of a radar echo single-component amplitude distribution model, which can be used for radar target detection under a clutter background.
Background
Modern radars usually use higher resolution to improve the performance of detecting and identifying weak and small targets, and at this time, the non-gaussian characteristic of the echo amplitude distribution is very significant. In order to improve the goodness of fit between a theoretical model and an empirical Probability Density Function (PDF) of measured data, some two-parameter, three-parameter or multi-parameter non-Gaussian models are applied to radar echo amplitude distribution modeling. From the perspective of the number of model components, the single-component amplitude distribution model is a class of models that are more applied and in most cases work better. The models have a common characteristic that only a single component is adopted to model the radar echo in a mathematical form, and although the contributions of different types of scattering components may be considered in the model establishing process (for example, a composite Gaussian model respectively considers the scattering components of sea surface gravity waves and tension waves and models the scattering components into texture components and speckle components), the final distribution model is in a single-component form.
Typical single component models that are used more often mainly include lognormal, weibull, K, GK (texture component modeling is a complex Gaussian model of generalized Gamma distribution), GK-LNT (texture component modeling is a complex Gaussian model of lognormal distribution), CG-IG (texture component modeling is a complex Gaussian model of inverse Gaussian distribution), CG-GIG (texture component modeling is a complex Gaussian model of generalized inverse Gaussian distribution), Pareto (texture component modeling is a complex Gaussian model of inverse Gamma distribution). Under the conditions that the noise-to-noise ratio (CNR) is low (less than 5dB) and the thermal noise is not negligible, the influence of the thermal noise needs to be considered in a model, and the corresponding model mainly comprises K + noise, GK-LNT + noise, CG-IG + noise and Pareto + noise. A large amount of measured data of radar echoes prove that one or more of the 12 single-component models can meet the modeling precision requirement under most conditions, especially under the condition of low sea state (grade 3 and below).
In the radar target detection, the detection threshold is closely related to model parameters and modeling precision, so that how to apply echo data to realize effective parameter estimation and select a better candidate model from various single-component amplitude distribution models has important theoretical and practical engineering application values for better determining the detection threshold and obtaining better detection performance. In the prior art, a parameter estimation method of a single-component amplitude distribution model is mostly established on the basis of theoretical model characteristic quantity closed expression derivation, such as derivation of each moment, derivation of a maximum likelihood function, and the like. When there are abnormal samples in the echo data, the parameter estimation error is large. Therefore, the related patents apply the quantiles to model parameter estimation, such as a double quantile estimation method of sea clutter Pareto amplitude distribution parameters, a multi-quantile estimation method of sea clutter Weibull amplitude distribution parameters, a double quantile estimation method of sea clutter K distribution shape parameters, a generalized Pareto distribution parameter joint double quantile estimation method, a generalized Pareto distribution parameter explicit double quantile estimation method, a quantile estimation method and process based on inverse Gaussian texture sea clutter amplitude distribution parameters, and a quantile estimation method and process of sea clutter amplitude log-normal distribution parameters. The method can effectively overcome the influence of abnormal samples, but the number of the applied quantiles is at most 3, so that the utilization rate of the information of the quantile of the echo data is insufficient. Meanwhile, the parameter estimation method based on the quantile still cannot separate the derivation of the relational expression of the quantile and the model parameter, so that the parameter estimation precision strictly depends on the characteristic quantity of the theoretical model, the applicability of the parameter estimation method is poor, and the requirement of practical engineering application is difficult to meet.
Disclosure of Invention
The embodiment of the invention provides a method and a device for estimating parameters of a radar echo single-component amplitude distribution model, which are used for solving the problems that the utilization rate of echo quantile point information is insufficient, the applicability is poor and the practical engineering application requirements are difficult to meet in the parameter estimation method of the single-component amplitude distribution model in the prior art.
In a first aspect, an embodiment of the present invention provides a method for estimating parameters of a radar echo single-component amplitude distribution model, including:
based on radar echo data, determining experience CCDF, an experience CCDF interval range and corresponding experience quantile points; CCDF is a complementary cumulative distribution function;
determining an initial theoretical CCDF based on initial parameters of the radar echo single-component amplitude distribution model;
determining an initial theoretical quantile corresponding to each empirical quantile in the empirical CCDF interval range based on each empirical CCDF value in the empirical CCDF interval range and each initial theoretical CCDF value of which the difference value with each empirical CCDF value is in a preset difference value range;
and taking all the empirical quantiles in the empirical CCDF interval range and the theoretical quantile errors corresponding to the empirical quantile errors as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation value of the radar echo single-component amplitude distribution model.
Optionally, the determining an empirical CCDF, an empirical CCDF interval range, and an empirical quantile corresponding thereto based on the radar echo data includes:
determining the number of divisions of a statistical interval and the empirical CCDF based on radar echo data;
and determining the range of the empirical CCDF interval and the corresponding empirical quantile point based on the data point number of the radar echo data and the radar false alarm probability.
Optionally, the determining the empirical CCDF interval range and the corresponding empirical quantile thereof specifically includes:
determining quantiles of the empirical CCDF interval range based on the empirical CCDF interval range, and counting the number of the quantiles;
if the number of the sub-points in the empirical CCDF interval range is smaller than a preset threshold, increasing the upper value limit of the empirical CCDF interval range and/or decreasing the lower value limit of the empirical CCDF interval range;
counting the number of the loci of the experience CCDF within the adjusted experience CCDF interval until the number is greater than or equal to the preset threshold;
and taking the experience CCDF interval range adjusted for the last time as a final experience CCDF interval range.
Optionally, the errors of all the empirical quantiles and their corresponding theoretical quantiles in the empirical CCDF interval range are root mean square errors of all the empirical quantiles and their corresponding theoretical quantiles in the empirical CCDF interval range.
