CN106202892B - Fast DOA estimation algorithm based on single vector of noise subspace - Google Patents

Abstract

The invention relates to the field of signal processing, and discloses a fast DOA estimation algorithm based on a noise subspace single vector. Compared with the classical algorithm, under the condition of the same step length, the calculation amount of the method can be maximally reduced to 1/(M-P) of the original algorithm, the precision is improved, M is the number of array elements, and P is the number of information sources.

Description

Fast DOA estimation algorithm based on single vector of noise subspace

Technical Field

The invention relates to the field of signal processing, and is suitable for reducing the calculation time and improving the estimation performance in the application of adopting the MUSIC algorithm to carry out DOA estimation.

Background

Reducing the calculation amount of the MUSIC algorithm and shortening the estimation time of the DOA are always important research contents of array signal processing. The ROOT-MUSIC algorithm is intuitively considered to be short in calculation time, but studies of scholars show that the calculation amount is lower than that of the classical MUSIC algorithm only under the condition of small array dimension, and the MUSIC algorithm requires that the array is a uniform linear array. At present, most scholars focus on improving the calculation speed of two-dimensional angle estimation, and do not have good processing methods for improving the calculation speed of one-dimensional angles. The classical MUSIC algorithm has to use all noise vectors when doing DOA estimation, thus also causing an increase in the amount of computation, whereas if only one vector is used the amount of computation decreases, but false peaks occur. The invention greatly reduces the calculated amount of DOA estimation by using a vector, and can remove the false peaks by a method of slightly increasing spectral peak identification although the number of the false peaks is increased, thereby greatly reducing the calculated amount on the whole and simultaneously further reducing the quantization error caused by quantization step length by using an interpolation algorithm.

Disclosure of Invention

The invention aims to provide a fast DOA estimation algorithm based on a single vector of a noise subspace, so as to reduce the calculation time of a classic MUSIC algorithm and improve the estimation precision.

In order to achieve the technical purpose, the invention discloses a fast DOA estimation algorithm based on a single vector of a noise subspace, which comprises the following steps:

(1) acquiring data to be processed: x (t) as (t) n (t), 1 ≦ t ≦ L where x (t) is ≦ x₀(t),…,x_M-1(t)]^TReceiving data for an antenna to be processed, wherein t is a data sequence number, L is the number of data, and M is the number of array elements; a ═ a (θ)₁),…,a(θ_P)]^TA matrix of steering vectors, wherein a (θ)_p) Represents the array pair θ_pThe response vector of the direction incident signal is more than or equal to 1 and less than or equal to P, and the ith element a of the direction incident signal_i(θ_p)＝exp(j(i-1)2πdsinθ_pLambda), d is the array element spacing, and lambda is the signal wavelength; s (t) is an ambient signal; n (t) is channel noise, each channel noise is independent and is distributed

Noise is independent of signal;

(2) computing a covariance matrix

(3) Performing characteristic decomposition on the matrix, and arranging characteristic values from large to small

λ₁≥λ₂≥…≥λ_M；

(4) In the noise space vector u_P+1,...,u_MIn (1), optionally selecting a vector u_iCalculating spectral values

(5) Searching all spectral peak positions and corresponding peaks of p (theta) and ranking according to some criterion

K is the number of the spectrum peaks,

(6) by

Initially, data for pseudo-peak identification and angular interpolation estimation are computed sequentially

Wherein, Delta theta is the search step length,

(7) to angle

According to f_k,-1≤f_k,0And f_k,1≤f_k,0If the two are true, the peak corresponding to the real target is judged, and the position is recorded as

i represents the ith real position i of the record to be less than or equal to P;

(8) target

Corresponding spectral value data

Various interpolation algorithms may be employed

To estimate the target angle, a typical formula is

The invention has the following beneficial effects:

1. the invention can improve the calculation speed of the classic MUSIC algorithm, when the number of the array elements is M and the number of the information sources is P, the calculation amount is reduced to about 1/(M-P) of the original calculation amount, and if M is 10 and P is 4, the calculation amount can be reduced to 1/6.

2. The invention adopts the interpolation technology, reduces the quantization error caused by the search step length and improves the estimation precision while almost not increasing the calculation amount.

3. The method is suitable for linear arrays and any arrays, and is suitable for one-dimensional angle estimation and 2-dimensional angle estimation; the method is also suitable for the application that the existing rapid algorithm cannot be used, such as the antenna pattern inconsistent array and the like.

Drawings

FIG. 1 is a schematic flow chart of the present invention.

Fig. 2 is a single vector-based MUSIC algorithm and a classical MUSIC algorithm spectrogram for pseudo-peak identification.

