Multi-frame bayesian iterative estimation method of sea clutter spectrum center frequency and bandwidth

Abstract

The application relates to a multi-frame Bayesian iterative estimation method for sea clutter spectrum center frequency and bandwidth, and belongs to the technical field of radar signal processing. The steps comprise the following steps: 1) preliminary estimation of sea clutter spectrum parameters; and 2) iterative sensing of prior distribution of the clutter spectrum parameters and Bayesian estimation of the spectrum parameters. The application aims to improve the iterative mode of prior information in the original Bayesian estimation method, so that the test statistic after the Bayesian estimation has better distinguishing ability for the clutter and the target.

Description

Technical Field

[0001] This invention relates to a multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of sea clutter spectrum, belonging to the field of radar signal processing technology. Background Technology

[0002] Radar technology is increasingly widely used in marine monitoring, target detection, and navigation systems. However, in practical applications, electromagnetic wave signals reflected from the sea surface, known as "sea clutter," significantly impact the performance of radar systems. At high sea states (4 and 5), the frequency of sea spikes in sea clutter increases markedly. The Doppler spectrum and narrow Doppler bandwidth of these spikes easily trigger numerous false alarms in radar detection systems. Furthermore, the formation mechanism of sea clutter is complex and difficult to understand. Effective estimation of the spectral parameters of sea clutter is necessary to suppress it and improve the radar system's ability to detect maritime targets.

[0003] The adaptive parameters of existing traditional adaptive radar signal processing algorithms (adaptive moving target detection, adaptive matched filter detection, etc.) are usually determined by the clutter echoes that can be collected in the current environment. In coherent radar systems, suppressing clutter in the frequency domain requires examining the characteristic parameters of the clutter spectrum. In existing methods, the spectral characteristics of sea clutter are usually described by the center frequency and bandwidth. Once the clutter spectrum structure is determined, operations such as whitening can be used to process the echo of the signal to be detected, thereby achieving the purpose of suppressing clutter and enhancing the target echo. To ensure that the spectral parameter estimation results are adapted to the current detection scenario and detection area, existing methods often use the short-time FFT method to estimate the radar's short-time spectrum. However, since the number of pulses used for short-time spectrum estimation is usually small (around 64 pulses), the fluctuation of the spectrum estimation results is often very drastic, making it difficult to reflect the true situation of the current sea clutter spectrum. In existing estimation methods, multi-frame averaging or forgetting factors are often used to estimate the parameters of the sea clutter spectrum over multiple frames. Although these methods reduce the fluctuation of the sea clutter spectrum, they do not fully utilize the prior information of historical frames. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technology and propose a multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of sea clutter spectrum. This method aims to improve the iterative method of prior information in the original Bayesian estimation method, so that the test statistic after Bayesian estimation has a better ability to distinguish between clutter and targets.

[0005] The multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of the sea clutter spectrum of the present invention is characterized by including the following steps:

[0006] Step 1: Single-frame estimation of sea clutter spectral parameters

[0007] In the clutter region, a sequence of sea clutter radar echoes with a coherent cumulative time is received, the sequence is transformed by FFT, and the spectral parameters are initially estimated based on the clutter spectrum.

[0008] Step 2: Iterative sensing of prior distribution of clutter spectral parameters and Bayesian estimation of spectral parameters

[0009] By using historical frames to iteratively perceive the prior distribution used in Bayesian estimation, the prior distribution is made to have time-varying characteristics. As the number of iterations increases, the prior distribution gradually fits the parameter estimation background, which plays a positive role in Bayesian parameter estimation.