Optionally, the initial parameters of the radar echo single-component amplitude distribution model are determined based on the typical parameter values, or are determined based on a preset parameter estimation method.
Optionally, the performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by using a numerical optimization method to obtain the parameter estimation value of the radar echo single-component amplitude distribution model includes:
in a two-dimensional parameter space or a three-dimensional parameter space, carrying out iterative search solution on model parameters by using a numerical optimization method to obtain a parameter estimation value of the radar echo single-component amplitude distribution model;
the number of model parameters in the two-dimensional parameter space is two, and the models are correspondingly lognormal distribution, Weibull distribution, K distribution, GK-LNT distribution, CG-IG distribution and Pareto distribution;
the three model parameters in the three-dimensional parameter space are three, and the models correspond to GK distribution, CG-GIG distribution, K + noise distribution, GK-LNT + noise distribution, CG-IG + noise distribution and Pareto + noise distribution.
Optionally, the type of the radar echo single component amplitude distribution model is determined based on a noise to noise ratio of the radar echo data.
Optionally, the obtaining a parameter estimation value of the radar echo single-component amplitude distribution model further includes:
obtaining the modeling precision of each radar echo single-component amplitude distribution model by adopting a correction chi-square inspection method;
taking the radar echo single-component amplitude distribution model with the highest modeling precision as an optimal model;
representing an amplitude distribution of the echo data using the optimal model;
and determining a theoretical detection threshold according to the radar false alarm probability and the optimal model, judging whether a target exists or not according to the relation between the amplitude of the echo data and the theoretical detection threshold, if the amplitude of the echo data is higher than the theoretical detection threshold, judging that the target exists, otherwise, judging that the target does not exist.
In a second aspect, an embodiment of the present invention provides a radar echo single-component amplitude distribution model parameter estimation apparatus, including:
the experience CCDF determining unit is used for determining the experience CCDF, the range of the experience CCDF and the corresponding experience quantile point based on the radar echo data; CCDF is a complementary cumulative distribution function;
the initial theoretical CCDF determining unit is used for determining the initial theoretical CCDF based on the initial parameters of the radar echo single-component amplitude distribution model;
a quantile corresponding unit, configured to determine an initial theoretical quantile corresponding to each empirical quantile within the range of the empirical CCDF interval based on each empirical CCDF value within the range of the empirical CCDF interval and each initial theoretical CCDF value having a difference with each empirical CCDF value within a preset difference range;
and the iterative optimization unit is used for taking all the empirical quantiles in the empirical CCDF interval range and the theoretical quantile errors corresponding to the empirical quantile errors as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation values of the radar echo single-component amplitude distribution model.
In a third aspect, an embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor, when executing the computer program, implements the steps of the method for estimating parameters of a radar echo single-component amplitude distribution model according to the first aspect.
In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the method for estimating parameters of a radar echo single-component amplitude distribution model according to the first aspect.
According to the method and the device for estimating the parameters of the radar echo single-component amplitude distribution model, provided by the embodiment of the invention, the parameter of the radar echo single-component amplitude distribution model is iteratively optimized by determining the empirical CCDF interval range of radar echo data and minimizing the errors of all empirical quantiles and corresponding theoretical quantiles in the empirical CCDF interval range into a target function, so that the parameter estimation value of the model is obtained, a mode of combining multi-quantile points and numerical optimization is adopted in the parameter estimation process, a closed expression between the quantile points and the parameters of the distribution model is not required to be deduced, the method and the device have universal applicability to the parameter estimation of the radar echo single-component amplitude distribution model, and the requirement of practical engineering application can be met.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for estimating parameters of a radar echo single-component amplitude distribution model according to an embodiment of the present invention;
fig. 2 is a schematic diagram illustrating a condition of detecting a threshold loss when different parameter estimation methods are applied in a parameter estimation method of a radar echo single-component amplitude distribution model according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a radar echo single-component amplitude distribution model parameter estimation device according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the radar echo amplitude distribution modeling, the single component amplitude distribution models generally used mainly include lognormal distribution, weibull distribution, K distribution, GK distribution (texture component modeling is a complex Gaussian model of generalized Gaussian distribution), GK-LNT distribution (texture component modeling is a complex Gaussian model of lognormal distribution), CG-IG distribution (texture component modeling is a complex Gaussian model of inverse Gaussian distribution), CG-GIG distribution (texture component modeling is a complex Gaussian model of generalized inverse Gaussian distribution), Pareto distribution (texture component modeling is a complex Gaussian model of inverse Gamma distribution). Under the conditions that the noise-to-noise ratio (CNR) is low (less than 5dB) and the thermal noise is not negligible, the influence of the thermal noise needs to be considered in the model, and the corresponding model mainly comprises K + noise distribution, GK-LNT + noise distribution, CG-IG + noise distribution and Pareto + noise distribution. A large amount of measured data of radar echoes prove that one or more of the 12 single-component models can meet the modeling precision requirement under most conditions, especially under the condition of low sea state.
Each single-component amplitude distribution model corresponds to a plurality of parameter estimation methods. For example, for the K-distribution model, corresponding parameter estimation methods include maximum likelihood estimation, first order/second order moment estimation, second order/fourth order moment estimation, second order/fractional order moment estimation, geometric/arithmetic mean estimation, Log-type I estimation, Log-type II estimation, Log-type III estimation, maximum likelihood/moment estimation, moment estimation/neural network estimation, deep neural network estimation, Parameterized Curve Fitting Estimation (PCFE), and the like. The parameter estimation method is mostly established on the basis of theoretical model characteristic quantity closed expression derivation, such as derivation of each order moment, derivation of a maximum likelihood function and the like, and the accuracy of parameter estimation strictly depends on the model characteristic quantity, so that the applicability of the parameter estimation method is limited.
