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

Abstract

The invention relates to a multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of a sea clutter spectrum, and belongs to the technical field of radar signal processing. The method comprises the following steps: 1) preliminarily estimating sea clutter spectrum parameters; and 2) carrying out prior distribution iterative perception on clutter spectrum parameters and carrying out Bayesian estimation on the spectrum parameters. The objective of the invention is to improve an iteration mode of prior information in an original Bayesian estimation method, so that test statistics after Bayesian estimation have better capability of distinguishing clutters and targets.

Description

Technical Field

[0001] The invention relates to a multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of a sea clutter spectrum, and belongs to the technical field of radar signal processing. Background Art

[0002] Radar technology is increasingly used in ocean monitoring, target detection and navigation systems. However, in practical applications, the electromagnetic wave signals reflected from the sea surface, namely "sea clutter", have a significant impact on the performance of radar systems. Under high sea conditions (level 4 and 5), the frequency of sea spikes in sea clutter increases significantly. The Doppler spectrum and narrow Doppler bandwidth of sea spikes can easily cause a large number of false alarms in radar detection systems. In addition, the formation mechanism of sea clutter is complex and difficult to recognize. It is necessary to effectively estimate the spectral parameters of sea clutter to suppress sea clutter, thereby improving the radar system's ability to detect targets at sea.

[0003] The adaptive parameters of the 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 the coherent radar system, it is necessary to examine the characteristic parameters of the clutter spectrum to suppress clutter in the frequency domain. In the 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. In order to ensure that the spectrum parameter estimation results are compatible with the current detection scene and detection area, the short-time FFT method is often used in the existing methods to estimate the short-time spectrum of the radar. However, since the number of pulses used in the short-time spectrum estimation is usually small (about 64 pulses), the fluctuation of the spectrum estimation results is often very drastic, and it is difficult to reflect the true situation of the sea clutter spectrum in the current environment. In the existing estimation methods, multi-frame averaging or forgetting factors are often used to estimate the parameters of the sea clutter spectrum in multiple frames. Although these methods reduce the fluctuation of the sea clutter spectrum, they do not make full use of the prior information of the historical frame. Summary of the invention

[0004] The purpose of the present invention is to solve the shortcomings of the above-mentioned prior art and propose a multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of sea clutter spectrum, aiming to improve the iterative mode of prior information in the original Bayesian estimation method so that the test statistic after Bayesian estimation has better ability to distinguish 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 special in that it comprises the following steps:

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

[0007] In the clutter area, a sea clutter radar echo sequence of a coherent accumulation time length is received, the sequence is subjected to FFT transformation, and a preliminary estimation of spectrum parameters is performed based on the clutter spectrum;

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

[0009] The historical frame is used to iteratively perceive the prior distribution used in Bayesian estimation, so that the prior distribution has time-varying characteristics. 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 the parameters.

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

[0011] The radar collects sea clutter echo data of multiple range units in a certain direction in scanning mode, which is shown in the following form:

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

[0013] Among them, x i represents the complex echo sequence of the ith clutter range unit, x i,1 represents the first coherent echo sequence of the i-th clutter range unit;

[0014] First, the echo signal x i =[x i,1 ,x i,2 ,x i,3 ,...], the spectral parameters of the sea clutter spectrum are preliminarily estimated, and the method for preliminarily estimating the centroid of the sea clutter spectrum is referred to formula (2):

[0015]

[0016] In the formula, y (k) It is expressed as the spectrum amplitude value of the kth point of the M-point FFT of the echo sequence, f k Indicates the actual frequency value represented by the kth frequency point of the M-point FFT, Represents the estimated value of the Doppler shift (center frequency of the sea clutter spectrum).

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

[0018]

[0019] In the formula, y (k) It is represented by the spectrum value of the kth point of the M-point FFT of the echo sequence, fk Indicates the actual frequency value represented by the kth frequency point of the M-point FFT, represents the estimated value of Doppler shift (center frequency of sea clutter spectrum), represents the estimated value of the Doppler spectrum bandwidth of sea clutter.

