Short-time iteration minimum variance undistorted response frequency spectrum estimation method

Abstract

The invention belongs to the technical field of signal processing, and particularly relates to a short-time iteration minimum variance undistorted response frequency spectrum estimation method. The method comprises the following steps: firstly, setting a signal discrete time sampling number, a signal discrete time sampling number, a frequency search number, a frequency search set, a frequency vector corresponding to each search frequency, and a discrete time sampling number of a short-time signal segment; regularizing parameters, and initializing an autocorrelation inverse matrix of short-time signal segments and the number of the short-time signal segments for each frequency spectrum estimation; dividing the signal discrete time sampling into short-time fragment signal discrete time sampling, and determining the short-time fragment signal discrete time sampling; then iteratively determining an addition inverse matrix and an exit inverse matrix; and finally, determining short-time iteration minimum variance undistorted response frequency spectrum estimation according to the incremental inverse matrix and the added inverse matrix.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a short-time iterative minimum variance distortion-free response spectrum estimation method. Background Art

[0002] In the field of signal processing technology, signal spectrum estimation is of great significance to information acquisition and detection systems such as radar, sonar, communication, navigation, and radio monitoring. For example, in detection systems such as radar and sonar, the incoming signal spectrum estimation can determine the target Doppler frequency, target speed and other information, and the incoming signal spatial spectrum estimation can determine the incoming wave azimuth, pitch angle and other information.

[0003] For signals whose spectrum does not change with time, the spectrum estimation method based on discrete-time Fourier transform is commonly used. The longer the signal duration, the higher the spectrum estimation accuracy and resolution of the spectrum estimation method based on discrete-time Fourier transform. Even if two signals with a relatively small frequency interval are mixed together, they can be distinguished to obtain a higher-precision spectrum estimation. When the signal spectrum changes with time, the spectrum estimation method based on discrete-time Fourier transform can only give the frequency band where the signal frequency is located, but cannot give the law of how the signal spectrum changes with time.

[0004] For non-stationary signals whose spectrum varies with time, a spectrum estimation method based on short-time Fourier transform is commonly used. This method first divides the signal into multiple shorter segment signals with or without overlap, and performs a discrete-time Fourier transform on each segment signal under the assumption that the spectrum of the segment signal does not vary with time, and then determines the spectrum of each segment signal, thereby determining the law of how the signal spectrum varies with time. However, the spectrum estimation method based on short-time Fourier transform can hardly take into account both the resolution and accuracy of spectrum estimation while obtaining the law of how the spectrum varies with time. High-precision and high-resolution spectrum estimation requires a long duration of the segment signal. Since the signal spectrum actually varies with time, the longer the duration of the segment signal, the more difficult it is to obtain the law of how the signal spectrum varies with time within the duration of the segment signal.

[0005] Therefore, it is necessary to develop a method that can take into account both the resolution and accuracy of spectrum estimation for non-stationary signals whose spectrum varies with time, so that high-resolution and high-accuracy spectrum estimation can be obtained even for signals with shorter duration of segment signals. The spectrum estimation method based on minimum variance distortionless response (MVDR) has higher resolution and accuracy, and is superior to the spectrum estimation method based on short-time Fourier transform when the duration of segment signals is the same. However, the spectrum estimation method based on MVDR needs to determine the sample autocorrelation matrix and its inverse matrix of the segment signal, which has a large computational complexity, which not only greatly increases the processor's occupancy time and energy consumption, but also reduces the spectrum estimation speed of non-stationary signals whose spectrum varies with time. Summary of the invention

[0006] In view of the above problems, the present invention proposes a short-time iterative minimum variance distortion-free response spectrum estimation method, which first sets the number of signal discrete time sampling, signal discrete time sampling, number of frequency searches, frequency search set, frequency vector corresponding to each search frequency, number of discrete time sampling of short-time signal segments, regularization parameters, initialize the autocorrelation inverse matrix of the short-time signal segments, and the number of short-time signal segments used for each spectrum estimation; then divides the signal discrete time sampling into short-time segment signal discrete time sampling, and determines the short-time segment signal discrete time sampling; then iteratively determines the addition inverse matrix and the exit inverse matrix; finally, the short-time iterative minimum variance distortion-free response spectrum estimation is determined by increasing the inverse matrix and adding the inverse matrix.