FIG. 3 is a graph comparing the estimated performance of the present algorithm and the classical MUSIC algorithm at different search steps.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.

Example 1

As shown in fig. 1, the signal processing flow diagram of the present invention includes the following steps:

(1) acquiring received data x (t);

(2) calculating a cross-correlation matrix R;

(3) feature decomposition to obtain a noise space vector u_P+1,...,u_MPerforming the following steps;

(4) optionally a vector u_iCalculating a spectrum function, finding out the position of a peak point and sequencing according to the size of the peak point

(5) Calculating a pseudo peak identification criterion f at a peak point_k,m,1≤k≤K,|m|≤q；

(6) According to a criterion f_k,-1≤f_k,0And f_k,1≤f_k,0Performing false peak identification and real target recording

(7) To the target

Using interpolation algorithm G (f)_i,-q,...,f_i,q) To estimate the target angle.

Example 2

The experimental purposes and methods: to illustrate that a single noise vector can generate a pseudo peak, and the classical MUSIC for pseudo peak identification can remove the pseudo peak, the example adopts a method of MATLAB simulation for verification. The specific conditions are that the incident angles of 2 independent signal sources are respectively 20 degrees and 40 degrees, the signal-to-noise ratio is 25dB, 128 snapshots are obtained, and the experimental results of MUSIC based on a single vector and all vectors are compared and shown in figure 3.

The experimental results are as follows: as shown in fig. 3, the spectrogram (dotted line) based on any one noise vector contains a target position spectral peak, but also generates a plurality of pseudo peaks, the number of the pseudo peaks is limited, and the pseudo peaks are selected to be smaller than the spectral density point, so that a plurality of peak position positions containing a target can be obtained by using any dotted line; a classical MUSIC spectrogram (thick solid line) based on all noises has a spectral peak only at a target position, and other positions do not, and therefore can be used to determine whether a specific position is a target, and positions where determination is required are few, and thus the amount of calculation for determination is small.

Example 3

The experimental purposes and methods: in order to illustrate that the accuracy is improved due to the reduction of quantization errors under the condition that the calculation amount is less than the accuracy MUSIC after the algorithm adopts interpolation estimation, the MATLAB simulation method is adopted for verification in the embodiment. The specific conditions are that the incident angles of 2 independent signal sources are respectively 20 degrees and 40 degrees plus a small random disturbance, the signal-to-noise ratio is 25dB, 128 snapshots are obtained, 1000 Monte Carlo experiments are carried out, and the comparison of simulation results is shown in figure 3.

The experimental results are as follows: it can be seen from fig. 3 that the accuracy of the classical MUSIC algorithm is rapidly reduced due to the quantization step as the step increases, and the performance of the algorithm relative to the MUSIC algorithm is improved while the calculation amount is effectively reduced in the early stage by adopting the interpolation algorithm.

Claims (1)

1. A fast DOA estimation algorithm based on a noise subspace single vector is characterized in that the following 8 steps are adopted to estimate a target angle:

(1) acquiring data to be processed: x (t) as (t) n (t), 1 ≦ t ≦ L where x (t) is ≦ x₀(t)，…，x_M-1(t)]^TReceiving data for an antenna to be processed, wherein t is a data sequence number, L is the number of data, and M is the number of array elements; a ═ a (θ)₁)，…，a(θ_P)]^TA matrix of steering vectors, wherein a (θ)_p) Represents the array pair θ_pThe response vector of the direction incident signal, P is more than or equal to 1 and less than or equal to P, and the ith element a_i(θ_p)＝exp(j(i-1)2πdsinθ_pLambda), d is the array element spacing, and lambda is the signal wavelength; s (t) is an ambient signal; n (t) is channel noise, each channel noise is independent and is distributed

Noise is independent of signal;

(2) computing a covariance matrix

(3) Performing characteristic decomposition on the matrix, and arranging characteristic values from large to small

λ₁≥λ₂≥…≥λ_M；

(4) In the noise space vector u_P+1，...，u_MIn (1), optionally selecting a vector u_iCalculating spectral values

(5) Searching all spectral peak positions and corresponding peaks of p (theta) and ranking according to some criterion

K is the number of the spectrum peaks,

1≤k≤K：

(6) by

Initially, data for pseudo-peak identification and angular interpolation estimation are computed sequentially

Where Δ θ is the search step, U_N＝[u_P+1，...，u_M]，|m|≤q，

(7) To angle

According to f_k，-1≤f_k，0And f_k，1≤f_k，0If the two are true, the peak corresponding to the real target is judged, and the position is recorded as

i represents the ith real position i of the record to be less than or equal to P;

(8) target

Corresponding spectral value data

The following formula can be adopted

Calculating the i-th target incident angle

Images