In view of the deficiency of the prior art, fig. 1 is a schematic flow chart of a method for estimating parameters of a radar echo single-component amplitude distribution model provided in an embodiment of the present invention, as shown in fig. 1, the method includes:
step 110, determining an empirical CCDF, an empirical CCDF interval range and corresponding empirical quantile points based on radar echo data; CCDF is a complementary cumulative distribution function;
specifically, CCDF is an abbreviation of Complementary Cumulative distribution function (Complementary Cumulative distributing function). According to the radar echo data, an empirical CCDF (combined cycle-resolved Doppler) can be obtained by adopting a histogram statistical method, and the range of the empirical CCDF interval and the corresponding empirical quantile point are determined according to the data point number of the echo data and the radar false alarm probability.
Step 120, determining an initial theoretical CCDF based on initial parameters of the radar echo single-component amplitude distribution model;
specifically, the initial parameters of the radar echo single-component amplitude distribution model can be obtained by a preset parameter estimation method, and the typical parameter values can also be used as the initial parameters of the model. Substituting the initial parameters into the model theoretical expression to obtain initial theoretical PDF (Probability Density Function) and initial theoretical CDF (Cumulative Distribution Function) of the single-component amplitude Distribution model, respectively using pR(r) and PR(r) is as follows. On this basis, the initial theoretical CCDF can be obtained.
Step 130, determining an initial theoretical quantile corresponding to each empirical quantile within the range of the empirical CCDF interval based on each empirical CCDF value within the range of the empirical CCDF interval and each initial theoretical CCDF value of which the difference value with each empirical CCDF value is within a preset difference value range;
specifically, the CCDF value is the complementary cumulative distribution function value. According to the CCDF function relation, the CCDF value can be converted into the quantile point corresponding to the function value.
And for any empirical CCDF value within the range of the empirical CCDF interval, determining an initial theoretical CCDF value, and if the difference between the initial theoretical CCDF value and the empirical CCDF value is within a preset difference range, considering that the initial theoretical CCDF value is adjacent to the empirical CCDF value. The preset difference may be set according to actual conditions, and this is not specifically limited in the embodiment of the present invention.
And for each empirical CCDF value in the range of the empirical CCDF interval, respectively counting the initial theoretical CCDF value adjacent to the empirical CCDF value, converting the adjacent initial theoretical CCDF value into the initial theoretical quantile, and obtaining a group of initial theoretical quantiles corresponding to the empirical quantiles one by one after the conversion is completed.
And 140, taking all the empirical quantiles in the empirical CCDF interval range and the theoretical quantile errors corresponding to the empirical CCDF interval range as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation value of the radar echo single-component amplitude distribution model.
Specifically, for a radar echo single-component amplitude distribution model, an initial parameter is used as an initial value, the minimum error of each empirical quantile and a corresponding theoretical quantile in an empirical CCDF interval range is used as a target function, and a numerical optimization method is adopted to carry out iterative search solution in a parameter space corresponding to the model. And in each iteration, new model parameters are obtained and updated to the initial parameters of the model in the next iteration. The iterative search algorithm may adopt a Nelder-mead (nm) simplex search method, and the selection of the iterative search algorithm in the embodiment of the present invention is not particularly limited.
If the errors of all the empirical quantiles and the corresponding theoretical quantiles in the range of the empirical CCDF interval are smaller than a preset error value or the iterative search times are greater than preset solving times, the difference between the empirical quantile and the corresponding theoretical quantile is considered to be minimized, and the iterative optimization algorithm is converged; otherwise, the iterative solution process is continued.
And after the iterative solving process is finished, taking the finally iterated parameters as parameter estimation values of the radar echo single-component amplitude distribution model, substituting the parameter estimation values into a model theoretical expression, and obtaining a final theoretical PDF (Portable document Format) and theoretical CDF (compact disc) modeling result. And in different scanning periods and detection areas, the received echo data are respectively utilized to carry out model parameter estimation, so that model parameter updating is realized.
For distribution models such as lognormal, Weibull, K, GK-LNT, CG-IG and Pareto, the number of model parameters is two, and the corresponding parameter space is a two-dimensional parameter space; for distribution models such as GK, CG-GIG, K + noise, GK-LNT + noise, CG-IG + noise and Pareto + noise, the number of model parameters is three, and the corresponding parameter space is a three-dimensional parameter space.
And performing subsequent processing on the echo data by using the amplitude distribution of the echo data represented by the modeling result. The radar echo single-component amplitude distribution model obtained by using the parameter estimation method in the embodiment can be applied to radar target detection, and the method specifically comprises the following steps: determining a quantile point corresponding to the false alarm probability according to the preset false alarm probability and the theoretical CCDF, taking the quantile point as a theoretical detection threshold, judging whether a target exists or not according to the relation between the amplitude of echo data received by the current radar and the theoretical detection threshold, if the target exists or not, judging that the target does not exist. Compared with the existing parameter estimation method, the parameter estimation method provided by the embodiment is specially optimized for the amplitude distribution tailing area, and can suppress the influence of abnormal samples, so that the obtained theoretical CCDF model curve has higher goodness of fit with the actually-measured data empirical CCDF curve in the tailing area, the detection threshold obtained according to the theoretical CCDF model better conforms to the radar echo characteristics, and the method has an obvious effect of reducing the actual false alarm probability.