[0007] The technical solution of the present invention is:

[0008] A short-time iterative minimum variance distortion-free response spectrum estimation method comprises the following steps:

[0009] S1. Set the number of discrete time samples of the non-stationary signal whose spectrum changes with time as input to the spectrum estimation module to N, and the signal discrete time sampling to x = [x(1), x(2), ..., x(N)] T , superscript T represents the transpose of a vector; the number of frequency searches in the spectrum estimation module is L, and the frequency search set is {f1,f2,…,f L}, each search frequency f l The corresponding frequency vector is l=1,2,…,L; the number of discrete time samples of the short-time signal segment of the spectrum estimation module is M, and the regularization parameter is α; the inverse autocorrelation matrix of the initialized short-time signal segment is R0=αI M , I M is an M-order unit matrix; the number of short-time signal segments used by the spectrum estimation module for each spectrum estimation is K;

[0010] S2, the spectrum estimation module divides the signal discrete time sampling into short-time segment signal discrete time sampling, and determines the nth short-time segment signal discrete time sampling y n for

[0011] y n =[x(n+M-1) x(n+M-2)…x(n)] T

[0012] Where n = 1, 2, ..., N-M + 1;

[0013] S3. For n=1, 2, ..., K, iteratively determine the addition of the inverse matrix R n for

[0014]

[0015] Among them, the superscript -1 represents the inverse matrix;

[0016] S4. For n=K+1, K+2, ..., N, iteratively determine the exit inverse matrix Q n for

[0017]

[0018] Iteratively determine the addition of the inverse matrix R n for

[0019]

[0020] S5, the incremental inverse matrix determined by S3 and the added inverse matrix determined by S4, determine the short-time iterative minimum variance distortion-free response spectrum estimation as

[0021]

[0022] Among them, n=1,2,…,N, l=1,2,…,L.

[0023] The beneficial effects of the present invention are: on the one hand, it can take into account both the resolution and accuracy of spectrum estimation, and obtain high-resolution and high-accuracy spectrum estimation even when the duration of the segment signal is shorter; on the other hand, it can quickly determine the inverse matrix of the sample autocorrelation matrix of the segment signal, significantly reduce the calculation complexity, and improve the speed of spectrum estimation of non-stationary signals whose spectrum changes with time. DETAILED DESCRIPTION

[0024] The practicability of the present invention is described below in conjunction with embodiments.

[0025] Example

[0026] In this example, the number of discrete time samples of the non-stationary signal whose spectrum changes with time is set to 10000, including two linear frequency modulation signals, with a time width of 10000 sampling points. Relative to the sampling frequency, the normalized bandwidth is 0.0500, the center frequencies are 0.2600 and 0.2570 respectively, and the center frequency interval is 0.0030; the number of discrete time samples of the short-time signal fragment of the spectrum estimation module is 32, the number of frequency searches is 1000, and the frequency search set is f l =-0.5+(l-1) / 2048, each search frequency f l The corresponding frequency vector is l=1,2,…,2048; the regularization parameter of the spectrum estimation module is α=1, and the autocorrelation inverse matrix of the initial short-time signal segment is R0=I 32 , I 32 is a 32-order unit matrix; the number of short-time signal segments used by the spectrum estimation module for each spectrum estimation is 128.

[0027] The present invention proposes a short-time iterative minimum variance distortion-free response spectrum estimation method, using the discrete time sampling of the first 97 short-time signal segments, and iteratively determining the addition of the inverse matrix R 97 The values ​​of the first 10 elements in the first row are 0.8799-0.0000i, -0.0113-0.1136i, 0.1062-0.0214i, 0.0301+0.0979i, -0.0890+0.0374i, -0.0433-0.0797i, 0.0702-0.0478i, 0.0508+0.0606i, -0.0512+0.0524i, -0.0527-0.0421i

[0028] In comparison, the sample autocorrelation matrix of the discrete time sampling of the first 97 short-time signal fragments is directly estimated and then its inverse matrix is ​​determined. The values ​​of the first 10 elements of the first row of the inverse matrix are 0.8799-0.0000i, -0.0113-0.1136i, 0.1062-0.0214i, 0.0301+0.0979i, -0.0890+0.0374i, -0.0433-0.0797i, 0.0702-0.0478i, 0.0508+0.0606i, -0.0512+0.0524i, -0.0527-0.0421i minus the iteratively determined added inverse matrix, and the second norm of the error matrix is ​​1.3065e-10. The influence of this error on the spectrum estimation can be ignored.