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

[0021] According to the Bayesian estimation method under Gaussian background, the center frequency of the spectrum to be estimated is modeled as follows:

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

[0023] where f c is the true value of the center frequency of the sea clutter spectrum, w is zero mean and the variance is Gaussian random noise (sample variance) of length 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 Hereinafter, this distribution is referred to as the prior distribution. Then, when a set of x feature samples with a sample number of M is collected, the parameter f can be calculated under the condition of minimum quadratic loss. c The Bayesian estimate of a e :

[0024]

[0025] In formula (5), m f is the unbiased estimate of the center frequency of the M-frame clutter spectrum, a e is the Bayesian estimate of the center frequency of the clutter spectrum, is the sample variance, μ f and They are the prior distributions The mean and variance parameters of . From formula (5), we can see that for the center frequency f c The Bayesian estimation of is essentially a sample unbiased estimate of the parameter f c Prior distribution mean parameter μ f The weighted addition of the prior distribution variance and the variance of the current sample Determine the weight. If the variance of the prior distribution is smaller, it means that the prior distribution is better than m. f The distribution is more stable, and the Bayesian estimate a e It should be more inclined to the prior distribution mean μ f Rather than leaning towards unstable m f ;

[0026] Formula (5) gives the Bayesian estimation expression of the characteristic parameters of the sea clutter spectrum. However, due to the lack of prior distribution, the characteristic parameters cannot be estimated directly. 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 before parameter estimation begins, the initial parameters μ of the prior distribution have been obtained through data collection and other means. 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 matches the environment be Under the condition of mismatch in prior distribution, m f The Gaussian distribution is shown in formula (6).

[0028]

[0029] In the formula, and is a prior distribution that matches the environment The mean and variance parameters of is the sample variance.

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

[0031]

[0032] In formula (7), μ f and is the preset prior distribution mean and variance, and are the actual mean and variance of the prior distribution, is the sample variance, and M is the number of samples used for a single Bayesian estimation. The distribution model of the Bayesian estimate under mismatched priors contains not only the true prior information, but also the deviation caused by the wrong prior. Under mismatched prior distribution, a e The mean μ of the distribution e and variance Through sample estimation, according to the distribution parameters of the estimated Bayesian estimated value, the iterative estimation of the mismatch prior distribution parameters is completed, and according to the mean μ of the Bayesian estimated value e and variance As well as the preset prior distribution parameters, the true parameters of the prior distribution are inferred, expressed as:

[0033]

[0034] In formula (8), μ e , Refers to the Bayesian test statistic a e The mean and variance of and refers to the mean and variance of the modified prior distribution, is the sample variance, and M is the number of samples used in a single Bayesian estimation. Considering that the sea surface changes slowly in a large-scale sea scene, 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 used to update the prior distribution parameters, and the Bayesian test statistic a is iterated according to formula (9): e The distribution parameter μ e and Prior distribution parameters and The iterative method is given in formula (10):

[0035]

[0036]

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

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

[0039]

[0040] The iterative perception method of the prior distribution of the clutter spectrum bandwidth is consistent with the process of Bayesian estimation and centroid estimation. It only needs to replace the centroid in equation (4) with the clutter spectrum bandwidth.

[0041] In step 2, the key steps are: first, using 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, using equation (5) to perform Bayesian estimation on the centroid and bandwidth of the sea clutter spectrum, reduce the fluctuation of the estimation result and make full use of the prior information to reduce the error of the estimation result.

[0042] Compared with the prior art, the multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of the sea clutter spectrum described in the technical solution has the following beneficial effects:

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

[0044] (2) The present invention performs Bayesian estimation on spectral parameters based on a prior distribution containing historical frame information to achieve a more accurate estimation effect. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0046] Figure 2 The figure is a comparison diagram of the clutter spectrum centroid estimation results of the present invention and the existing method. In the figure, (a) is the clutter spectrum centroid estimation result diagram of the multi-frame Bayesian estimation method of the present invention, (b) is the clutter spectrum centroid estimation result diagram of the forgetting factor estimation method; (c) is the clutter spectrum centroid estimation result diagram of the single-frame estimation method. DETAILED DESCRIPTION

[0047] For better understanding and implementation, a specific embodiment is given below to describe in detail the multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of the sea clutter spectrum of the present invention. The steps are as follows:

[0048] 1) Preliminary estimation of sea clutter spectrum parameters

[0049] The radar collects sea clutter echo data of multiple range units in a certain direction in scanning mode, which is shown in the following form:

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

[0051] Among them, x i represents the complex echo sequence of the ith clutter range unit, x i,1 represents the first coherent echo sequence of the i-th clutter range unit;

[0052] First, the echo signal x i =[x i,1 ,x i,2 ,x i,3,...], the spectral parameters of the sea clutter spectrum are preliminarily estimated, and the method for preliminarily estimating the centroid of the sea clutter spectrum is referred to formula (2):

[0053]

[0054] In the formula, y (k) It is expressed as the spectrum amplitude value of the kth point of the M-point FFT of the echo sequence, f k Indicates the actual frequency value represented by the kth frequency point of the M-point FFT, Represents the estimated value of the Doppler shift (center frequency of the sea clutter spectrum).