FIG. 2 is a schematic diagram of a detection threshold loss situation when different parameter estimation methods are applied in a radar echo single component amplitude distribution model parameter estimation method provided by an embodiment of the present invention, as shown in FIG. 2, where r1And r2Method for estimating different parameters respectively representing same single component modelLoss of detection threshold under conditions. It can be seen that the model obtained by the parameter estimation method of the embodiment has smaller detection threshold loss and is very beneficial to target detection.
According to the method for estimating the parameters of the radar echo single-component amplitude distribution model, provided by the embodiment of the invention, the parameter of the radar echo single-component amplitude distribution model is iteratively optimized by determining the empirical CCDF interval range of radar echo data and minimizing the errors of all empirical quantiles and corresponding theoretical quantiles in the empirical CCDF interval range as a target function, so that the parameter estimation value of the model is obtained, a mode of combining multi-quantile points and numerical optimization is adopted in the parameter estimation process, a closed expression between the quantile points and the parameters of the distribution model is not required to be deduced, the method has universal applicability to the parameter estimation of the radar echo single-component amplitude distribution model, and can meet the requirements of practical engineering application.
Based on the above embodiment, step 110 includes:
determining the number of divisions of a statistical interval and an empirical CCDF based on radar echo data;
and determining the range of the empirical CCDF interval and the corresponding empirical quantile point based on the data point number of the radar echo data and the radar false alarm probability.
In particular, for each coherent burst echo sequence X ═ (X) received by the radar1,x2,…,xN) And N is the number of data points. If the sequence is a complex number formed by I and Q channel data, firstly, taking a module of the I and Q channel data to obtain an envelope amplitude data sequence. And if the radar works in a scanning mode, extracting echo data in a pulse dimension and a distance dimension to obtain a data matrix, and converting the data matrix into a one-dimensional data vector. And if the radar works in a staring mode, extracting echo data in a pulse dimension to obtain a one-dimensional data vector. In order to ensure the model accuracy, the number of data points N of the echo data should be greater than a preset value, such as 2000.
And determining the division number of the statistical interval according to the number of echo data points.
For example, the division number is the number of data points of the echo data divided by a preset constant, such as 10. It is also possible to divide the number of data points of the echo data by a preset constant as an upper limit of the division number, and another preset constant as a lower limit of the division number, for example, the division number ranges from 50 to N/10, and arbitrarily take a value from this range as the division number.
Then, the maximum value and the minimum value of the echo amplitude are counted, and the echo amplitude range is divided into statistical intervals with equal intervals according to the division number of the statistical intervals in the echo amplitude range determined by the maximum value and the minimum value.
Obtaining the empirical PDF of the echo data by a histogram statistical method, which is expressed as
Figure BDA0002577400490000111
Integrate it to obtain an empirical CDF, expressed as
Figure BDA0002577400490000112
Further empirical CCDF was obtained, formulated as:
Figure BDA0002577400490000113
according to the number N of data points and the radar false alarm probability PfaAnd determining the range of the empirical CCDF interval corresponding to the empirical CCDF. Wherein the false alarm probability PfaWhen the threshold detection method is adopted in the radar detection process, due to the common existence and fluctuation of clutter, the probability that a target does not exist actually but is judged to be a target exists. The false alarm probability may be adjusted by adjusting the threshold value of the radar detection.
The lower limit of the range of the empirical CCDF interval is used for ensuring the accuracy of the statistical result and simultaneously has a certain inhibiting effect on abnormal samples. In terms of compromise, the lower limit of the range of the CCDF interval is [ C1/N, C2/N ], wherein C1 and C2 are preset constants, C1 is less than C2, for example, C1 is 10, and C2 is 100.
The upper limit of the range of the empirical CCDF interval corresponds to the starting point of the tailing area of the empirical CCDF curve, which is related to the false alarm probability PfaThe setting and its corresponding threshold value. The threshold value corresponding to the false alarm probability in the theoretical CCDF curve should be compared with the empirical CCDThe threshold values obtained by F are as consistent as possible. To ensure accuracy, the upper limit of the interval is greater than the false alarm probability Pfa. Verified that the upper limit value range of the CCDF interval is [ C3P ]fa，C4*Pfa]Wherein C3 and C4 are predetermined constants, C3 is smaller than C4, e.g., C3 is 10 and C4 is 100.
In summary, the lower limit of the range of CCDF interval is [ C1/N, C2/N]One value is taken as the lower limit of the CCDF interval range, and the corresponding amplitude interval number is Q. The upper limit of the range of CCDF interval is [ C3P ]fa，C4*Pfa]One value is taken as the upper limit of the range of the CCDF interval, and the corresponding amplitude interval is numbered as q.
Further, the quantile of the range of the empirical CCDF interval may be determined based on the range of the empirical CCDF interval.
According to the method for estimating the parameters of the radar echo single-component amplitude distribution model, provided by the embodiment of the invention, the influence of a certain amount of abnormal sample data can be effectively inhibited on the premise of ensuring the statistical accuracy by optimizing and selecting the range of the empirical CCDF interval, and meanwhile, the requirement of parameter estimation on the sample data volume can be effectively reduced.
Based on any of the above embodiments, determining an empirical CCDF interval range and its corresponding empirical quantile specifically includes:
determining quantiles of the empirical CCDF interval range based on the empirical CCDF interval range, and counting the number of the quantiles;
if the number of the quantile points in the empirical CCDF interval range is smaller than a preset threshold value, the upper value limit of the empirical CCDF interval range is increased and/or the lower value limit of the empirical CCDF interval range is decreased;
counting the number of the loci of the empirical CCDF within the adjusted empirical CCDF interval until the number is greater than or equal to a preset threshold;
and taking the last adjusted empirical CCDF interval range as the final empirical CCDF interval range.