[0010] Preferably, the specific steps of step 1 are as follows:

[0011] When the radar collects sea clutter echo data from multiple range cells in a certain azimuth during scanning mode, the data appears as follows:

[0012] x i =[x i,1 ,x i,2 ,x i,3 ,...]; (12)

[0013] Where, x i Let x represent the complex sequence of echoes from the i-th clutter range cell. i,1 This represents the first segment of the coherent echo sequence of the i-th clutter range cell;

[0014] First, regarding the echo signal x i =[x i,1 ,x i,2 ,x i,3 The spectral parameters of the sea clutter spectrum are initially estimated, and the method for initially estimating the centroid of the sea clutter spectrum is based on equation (2):

[0015]

[0016] In the formula, y (k) f is represented as the spectral amplitude value at the k-th point of the M-point FFT of the echo sequence. k This represents the actual frequency value represented by the k-th frequency point in the M-point FFT. This represents an estimate of the Doppler shift (center frequency of the sea clutter spectrum).

[0017] To fully observe the time-varying characteristics of the sea clutter spectral parameters, the bandwidth estimation method of equation (3) is used instead of the traditional 3dB spectrum estimation method, as shown below:

[0018]

[0019] In the formula, y (k) Let f be the spectral value of the k-th point of the M-point FFT of the echo sequence.k This represents the actual frequency value represented by the k-th frequency point in the M-point FFT. This represents an estimate of the Doppler frequency shift (center frequency of the sea clutter spectrum). This represents the estimated bandwidth of the Doppler spectrum of the sea clutter wave.

[0020] Preferably, the specific steps of step 2 are as follows:

[0021] Based on the Bayesian estimation method under Gaussian background, the center frequency of the spectrum to be estimated is modeled in the following form:

[0022] f c =f c +w (15)

[0023] Where f c Let w be the true value of the center frequency of the sea clutter spectrum, and w be zero mean with variance. The Gaussian random noise (sample variance) has a length of M. Due to the non-stationarity of the sea surface, the true value f c It is usually a random variable, assuming f c The distribution is Let this distribution be called the prior distribution. Then, we can find the condition that minimizes the quadratic loss when a set of feature samples of size M is collected, for the parameter f. c Bayesian estimation a e :

[0024]

[0025] In equation (5), m f For an unbiased estimate of the center frequency of the clutter spectrum in M ​​frames, a e It is a Bayesian estimate of the center frequency of the clutter spectrum. Let μ be the sample variance. f and These are the prior distributions. The mean and variance parameters. From equation (5), it can be seen that for the center frequency f of the spectrum... c Bayesian estimation is essentially an unbiased estimate of the sample and the parameter f. c Prior distribution mean parameter μ f The weighted summation is determined by the variance of the prior distribution. variance of the current sample The weights are determined by the variance of the prior distribution; a smaller variance indicates that the prior distribution is more favorable than m. f The distribution is more stable, and the Bayesian estimate a e Therefore, we should lean more towards the prior distribution mean μ. f Instead of favoring the unstable m f ;

[0026] Equation (5) gives the Bayesian estimation expression for the spectral characteristic parameters of sea clutter. However, due to the lack of prior distribution, the characteristic parameters cannot be directly estimated. To ensure the rationality of Bayesian estimation, the parameters of the prior distribution need to fit the current estimation background. In the time-varying sea surface environment, the parameters of the prior distribution also need to be continuously adjusted during the iterative estimation process to adapt to the changes in the sea surface environment.

[0027] Assume that the initial parameters μ of the prior distribution have been obtained through data collection and other means before parameter estimation begins. f and Due to the time-varying detection environment of the sea surface, there is a mismatch between the initial parameters of the prior distribution and the prior distribution parameters of the current environment. Let the prior distribution that conforms to the environment be... Under the condition of prior distribution mismatch, m f The Gaussian distribution to which it belongs is shown in equation (6).

[0028]

[0029] In the formula, and Prior distributions that match the environment The mean and variance parameters, This represents the sample variance.

[0030] Based on equations (5) and (6), the distribution of the Bayesian estimate of the spectral center frequency is derived as shown in equation (7).