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

[0056]

[0057] In the formula, y (k) It is represented by the spectrum value of the kth point of the M-point FFT of the echo sequence, f k Indicates the actual frequency value represented by the kth frequency point of the M-point FFT, represents the estimated value of Doppler shift (center frequency of sea clutter spectrum), represents the estimated value of the Doppler spectrum bandwidth of sea clutter.

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

[0059] Step 1 represents the single-frame estimation method of sea clutter spectrum parameters. The estimation results have large fluctuations and cannot accurately represent the true level of sea clutter spectrum parameters. Therefore, it is necessary to use Bayesian estimation to accurately estimate the sea clutter spectrum characteristic parameters. The following will take the Bayesian estimation of the centroid of the sea clutter spectrum as an example to illustrate the Bayesian estimation method and the prior distribution iterative perception method.

[0060] According to the Bayesian estimation method under Gaussian background, the center frequency of the spectrum to be estimated is modeled as follows:

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

[0062] where f c is the true value of the center frequency of the sea clutter spectrum, w is zero mean and the variance is Gaussian random noise (sample variance) of length 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 Hereinafter, this distribution is referred to as the prior distribution. Then, when a set of x feature samples with a sample number of M is collected, the parameter f can be calculated under the condition of minimum quadratic loss. c The Bayesian estimate of a e :

[0063]

[0064] In formula (5), m f is the unbiased estimate of the center frequency of the M-frame clutter spectrum, a e is the Bayesian estimate of the center frequency of the clutter spectrum, is the sample variance, μ f and They are the prior distributions The mean and variance parameters of . From formula (5), we can see that for the center frequency f c The Bayesian estimation of is essentially a sample unbiased estimate of the parameter f c Prior distribution mean parameter μ f The weighted addition of the prior distribution variance and the variance of the current sample Determine the weight. If the variance of the prior distribution is smaller, it means that the prior distribution is better than m. f The distribution is more stable, and the Bayesian estimate a e It should be more inclined to the prior distribution mean μ f Rather than leaning towards unstable m f ;

[0065] Formula (5) gives the Bayesian estimation expression of the characteristic parameters of the sea clutter spectrum. However, due to the lack of prior distribution, the characteristic parameters cannot be estimated directly. 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 before parameter estimation begins, the initial parameters μ of the prior distribution have been obtained through data collection and other means. 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 matches the environment be Under the condition of mismatch in prior distribution, m f The Gaussian distribution is shown in formula (6).

[0067]

[0068] In the formula, and is a prior distribution that matches the environment The mean and variance parameters of is the sample variance.

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

[0070]

[0071] In formula (7), μ f and is the preset prior distribution mean and variance, and are the actual mean and variance of the prior distribution, is the sample variance, and M is the number of samples used for a single Bayesian estimation. The distribution model of the Bayesian estimate under mismatched priors contains not only the true prior information, but also the deviation caused by the wrong prior. Under mismatched prior distribution, a e The mean μ of the distribution e and variance Through sample estimation, according to the distribution parameters of the estimated Bayesian estimated value, the iterative estimation of the mismatch prior distribution parameters is completed, and according to the mean μ of the Bayesian estimated value e and variance As well as the preset prior distribution parameters, the true parameters of the prior distribution are inferred, expressed as:

[0072]

[0073] In formula (8), μ e , Refers to the Bayesian test statistic a e The mean and variance of and refers to the mean and variance of the modified prior distribution, is the sample variance, and M is the number of samples used in a single Bayesian estimation. Considering that the sea surface changes slowly in a large-scale sea scene, 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 used to update the prior distribution parameters, and the Bayesian test statistic a is iterated according to formula (9): e The distribution parameter μ e and Prior distribution parameters and The iterative method is given in formula (10):

[0074]

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

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

[0077]

[0078] The iterative perception method of the prior distribution of the clutter spectrum bandwidth is consistent with the process of Bayesian estimation and centroid estimation. It only needs to replace the centroid in equation (4) with the clutter spectrum bandwidth, which will not be elaborated here.

[0079] In step 2, the key steps are 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, use equation (5) to perform Bayesian estimation on the centroid and bandwidth of the sea clutter spectrum, reduce the fluctuation of the estimation results and make full use of the prior information to reduce the error of the estimation results. The comparison results with the existing methods can be referred to 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 width estimation result easily affected by noise, resulting in large estimation errors. Figure 1 (b) shows the estimation method using the forgetting factor in the existing methods. The historical frame information is forgotten by setting the forgetting factor. With the support of the historical frame, the estimation result is smoothed to a certain extent. The resulting estimation error is smaller than that of the traditional method. However, the use of the historical frame is not rigorous, resulting in insufficient use of the historical frame information. Figure 1 (a) shows the spectral bandwidth estimation error of the present invention. After fully exploring and using the historical frame information, it has a smaller spectral parameter estimation error than the first two methods. Figure 2 The above phenomenon can also be observed in the experiment, which proves the effectiveness of the present invention.