Specifically, according to the empirical CCDF interval range, all quantiles of the empirical CCDF interval range are obtained through statistics, and the lower limit and the upper limit of the obtained quantiles are respectively expressed as
Figure BDA0002577400490000131
And
Figure BDA0002577400490000132
the number of quantiles that can be obtained is Q-Q + 1.
If the number of the quantiles in the empirical CCDF interval range is smaller than a preset threshold value, the estimation precision of the parameters is influenced, and the false alarm probability P of the radar can be determinedfaAdjusting the upper limit of the value of the range of the empirical CCDF interval to be [ C3P ]fa，C4*Pfa]The upper limit of the value is increased internally, and/or the lower limit of the value of the range of the empirical CCDF interval is adjusted to be (C1/N, C2/N)]And the lower limit of the value is internally adjusted to ensure that the number of the loci in the range of the empirical CCDF interval meets the requirement of a preset threshold value. The preset threshold may be set according to actual requirements, for example, 10, and the preset threshold is not specifically limited in the embodiment of the present invention.
Based on any of the above embodiments, all the empirical quantiles and their corresponding theoretical quantile errors in the empirical CCDF interval range are root mean square errors of all the empirical quantiles and their corresponding theoretical quantiles in the empirical CCDF interval range.
Specifically, the lower and upper limits of all quantiles of the empirical CCDF interval range are expressed as
Figure BDA0002577400490000133
And
Figure BDA0002577400490000134
the lower limit and the upper limit of the theoretical quantile point corresponding to the upper limit are respectively expressed as
Figure BDA0002577400490000135
And
Figure BDA0002577400490000136
the error of all the empirical quantiles and the corresponding theoretical quantile within the range of the empirical CCDF interval may be the root mean square error of all the empirical quantiles and the corresponding theoretical quantile within the range of the empirical CCDF interval.
Accordingly, in the above embodiment, the objective of minimizing the errors of all the empirical quantiles and the corresponding theoretical quantile within the range of the empirical CCDF interval is implemented by an objective function, where the objective function is a quantile Root Mean Square Error (RMSE) and is expressed by a formula:
Figure BDA0002577400490000137
in the formula (I), the compound is shown in the specification,
Figure BDA0002577400490000141
the minimum value of the root mean square error of the quantile is; theta is a parameter of the radar echo single-component amplitude distribution model, and the parameter is related to the type of the single-component amplitude distribution model;
Figure BDA0002577400490000142
is an empirical quantile within an empirical CCDF interval;
Figure BDA0002577400490000143
is divided into sites according to experience
Figure BDA0002577400490000144
A corresponding theoretical quantile; i is the sequence number of the quantile; q is the amplitude interval number corresponding to the lower limit of the empirical CCDF interval range, and Q is the amplitude interval number corresponding to the upper limit of the empirical CCDF interval range.
Based on any embodiment, the initial parameters of the radar echo single-component amplitude distribution model are determined based on the typical parameter values, or determined based on a preset parameter estimation method.
Specifically, for the initial parameters of the radar echo single-component amplitude distribution model, the initial parameters can be determined according to typical parameter values or according to a preset parameter estimation method.
The initial parameters are determined according to the typical parameter values, the principle of efficiency priority is embodied, specifically, the typical parameter values obtained by the existing data analysis results are directly used as the initial parameters, and the typical parameter values are updated when the parameter estimation of the final step is completed.
The initial parameters are determined according to a preset parameter estimation method, and the principle of precision priority is embodied. The preset parameter estimation method can be moment estimation, maximum likelihood estimation and the like. According to the preset parameter estimation method, a rough parameter estimation value can be obtained, compared with a random parameter, the rough parameter estimation value has certain precision, is suitable for ideal conditions, cannot meet the requirements of actual engineering, can be used as an initial parameter for iterative optimization, and then a final parameter with higher precision is obtained.
For example, if the radar echo single-component amplitude distribution model is a K distribution model, the preset parameter estimation method is selected as a second order/fourth order moment method, and the shape parameter can be obtained
Figure BDA0002577400490000145
And scale parameter
Figure BDA0002577400490000146
Is formulated as:
Figure BDA0002577400490000147
in the formula, the n-order moment E (R)n) Directly estimated from radar echo samples, n is 2 or 4, namely:
Figure BDA0002577400490000151
wherein x (i) represents the ith radar echo data, and the number of samples is N.
According to the method for estimating the parameters of the radar echo single-component amplitude distribution model, the initial parameters of the model are assigned according to a certain criterion instead of being set as random numbers, so that the iterative optimization method is guaranteed to be converged at a higher speed.
Based on any one of the above embodiments, a numerical optimization method is adopted to perform iterative optimization on the model parameters of the radar echo single-component amplitude distribution model to obtain the parameter estimation value of the radar echo single-component amplitude distribution model, and the method includes:
in a two-dimensional parameter space or a three-dimensional parameter space, carrying out iterative search solution on model parameters by using a numerical optimization method to obtain a parameter estimation value of a radar echo single-component amplitude distribution model;
the two-dimensional parameter space has two model parameters, and the models are correspondingly distributed in a log-normal mode, a Weibull mode, a K mode, a GK-LNT mode, a CG-IG mode and a Pareto mode;
the three model parameters in the three-dimensional parameter space are three, and the models correspond to GK distribution, CG-GIG distribution, K + noise distribution, GK-LNT + noise distribution, CG-IG + noise distribution and Pareto + noise distribution.
Based on any of the above embodiments, the type of the radar echo single component amplitude distribution model is determined based on the noise to noise ratio of the radar echo data.