[0031]

[0032] In equation (7), μ f and These are the pre-defined mean and variance of the prior distribution. and These are the actual mean and variance of the prior distribution. Let be the sample variance, and M be the number of samples used in a single Bayesian estimation. The Bayesian estimate distribution model under prior mismatch includes not only true prior information but also bias caused by erroneous priors. Under the mismatch prior distribution, a e The mean μ of the distribution e and variance The parameters of the mismatch prior distribution are obtained through sample estimation. Based on the distribution parameters of the estimated Bayesian values, iterative estimation of the parameters of the mismatch prior distribution is completed, using the mean μ of the Bayesian estimates. e and variance Given the preset prior distribution parameters, the true parameters of the prior distribution are inferred, expressed as:

[0033]

[0034] In equation (8), μ e , The Bayesian test statistic a e The mean and variance, and This refers to the mean and variance of the corrected prior distribution. Let be the sample variance, and M be the number of samples used in a single Bayesian estimation. Considering that the sea surface changes slowly in a large-scale sea scene, and the statistical characteristics of sea clutter will not change significantly over a long period of time, it is reasonable to use sufficiently long historical frame information to estimate the prior distribution. Therefore, a sequential estimation method is adopted to update the prior distribution parameters, and the Bayesian test statistic a is obtained iteratively according to Equation (9). e The distribution parameter μ e and Prior distribution parameters and The iterative method is given in equation (10):

[0035]

[0036]

[0037] Where M refers to the number of samples used in a single estimation, n refers to the number of iterations, and μ e (n) and This represents the nth iteration estimate of the mean and variance parameters of the distribution to which the Bayesian estimate belongs. The variance refers to the sample variance, which is obtained by performing an unbiased estimate of the variance using the sample. e (n+1) refers to the (n+1)th Bayesian estimate obtained based on the obtained sample.

[0038] In equation (11), α(n) is expressed as:

[0039]

[0040] The prior distribution iterative sensing method for clutter spectrum bandwidth and the Bayesian estimation and centroid estimation process are consistent; only the centroid in equation (4) needs to be replaced with the clutter spectrum bandwidth.

[0041] In step 2, the key steps are: first, to use equations (9) and (10) to estimate and iterate the prior distribution parameters required for Bayesian estimation, so as to adapt the prior distribution to the current sea surface environment; second, under the condition that the prior distribution matches the sea surface environment, to use equation (5) to estimate the centroid and bandwidth of the sea clutter spectrum in Bayesian estimation, reduce the fluctuation of the estimation results and make full use of prior information to reduce the error of the estimation results.

[0042] Compared with existing technologies, the multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of sea clutter spectrum described in this technical solution has the following advantages:

[0043] (1) This invention makes full use of the historical frame spectrum estimation results and uses historical frame data to iteratively perceive the prior distribution, thereby making up for the estimation result deviation caused by the fixed prior distribution in the traditional Bayesian algorithm.

[0044] (2) Based on the prior distribution containing historical frame information, the present invention performs Bayesian estimation of spectral parameters to achieve a more accurate estimation effect. Attached Figure Description

[0045] Figure 1 This is a comparison chart of the clutter spectrum bandwidth estimation results of the present invention and existing methods; in the figure, (a) is the clutter spectrum bandwidth estimation result of the multi-frame Bayesian estimation method of the present invention, (b) is the clutter spectrum bandwidth estimation result of the forgetting factor estimation method, and (c) is the clutter spectrum bandwidth estimation result of the single-frame estimation method.

[0046] Figure 2 This is a comparison chart of the clutter spectrum centroid estimation results of the present invention and existing methods. In the chart, (a) is the clutter spectrum centroid estimation result of the multi-frame Bayesian estimation method of the present invention, (b) is the clutter spectrum centroid estimation result of the forgetting factor estimation method, and (c) is the clutter spectrum centroid estimation result of the single-frame estimation method. Detailed Implementation

[0047] To better understand and implement this invention, specific embodiments are provided below to illustrate the multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of the sea clutter spectrum. The steps are as follows:

[0048] 1) Preliminary estimation of marine clutter spectral parameters

[0049] When the radar collects sea clutter echo data from multiple range cells in a certain azimuth during scanning mode, the data appears as follows:

[0050] x i =[x i,1 ,x i,2 ,x i,3 ,...]; (twenty three)