Claims

1. A multi-frame Bayesian iterative estimation method for the center frequency and bandwidth of sea clutter spectrum, characterized in that The following steps are involved: Step 1: Single-frame estimation of sea clutter spectral parameters In the clutter area, a sea clutter radar echo sequence of a coherent accumulation time length is received, the sequence is subjected to FFT transformation, and a preliminary estimation of spectrum parameters is performed based on the clutter spectrum; Step 2: Iterative perception of the prior distribution of clutter spectral parameters and Bayesian estimation of spectral parameters The historical frame is used to iteratively perceive the prior distribution used in Bayesian estimation, so that the prior distribution has time-varying characteristics. 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 the parameters.

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: The radar collects sea clutter echo data of multiple range units in a certain direction in scanning mode, which is shown in the following form: x i =[x i,1 ,x i,2 ,x i,3 ,...]; (1) Among them, x i represents the complex echo sequence of the ith clutter range unit, x i,1 represents the first coherent echo sequence of the i-th clutter range unit; First, the echo signal x i =[x i,1 ,x i,2 ,x i,3 ,...], the spectral parameters of the sea clutter spectrum are preliminarily estimated, and the method for preliminarily estimating the centroid of the sea clutter spectrum is referred to formula (2): In the formula, y (k) It is expressed as the spectrum amplitude value of the kth point of the M-point FFT of the echo sequence, f k Indicates the actual frequency value represented by the kth frequency point of the M-point FFT, represents the estimated value of Doppler shift; The bandwidth estimation method using formula (3) is as follows: In the formula, y (k) It is represented by the spectrum value of the kth point of the M-point FFT of the echo sequence, f k Indicates the actual frequency value represented by the kth frequency point of the M-point FFT, represents the estimated value of Doppler shift, represents the estimated value of the Doppler spectrum bandwidth of sea clutter.

3. 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 2 are: According to the Bayesian estimation method under Gaussian background, the center frequency of the spectrum to be estimated is modeled as follows: f c =f c +w (4) where f c is the true value of the center frequency of the sea clutter spectrum, w is zero mean and the variance is Gaussian random noise, length M, true value f c It is usually a random variable, assuming f c The distribution is Find the parameter f under the condition of minimum quadratic loss when a set of x feature samples with a sample number of M is collected. c Bayesian estimation of : In formula (5), m f is the unbiased estimate of the center frequency of the M-frame clutter spectrum, a e is the Bayesian estimate of the center frequency of the clutter spectrum; Assume that before parameter estimation begins, the initial parameters μ of the prior distribution have been obtained through data collection and other means. 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 matches the environment be Under the condition of mismatch in prior distribution, m f The distribution is shown in formula (6): According to equations (5) and (6), the distribution of the Bayesian estimate of the spectrum center frequency is derived as shown in equation (7): In formula (7), μ f and is the preset prior distribution mean and variance, and is the actual mean and variance of the prior distribution. The Bayesian estimation value distribution model under prior mismatch not only contains the true prior information, but also contains the deviation caused by the wrong prior. Under the mismatched prior distribution, a e The mean μ of the distribution e and variance Through sample estimation, according to the distribution parameters of the estimated Bayesian estimated value, the iterative estimation of the mismatch prior distribution parameters is completed, and according to the mean μ of the Bayesian estimated value e and variance As well as the preset prior distribution parameters, the true parameters of the prior distribution are inferred, expressed as: In formula (8), μ e , Refers to the Bayesian test statistic a e The mean and variance of and Refers to the mean and variance of the modified prior distribution. The prior distribution parameters are updated using the sequential estimation method. The Bayesian test statistic a is obtained by iteration according to formula (9): e The distribution parameter μ e and Prior distribution parameters and The iterative method is given in formula (10): Among them, N refers to the number of samples used in a single estimation, n refers to the number of iterations, Refers to the sample variance, which is obtained by unbiased estimation using samples. In formula (11), α(n) is expressed as: The iterative perception method of the prior distribution of the clutter spectrum bandwidth is consistent with the process of Bayesian estimation and centroid estimation. The centroid in equation (4) can be replaced by the clutter spectrum bandwidth.

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