Specifically, Fast Fourier Transform (FFT) is performed on coherent echo data before envelope taking along a pulse dimension to obtain a frequency spectrum of the radar echo data, spectral amplitudes of a clutter occupying dominant region (namely, a frequency spectrum peak region) and a noise occupying dominant region (namely, a region far away from a mainlobe frequency spectrum region) are compared, and a difference value is calculated to obtain a noise-to-noise ratio (CNR) estimation result.
The type of the radar echo single-component amplitude distribution model is determined according to the noise-to-noise ratio of radar echo data:
if the CNR is larger than 10dB, the thermal noise is considered to be negligible in the distribution model, and the corresponding candidate distribution models are 8 types, namely, lognormal distribution, Weibull distribution, K distribution, GK-LNT distribution, CG-IG distribution, CG-GIG distribution and Pareto distribution, wherein the GK distribution and the CG-GIG distribution are three-parameter models, and the rest are two-parameter models.
If the CNR is equal to or less than 10dB, the thermal noise is considered to be not negligible in the distribution model, and the corresponding candidate distribution models are 4 types, namely K + noise distribution, GK-LNT + noise distribution, CG-IG + noise distribution and Pareto + noise distribution, and are three-parameter models.
Based on any of the above embodiments, step 140 further includes:
obtaining the modeling precision of each radar echo single-component amplitude distribution model by adopting a correction chi-square inspection method;
taking a radar echo single-component amplitude distribution model with the highest modeling precision as an optimal model;
representing the amplitude distribution of the echo data by using an optimal model;
and determining a theoretical detection threshold according to the radar false alarm probability and the optimal model, judging whether the target exists or not according to the relation between the amplitude of the echo data and the theoretical detection threshold, if the amplitude of the echo data is higher than the theoretical detection threshold, judging that the target exists, otherwise, judging that the target does not exist.
Specifically, a correction chi-square test method is adopted to quantitatively analyze the modeling accuracy of different types of radar echo single-component amplitude distribution models. The fitting error of the modeling accuracy can be expressed by the goodness-of-fit return value η of the model as:
Figure BDA0002577400490000161
in the formula, m0Number of divisions, v, representing equally spaced statistical intervalsiAnd NPfapiRespectively representing the experience frequency and the theoretical frequency of the ith amplitude interval.
The smaller the return value eta of the goodness of fit is, the higher the modeling precision of the model is. And according to the return value of the goodness-of-fit of the multiple radar echo single-component amplitude distribution models of different types, applying the single-component amplitude distribution model with the minimum return value of the goodness-of-fit to the current radar echo data to complete parameter estimation.
According to the method for estimating the parameters of the radar echo single-component amplitude distribution model, the fitting error calculation of the distribution model is converted from a PDF domain or a CCDF domain into a quantile domain, namely the quantile errors are counted in a certain interval range, the probability distribution tailing region is given greater weight by the processing, and the method is closer to the setting requirement of a threshold value when the radar is subjected to Constant False Alarm Rate (CFAR) detection.
Based on any of the above embodiments, fig. 3 is a schematic structural diagram of a radar echo single-component amplitude distribution model parameter estimation apparatus provided in an embodiment of the present invention, as shown in fig. 3, the apparatus includes:
the empirical CCDF determining unit 310 is configured to determine an empirical CCDF based on the radar echo data, and determine an empirical CCDF interval range and an empirical quantile corresponding to the empirical CCDF interval range; CCDF is a complementary cumulative distribution function;
an initial theoretical CCDF determining unit 320, configured to determine an initial theoretical CCDF based on an initial parameter of the radar echo single-component amplitude distribution model;
an quantile point corresponding unit 330, configured to determine an initial theoretical quantile point corresponding to each empirical quantile point in the empirical CCDF interval range, based on each empirical CCDF value in the empirical CCDF interval range and each initial theoretical CCDF value having a difference with each empirical CCDF value within a preset difference range;
and the iterative optimization unit 340 is configured to take the minimum error of all the empirical quantiles and the corresponding theoretical quantile within the empirical CCDF interval as a target function, use the initial parameter as an initial value, and perform iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by using a numerical optimization method to obtain a parameter estimation value of the radar echo single-component amplitude distribution model. .
Specifically, the empirical CCDF determining unit 310 obtains an empirical CCDF according to the radar echo data, and determines an empirical CCDF interval range and an empirical quantile corresponding to the empirical CCDF interval range. The initial theoretical CCDF determining unit 320 is configured to substitute the initial parameters of the radar echo single-component amplitude distribution model into a model theoretical expression to obtain an initial theoretical CCDF.
And for any empirical CCDF value within the range of the empirical CCDF interval, determining an initial theoretical CCDF value, and if the difference between the initial theoretical CCDF value and the empirical CCDF value is within a preset difference range, considering that the initial theoretical CCDF value is adjacent to the empirical CCDF value.
The quantile point corresponding unit 330 is configured to count initial theoretical CCDF values adjacent to each empirical CCDF value in the range of the empirical CCDF interval, convert the adjacent initial theoretical CCDF values into quantiles, and obtain a group of initial theoretical quantiles corresponding to the empirical quantiles one to one after the conversion is completed.
The iterative optimization unit 340 is configured to use the initial parameter as an initial value, minimize the difference between each empirical quantile and its corresponding theoretical quantile within the empirical CCDF interval as a target, and perform iterative search solution in the parameter space corresponding to the model by using a numerical optimization method. And after the iterative solving process is finished, outputting the corresponding parameters as parameter estimation values of the radar echo single-component amplitude distribution model, substituting the parameter estimation values into a model theoretical expression, and obtaining a final theoretical PDF (Portable document Format) and theoretical CDF (compact disc) modeling result.