[0051] Where, x i Let x represent the complex sequence of echoes from the i-th clutter range cell. i,1 This represents the first segment of the coherent echo sequence of the i-th clutter range cell;

[0052] First, regarding the echo signal x i =[x i,1 ,x i,2 ,x i,3The spectral parameters of the sea clutter spectrum are initially estimated, and the method for initially estimating the centroid of the sea clutter spectrum is based on equation (2):

[0053]

[0054] In the formula, y (k) f is represented as the spectral amplitude value at the k-th point of the M-point FFT of the echo sequence. k This represents the actual frequency value represented by the k-th frequency point in the M-point FFT. This represents an estimate of the Doppler shift (center frequency of the sea clutter spectrum).

[0055] To fully observe the time-varying characteristics of the sea clutter spectral parameters, the bandwidth estimation method of equation (3) is used instead of the traditional 3dB spectrum estimation method, as shown below:

[0056]

[0057] In the formula, y (k) Let f be the spectral value of the k-th point of the M-point FFT of the echo sequence. k This represents the actual frequency value represented by the k-th frequency point in the M-point FFT. This represents an estimate of the Doppler frequency shift (center frequency of the sea clutter spectrum). This represents the estimated bandwidth of the Doppler spectrum of the sea clutter wave.

[0058] 2) Multi-frame Bayesian estimation of clutter spectral parameters and iterative sensing of prior distribution

[0059] Step 1 describes a single-frame estimation method for sea clutter spectral parameters. The estimation results exhibit significant fluctuations and cannot accurately represent the true levels of these parameters. Therefore, Bayesian estimation is needed to accurately estimate the characteristic parameters of the sea clutter spectrum. The following section will use Bayesian estimation of the sea clutter spectral centroid as an example to illustrate the Bayesian estimation method and the prior distribution iterative sensing method.

[0060] Based on the Bayesian estimation method under Gaussian background, the center frequency of the spectrum to be estimated is modeled in the following form:

[0061] f c =f c +w (26)

[0062] Where f c Let w be the true value of the center frequency of the sea clutter spectrum, and w be zero mean with variance. The Gaussian random noise (sample variance) has a length of M. Due to the non-stationarity of the sea surface, the true value f c It is usually a random variable, assuming f c The distribution is Let this distribution be called the prior distribution. Then, we can find the condition that minimizes the quadratic loss when a set of feature samples of size M is collected, for the parameter f. c Bayesian estimation a e :

[0063]

[0064] In equation (5), m f For an unbiased estimate of the center frequency of the clutter spectrum in M ​​frames, a e It is a Bayesian estimate of the center frequency of the clutter spectrum. Let μ be the sample variance. f and These are the prior distributions. The mean and variance parameters. From equation (5), it can be seen that for the center frequency f of the spectrum... c Bayesian estimation is essentially an unbiased estimate of the sample and the parameter f. c Prior distribution mean parameter μ f The weighted summation is determined by the variance of the prior distribution. variance of the current sample The weights are determined by the variance of the prior distribution; a smaller variance indicates that the prior distribution is more favorable than m. f The distribution is more stable, and the Bayesian estimate a e Therefore, we should lean more towards the prior distribution mean μ. f Instead of favoring the unstable m f ;

[0065] Equation (5) gives the Bayesian estimation expression for the spectral characteristic parameters of sea clutter. However, due to the lack of prior distribution, the characteristic parameters cannot be directly estimated. To ensure the rationality of Bayesian estimation, the parameters of the prior distribution need to fit the current estimation background. In the time-varying sea surface environment, the parameters of the prior distribution also need to be continuously adjusted during the iterative estimation process to adapt to the changes in the sea surface environment.

[0066] Assume that the initial parameters μ of the prior distribution have been obtained through data collection and other means before parameter estimation begins. f and Due to the time-varying detection environment of the sea surface, there is a mismatch between the initial parameters of the prior distribution and the prior distribution parameters of the current environment. Let the prior distribution that conforms to the environment be... Under the condition of prior distribution mismatch, m f The Gaussian distribution to which it belongs is shown in equation (6).