[0029] Using the short-time iterative minimum variance distortion-free response spectrum estimation method proposed by the present invention, the inverse matrix R is added to the 9873rd iteration. 9873 The values ​​of the first 10 elements in the first row are 0.8782-0.0000i, 0.0238-0.1131i, 0.1002+0.0442i, -0.0603+0.0840i, -0.0657-0.0718i, 0.0786-0.0464i, 0.0273+0.0808i, -0.0787+0.0094i, 0.0065-0.0730i, 0.0645+0.0196i;

[0030] For comparison, the sample autocorrelation matrix of the 128 short-time signal segments from the 9746th to the 9873th is directly estimated and then its inverse matrix is ​​determined. The values ​​of the first 10 elements of the first row of the inverse matrix are 0.8782+0.0000i, 0.0238-0.1131i, 0.1002+0.0442i, -0.0603+0.0840i, -0.0657-0.0718i, 0.0786-0.0464i, 0.0273+0.0808i, -0.0787+0.0094i, 0.0065-0.0730i, 0.0645+0.0196i. After subtracting the iteratively determined addition inverse matrix, the second norm of the error matrix is ​​2.3042e-04, and the influence of this error on the spectrum estimation can be ignored.

[0031] When the number of short-time signal segments used for each spectrum estimation is 128, the spectrum resolution is 0.0078 using the spectrum estimation method based on short-time Fourier transform, and the spectrum of two linear frequency modulation signals with a center frequency interval of 0.0030 cannot be distinguished. Using a short-time iterative minimum variance distortion-free response spectrum estimation method proposed by the present invention, the spectrum of two linear frequency modulation signals with a center frequency interval of 0.0030 can be clearly distinguished, and the time taken on the Intel i7-13700k platform is about 0.1560 seconds. Compared with the method of directly estimating the sample autocorrelation matrix and then determining its inverse matrix, which takes about 0.26367 seconds, the present invention is accelerated by about 40.84%, achieving the purpose of reducing computational complexity.

Claims

1. A short-time iterative minimum variance distortion-free response spectrum estimation method, characterized in that: The following steps are involved: S1. Set the number of discrete time samples of the non-stationary signal whose spectrum changes with time as input to the spectrum estimation module to N, and the signal discrete time sampling to x = [x(1), x(2), ..., x(N)] T , superscript T represents the transpose of a vector; the number of frequency searches in the spectrum estimation module is L, and the frequency search set is {f1,f2,…,f L }, each search frequency f l The corresponding frequency vector is The number of discrete time samples of the short-time signal segment of the spectrum estimation module is M, and the regularization parameter is α; the inverse autocorrelation matrix of the initialized short-time signal segment is R0 = αI M , I M is the M-order unit matrix; The number of short-time signal segments used by the spectrum estimation module for each spectrum estimation is K; S2, the spectrum estimation module divides the signal discrete time sampling into short-time segment signal discrete time sampling, and determines the nth short-time segment signal discrete time sampling y n for y n =[x(n+M-1)x(n+M-2)…x(n)] T Where n = 1, 2, ..., N-M + 1; S3. For n=1, 2, ..., K, iteratively determine the addition of the inverse matrix R n for Among them, the superscript -1 represents the inverse matrix; S4. For n=K+1, K+2, ..., N, iteratively determine the exit inverse matrix Q n for Iteratively determine the addition of the inverse matrix R n for S5, the incremental inverse matrix determined by S3 and the added inverse matrix determined by S4, determine the short-time iterative minimum variance distortion-free response spectrum estimation as Among them, n=1,2,…,N, l=1,2,…,L.

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