The radar echo single-component amplitude distribution model parameter estimation device provided by the embodiment of the invention has the advantages that the empirical CCDF interval of radar echo data is determined, the target is the minimization of the difference between each empirical quantile point and the corresponding theoretical quantile point in the empirical CCDF interval range, the iterative optimization is carried out on the initial parameters of the radar echo single-component amplitude distribution model to obtain the final parameters of the model, the mode of combining multi-quantile point and numerical optimization is adopted in the parameter estimation process, the closed expression between the quantile point and the distribution model parameters is not required to be deduced, the general applicability to the parameter estimation of the radar echo single-component amplitude distribution model is realized, and the requirements of practical engineering application can be met.
Based on any of the above embodiments, the empirical CCDF determining unit 310 includes:
the empirical CCDF determining subunit is used for determining the number of the divisions of the statistical interval and the empirical CCDF based on the radar echo data;
and the empirical CCDF interval determining subunit is used for determining the range of the empirical CCDF interval and the corresponding empirical quantile point based on the data point number of the radar echo data and the radar false alarm probability.
Based on any of the embodiments described above, the empirical CCDF interval determination subunit is specifically configured to:
determining quantiles of the empirical CCDF interval range based on the empirical CCDF interval range, and counting the number of the quantiles;
if the number of the quantile points in the empirical CCDF interval range is smaller than a preset threshold value, the upper value limit of the empirical CCDF interval range is increased and/or the lower value limit of the empirical CCDF interval range is decreased;
counting the number of the loci of the empirical CCDF within the adjusted empirical CCDF interval until the number is greater than or equal to a preset threshold;
and taking the last adjusted empirical CCDF interval range as the final empirical CCDF interval range.
Based on any of the above embodiments, all the empirical quantiles and their corresponding theoretical quantile errors in the empirical CCDF interval range are root mean square errors of all the empirical quantiles and their corresponding theoretical quantiles in the empirical CCDF interval range.
Based on any embodiment, the initial parameters of the radar echo single-component amplitude distribution model are determined based on the typical parameter values, or determined based on a preset parameter estimation method.
Based on any of the above embodiments, the iterative optimization unit 340 includes:
the search solving subunit is used for carrying out iterative search solving on the model parameters by a numerical optimization method in a two-dimensional parameter space or a three-dimensional parameter space to obtain a parameter estimation value of the radar echo single-component amplitude distribution model;
the two-dimensional parameter space has two model parameters, and the models are correspondingly distributed in a log-normal mode, a Weibull mode, a K mode, a GK-LNT mode, a CG-IG mode and a Pareto mode;
the three model parameters in the three-dimensional parameter space are three, and the models correspond to GK distribution, CG-GIG distribution, K + noise distribution, GK-LNT + noise distribution, CG-IG + noise distribution and Pareto + noise distribution.
Based on any of the above embodiments, the type of the radar echo single component amplitude distribution model is determined based on the noise to noise ratio of the radar echo data.
Based on any embodiment above, the apparatus further comprises:
the goodness-of-fit inspection unit is used for acquiring the modeling precision of each radar echo single-component amplitude distribution model by adopting a correction chi-square inspection method; taking a radar echo single-component amplitude distribution model with the highest modeling precision as an optimal model; representing the amplitude distribution of the echo data by using an optimal model; and determining a theoretical detection threshold according to the radar false alarm probability and the optimal model, judging whether the target exists or not according to the relation between the amplitude of the echo data and the theoretical detection threshold, if the amplitude of the echo data is higher than the theoretical detection threshold, judging that the target exists, otherwise, judging that the target does not exist.
Fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, and as shown in fig. 4, the electronic device may include: a processor (processor)410, a communication Interface 420, a memory (memory)430 and a communication bus 440, wherein the processor 410, the communication Interface 420 and the memory 430 are communicated with each other via the communication bus 440. The processor 410 may call logical commands in the memory 430 to perform the following method:
based on radar echo data, determining experience CCDF, an experience CCDF interval range and corresponding experience quantile points; CCDF is a complementary cumulative distribution function; determining an initial theoretical CCDF (complementary continuous function) based on initial parameters of a radar echo single-component amplitude distribution model; determining an initial theoretical quantile corresponding to each empirical quantile in the range of the empirical CCDF interval based on each empirical CCDF value in the range of the empirical CCDF interval and each initial theoretical CCDF value of which the difference value with each empirical CCDF value is in a preset difference value range; and (3) taking all the empirical quantiles in the range of the empirical CCDF interval and the theoretical quantile errors corresponding to the empirical quantile as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation value of the radar echo single-component amplitude distribution model.
In addition, the logic commands in the memory 430 may be implemented in the form of software functional units and stored in a computer readable storage medium when the logic commands are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes a plurality of commands for enabling a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Embodiments of the present invention further provide a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program is implemented to perform the method provided in the foregoing embodiments when executed by a processor, and the method includes:
based on radar echo data, determining experience CCDF, an experience CCDF interval range and corresponding experience quantile points; CCDF is a complementary cumulative distribution function; determining an initial theoretical CCDF (complementary continuous function) based on initial parameters of a radar echo single-component amplitude distribution model; determining an initial theoretical quantile corresponding to each empirical quantile in the range of the empirical CCDF interval based on each empirical CCDF value in the range of the empirical CCDF interval and each initial theoretical CCDF value of which the difference value with each empirical CCDF value is in a preset difference value range; and (3) taking all the empirical quantiles in the range of the empirical CCDF interval and the theoretical quantile errors corresponding to the empirical quantile as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation value of the radar echo single-component amplitude distribution model.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes commands for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A method for estimating parameters of a radar echo single-component amplitude distribution model is characterized by comprising the following steps:
based on radar echo data, determining experience CCDF, an experience CCDF interval range and corresponding experience quantile points; CCDF is a complementary cumulative distribution function;
determining an initial theoretical CCDF based on initial parameters of the radar echo single-component amplitude distribution model;
determining an initial theoretical quantile corresponding to each empirical quantile in the empirical CCDF interval range based on each empirical CCDF value in the empirical CCDF interval range and each initial theoretical CCDF value of which the difference value with each empirical CCDF value is in a preset difference value range;
and taking all the empirical quantiles in the empirical CCDF interval range and the theoretical quantile errors corresponding to the empirical quantile errors as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation value of the radar echo single-component amplitude distribution model.