[0067]

[0068] In the formula, and Prior distributions that match the environment The mean and variance parameters, This represents the sample variance.

[0069] Based on equations (5) and (6), the distribution of the Bayesian estimate of the spectral center frequency is derived as shown in equation (7).

[0070]

[0071] In equation (7), μ f and These are the pre-defined mean and variance of the prior distribution. and These are the actual mean and variance of the prior distribution. Let be the sample variance, and M be the number of samples used in a single Bayesian estimation. The Bayesian estimate distribution model under prior mismatch includes not only true prior information but also bias caused by erroneous priors. Under the mismatch prior distribution, a e The mean μ of the distribution e and variance The parameters of the mismatch prior distribution are obtained through sample estimation. Based on the distribution parameters of the estimated Bayesian values, iterative estimation of the parameters of the mismatch prior distribution is completed, using the mean μ of the Bayesian estimates. e and variance Given the preset prior distribution parameters, the true parameters of the prior distribution are inferred, expressed as:

[0072]

[0073] In equation (8), μ e , The Bayesian test statistic a e The mean and variance, and This refers to the mean and variance of the corrected prior distribution. Let be the sample variance, and M be the number of samples used in a single Bayesian estimation. Considering that the sea surface changes slowly in a large-scale sea scene, and the statistical characteristics of sea clutter will not change significantly over a long period of time, it is reasonable to use sufficiently long historical frame information to estimate the prior distribution. Therefore, a sequential estimation method is adopted to update the prior distribution parameters, and the Bayesian test statistic a is obtained iteratively according to Equation (9). e The distribution parameter μ e and Prior distribution parameters and The iterative method is given in equation (10):

[0074]

[0075] Where M refers to the number of samples used in a single estimation, n refers to the number of iterations, and μ e (n) and This represents the nth iteration estimate of the mean and variance parameters of the distribution to which the Bayesian estimate belongs. The variance refers to the sample variance, which is obtained by performing an unbiased estimate of the variance using the sample. e (n+1) refers to the (n+1)th Bayesian estimate obtained based on the obtained sample.

[0076] In equation (11), α(n) is expressed as:

[0077]

[0078] The prior distribution iterative sensing method for clutter spectrum bandwidth and the Bayesian estimation and centroid estimation process are the same. Only the centroid in equation (4) needs to be replaced with the clutter spectrum bandwidth, which will not be elaborated here.

[0079] In step 2, the key steps are: first, to estimate and iterate the prior distribution parameters required for Bayesian estimation using equations (9) and (10), thereby adapting the prior distribution to the current sea surface environment; second, under the condition that the prior distribution matches the sea surface environment, to perform Bayesian estimation of the centroid and bandwidth of the sea clutter spectrum using equation (5), reducing the fluctuation of the estimation results and making full use of prior information to reduce the error of the estimation results. The comparison results with existing methods can be found in [reference needed]. Figure 1 , 2 . Figure 1 (c) shows the traditional single-frame estimation method. Since a single frame contains only 64 pulses, the information reflected by the spectrum is inaccurate and unstable, which makes the spectrum estimation result easily affected by noise, resulting in a large estimation error. Figure 1 (b) shows the estimation method using the forgetting factor in the existing methods. By setting the forgetting factor, the historical frame information is forgotten. With the support of the historical frames, the estimation results are smoothed to a certain extent. The resulting estimation error is smaller than that of the traditional method. However, the use of historical frames is not rigorous, resulting in insufficient use of historical frame information. Figure 1 (a) shows the spectral bandwidth estimation error of the present invention, which has a smaller spectral parameter estimation error compared to the previous two methods after fully exploring and using historical frame information. Figure 2 The same phenomenon can be observed in the sample, proving the effectiveness of the present invention.