2. The method of estimating radar echo single component amplitude distribution model parameters of claim 1, wherein the determining an empirical CCDF, an empirical CCDF interval range, and its corresponding empirical quantile based on radar echo data comprises:
determining the number of divisions of a statistical interval and the empirical CCDF based on radar echo data;
and determining the range of the empirical CCDF interval and the corresponding empirical quantile point based on the data point number of the radar echo data and the radar false alarm probability.
3. The method for estimating parameters of a radar echo single-component amplitude distribution model according to claim 2, wherein the determining an empirical CCDF interval range and an empirical quantile corresponding thereto specifically includes:
determining quantiles of the empirical CCDF interval range based on the empirical CCDF interval range, and counting the number of the quantiles;
if the number of the sub-points in the empirical CCDF interval range is smaller than a preset threshold, increasing the upper value limit of the empirical CCDF interval range and/or decreasing the lower value limit of the empirical CCDF interval range;
counting the number of the loci of the experience CCDF within the adjusted experience CCDF interval until the number is greater than or equal to the preset threshold;
and taking the experience CCDF interval range adjusted for the last time as a final experience CCDF interval range.
4. The method for estimating the parameters of the radar echo single-component amplitude distribution model according to claim 1, wherein the errors of all the empirical quantiles and the corresponding theoretical quantile within the empirical CCDF interval are root mean square errors of all the empirical quantiles and the corresponding theoretical quantile within the empirical CCDF interval.
5. The method of claim 1, wherein the initial parameters of the radar echo single component amplitude distribution model are determined based on typical parameter values or are determined based on a preset parameter estimation method.
6. The method for estimating the parameters of the radar echo single-component amplitude distribution model according to claim 1, wherein the using a numerical optimization method to perform iterative optimization on the model parameters of the radar echo single-component amplitude distribution model to obtain the parameter estimation values of the radar echo single-component amplitude distribution model comprises:
in a two-dimensional parameter space or a three-dimensional parameter space, carrying out iterative search solution on model parameters by using a numerical optimization method to obtain a parameter estimation value of the radar echo single-component amplitude distribution model;
the number of model parameters in the two-dimensional parameter space is two, and the models are correspondingly lognormal distribution, Weibull distribution, K distribution, GK-LNT distribution, CG-IG distribution and Pareto distribution;
the three model parameters in the three-dimensional parameter space are three, and the models correspond to GK distribution, CG-GIG distribution, K + noise distribution, GK-LNT + noise distribution, CG-IG + noise distribution and Pareto + noise distribution.
7. The method of estimating parameters of a radar echo single component amplitude distribution model according to any one of claims 1 to 6, wherein the type of the radar echo single component amplitude distribution model is determined based on a noise to noise ratio of radar echo data.
8. The method for estimating parameters of a radar echo single component amplitude distribution model according to any one of claims 1 to 6, wherein the obtaining of the parameter estimation value of the radar echo single component amplitude distribution model further comprises:
obtaining the modeling precision of each radar echo single-component amplitude distribution model by adopting a correction chi-square inspection method;
taking the radar echo single-component amplitude distribution model with the highest modeling precision as an optimal model;
representing an amplitude distribution of the echo data using the optimal model;
and determining a theoretical detection threshold according to the radar false alarm probability and the optimal model, judging whether a target exists or not according to the relation between the amplitude of the echo data and the theoretical detection threshold, if the amplitude of the echo data is higher than the theoretical detection threshold, judging that the target exists, otherwise, judging that the target does not exist.
9. A radar echo single component amplitude distribution model parameter estimation device is characterized by comprising:
the experience CCDF determining unit is used for determining the experience CCDF, the range of the experience CCDF and the corresponding experience quantile point based on the radar echo data; CCDF is a complementary cumulative distribution function;
the initial theoretical CCDF determining unit is used for determining the initial theoretical CCDF based on the initial parameters of the radar echo single-component amplitude distribution model;
a quantile corresponding unit, configured to determine an initial theoretical quantile corresponding to each empirical quantile within the range of the empirical CCDF interval based on each empirical CCDF value within the range of the empirical CCDF interval and each initial theoretical CCDF value having a difference with each empirical CCDF value within a preset difference range;
and the iterative optimization unit is used for taking all the empirical quantiles in the empirical CCDF interval range and the theoretical quantile errors corresponding to the empirical quantile errors as a target function, taking the initial parameters as initial values, and performing iterative optimization on the model parameters of the radar echo single-component amplitude distribution model by adopting a numerical optimization method to obtain the parameter estimation values of the radar echo single-component amplitude distribution model.
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements the steps of the method for estimating parameters of a model of a single-component amplitude distribution of radar returns according to any one of claims 1 to 8.
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CN113504515A (en) * 2021-06-28 2021-10-15 中国人民解放军海军航空大学航空作战勤务学院 Method and device for estimating parameters and forming detection threshold of echo extreme value model
CN113504515B (en) * 2021-06-28 2023-08-29 中国人民解放军海军航空大学航空作战勤务学院 Method and device for parameter estimation and detection threshold formation of echo extremum model

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