Claims

1. A multi-frame Bayesian iterative estimation method of the center frequency and bandwidth of a sea clutter spectrum, characterized in that The process includes the following steps: Step 1: Single-frame estimation of sea clutter spectral parameters. In the clutter region, a sequence of sea clutter radar echoes with a coherent cumulative time is received. The sequence is transformed by FFT, and the spectral parameters are initially estimated based on the clutter spectrum. Step 2: Iterative sensing of the prior distribution of clutter spectral parameters and Bayesian estimation of spectral parameters. Historical frames are used to iteratively sense the prior distribution used for Bayesian estimation, making the prior distribution time-varying. As the number of iterations increases, the prior distribution gradually fits the parameter estimation background, which plays a positive role in the Bayesian estimation of parameters. The specific steps of step 2 are as follows: Based on the Bayesian estimation method under Gaussian background, the center frequency of the spectrum to be estimated is modeled in the following form: （4） in This represents the true value of the center frequency of the sea clutter spectrum. With zero mean and variance Gaussian random noise of length M, true value It is a random variable, assuming The distribution is Find the value when the number of collected samples is M. When considering the feature sample set, under the condition of minimizing the quadratic loss, the parameters... Bayesian estimation: （5） In equation (5), For the unbiased estimate of the center frequency of the clutter spectrum in the M-frame, It is a Bayesian estimate of the center frequency of the clutter spectrum; Assume that the initial parameters of the prior distribution have been obtained through data collection before parameter estimation begins. and Due to the time-varying detection environment of the sea surface, there is a mismatch between the initial parameters of the prior distribution and the prior distribution parameters of the current environment. Let the prior distribution that conforms to the environment be... Under the condition of prior distribution mismatch, The distribution is shown in equation (6): （6） Based on equations (5) and (6), the distribution of the Bayesian estimate of the spectral center frequency is derived as shown in equation (7): （7） In equation (7), and These are the pre-defined mean and variance of the prior distribution. and These are the actual mean and variance of the prior distribution. The Bayesian estimate distribution model under prior mismatch not only includes information from the true prior but also the bias caused by erroneous priors. Under a mismatched prior distribution... Mean of the distribution and variance By estimating from samples, and based on the distribution parameters of the estimated Bayesian values, iterative estimation of the mismatch prior distribution parameters is completed, using the mean of the Bayesian estimates. and variance Given the preset prior distribution parameters, the true parameters of the prior distribution are inferred, expressed as: （8） In equation (8), , Bayesian test statistic The mean and variance, and The mean and variance of the corrected prior distribution are used. The prior distribution parameters are updated using a sequential estimation method, and the Bayesian test statistic is obtained iteratively according to Equation (9). Distribution parameters and Prior distribution parameters and The iterative method is given in equation (10): （9） （10） Where N refers to the number of samples used in a single estimation, and n refers to the number of iterations. The sample variance is obtained by unbiased estimation using the sample, as shown in equation (11). Represented as: （11） The prior distribution iterative sensing method for clutter spectrum bandwidth and the Bayesian estimation and centroid estimation process are the same. The centroid in equation (4) can be replaced with clutter spectrum bandwidth.

2. The multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of the sea clutter spectrum according to claim 1, characterized in that... The specific steps of step 1 are as follows: The radar collects sea clutter echo data of multiple range cells in a certain azimuth in scanning mode, which is manifested in the following form: (1) in, Indicates the first Complex sequence of echoes from each clutter range cell Indicates the first The first coherent echo sequence of a clutter range cell; First, regarding the echo signal The spectral parameters are initially estimated, and the method for initially estimating the centroid of the sea clutter spectrum is based on equation (2): (2) In the formula, This is represented as the spectral amplitude value at point k of the M-point FFT of the echo sequence. This represents the actual frequency value represented by the k-th frequency point in the M-point FFT. This represents an estimate of the Doppler frequency shift; The bandwidth estimation method using equation (3) is as follows: (3) In the formula, This is represented as the spectral value of the k-th point in the M-point FFT of the echo sequence. This represents the actual frequency value represented by the k-th frequency point of the M-point FFT. This represents an estimate of the Doppler frequency shift. This represents the estimated bandwidth of the Doppler spectrum of the sea clutter wave.

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