CN109407047B

CN109407047B - Amplitude-phase error calibration and direction-of-arrival estimation method based on rank loss root finding

Info

Publication number: CN109407047B
Application number: CN201811094657.3A
Authority: CN
Inventors: 戴继生; 方忠驰; 王兰
Original assignee: Jiangsu University
Current assignee: Dragon Totem Technology Hefei Co ltd; Shanghai Fuyuan Zhiye Forge Co.,Ltd.
Priority date: 2018-09-19
Filing date: 2018-09-19
Publication date: 2022-08-23
Anticipated expiration: 2038-09-19
Also published as: CN109407047A

Abstract

The invention discloses an amplitude-phase error calibration and direction of arrival estimation method based on rank loss root finding, which comprises the following steps of 1: the output at the receiver after the radar signal received by the receiving system is matched and filtered is denoted as x (t). Step 2: covariance of matrix x (t)The matrix R is subjected to eigenvalue decomposition to obtain a noise subspace matrix E _N . And step 3: using a noise subspace matrix E _N And constructing a matrix U. And 4, step 4: using U, a polynomial f (x) about variable x is constructed, and let f (x) be 0, and N roots whose modulus is closest to 1 are obtained

And 5: by using

And obtaining estimated values of N DOAs. The method utilizes a polynomial root solving method to replace the solving of the matrix determinant value, thereby greatly reducing the calculation amount and saving the operation time.

Description

Amplitude-phase error calibration and direction-of-arrival estimation method based on rank loss root finding

Technical Field

The invention belongs to the field of radar signal processing, relates to the calibration of amplitude and phase errors of an array sensor, and particularly relates to a method suitable for automatic amplitude and phase error calibration and direction of arrival estimation of a uniform linear array.

Background

In recent decades, Direction of Arrival (DOA) estimation has been a hot point problem in array signal processing, and is widely applied to many fields such as radar, sonar, passive positioning, wireless communication, and the like. The main purpose of DOA estimation is to detect and estimate the orientation of multiple signals in noisy environments. In response to the DOA estimation problem, attempts have been made to propose new DOA estimation methods for calibrating the amplitude-phase error of the array sensor. For example in the literature: C.M.S.See and A.B.Gershman, Direction-of-arrival estimation in partial filtered subarray-based sensor array, IEEE Transactions on Signal Processing,52(2) 329) 338, a rank-loss (RARE) algorithm was proposed to calibrate the sensor amplitude-phase error and estimate the DOA, but the search interval of the algorithm was

And the determinant value of the matrix corresponding to each angle needs to be solved, so the original RARE algorithm has larger calculated amount and longer search time.

Disclosure of Invention

Aiming at the defects of the existing method, the invention provides a rank-loss (RARE) ROOT-finding (ROOT) based amplitude-phase error calibration and DOA estimation method, which is improved on the basis of the original RARE algorithm, reduces the operation amount by constructing a polynomial and then finding the ROOT of the polynomial, and shortens the operation time.

The technical solution for implementing the invention comprises the following steps:

step 1: the output at the receiver of the radar signal received by the receiving system after matched filtering is denoted as x (t).

Step 2: solving a covariance matrix R of the matrix x (t), and carrying out eigenvalue decomposition on the covariance matrix R to obtain a noise subspace matrix E _N 。

And step 3: using a noise subspace matrix E _N And constructing a matrix U.

And 4, step 4: a polynomial f (x) about a variable x is constructed by using U, and the N roots with the most modulus being close to 1 are obtained by making f (x) equal to 0

And 5: by using

And obtaining estimated values of N DOAs.

The invention has the beneficial effects that:

compared with the existing RARE algorithm, the method for solving the polynomial root replaces the method for solving the matrix determinant value, so that the calculation amount is greatly reduced, and the operation time is saved.

Drawings

FIG. 1 is a flow chart of an embodiment of the present invention.

Fig. 2 is a comparison of the rms errors of the separately estimated channels of the present invention and the original RARE method for 200 monte carlo experiments with snr from-10 dB to 10 dB.

Figure 3 is a comparison of the time taken for the present invention to estimate the channel separately from the original RARE method for 200 monte carlo experimental conditions with a signal-to-noise ratio from-10 dB to 10 dB.

Detailed Description

The invention will be further explained with reference to the drawings.

As shown in fig. 1, the method of the present invention includes the following steps (1) to (5):

(1) after a signal received by the system is subjected to matching filtering, output data of the uniform linear array obtained at a receiver at the time t is x (t) ═ Γ As (t) + n (t), wherein:

Γ denotes the amplitude-phase error matrix, which is defined as the matrix diag { τ } ₁ ,τ ₂ ,...,τ _M M represents the number of array elements, diag {. cndot } represents a diagonal matrix, and the diagonal element in the diagonal matrix is tau ₁ ,τ ₂ ,...,τ _M Amplitude-phase error coefficient tau _m ＝ρ _m exp(jδ _m ),m＝1,2,...M，ρ _m And delta _m Respectively representing the amplitude error and the phase error of the m-th array element. Assume that there are M out of a total of M array elements _c The array elements are not calibrated and are not generalized, and the serial numbers are recorded as {1,2 _c And then the amplitude and phase error coefficients of other array elements can be recorded as tau _m ＝1,m∈{M _c +1,M _c +2,...,M}。

A represents an array flow pattern matrix, which is defined as [ a (θ) ] ₁ ),a(θ ₂ ),...,a(θ _N )]Where N is the number of incident signals, θ _n N, denotes the nth true DOA value,

wherein j represents an imaginary number, and wherein,

d represents the array element spacing, and λ represents the wavelength of the electromagnetic wave, (. cndot.) ^T Representing a matrix transposition.

s (t) represents an N-dimensional incident signal vector at time t, and N (t) represents an M-dimensional zero mean value at time tA gaussian white noise vector.

(2) And (3) solving a covariance matrix of the array data by using the array output data:

R＝E{x(t)x ^H (t)}＝ΓAR _S A ^H Γ ^H +σ ² I _M

wherein sigma ² And I _M Respectively representing the variance of the noise and the M-dimensional identity matrix, (-) ^H Denotes the conjugate transpose, R _S Represents a signal covariance matrix, defined as R _S ＝E{s(t)s ^H (t) }, E {. cndot } represents expectation, and then the R characteristic is decomposed to obtain

Wherein Λ _S Is a diagonal matrix of N large eigenvalues of the covariance matrix, E _S Is the feature vector corresponding thereto; lambda _N A diagonal matrix formed by the other M-N small eigenvalues, and an eigenvector corresponding to the diagonal matrix is E _N Referred to herein as a noise subspace matrix.

(3) Construction using a noise subspace matrix

U is then divided into four sub-matrices, namely:

U ₁ is of dimension M _c ×M _c ，U ₂ Is of dimension M _c ×(M-M _c )，U ₃ Is (M-M) _c )×M _c ，U ₄ Is (M-M) _c )×(M-M _c )。

(4) Order to

Construct a (2M-2M) _c 1) x 1-dimensional vector v, the ith element v of which _i Defined as the sum of all elements on the kth diagonal of the matrix S. Constructing a polynomial for variable x:

let function f (x) be 0, find the N roots whose modulus is closest to 1

(5) Using the obtained

Obtaining estimated values of N DOAs:

wherein:

to represent

Phase angle of (a), theta _n The value range is

The effect of the present invention will be further explained with the simulation experiment.

In order to evaluate the performance of the method, a system is considered, the array element spacing of a transmitting array is a uniform linear array of half-wavelength electromagnetic waves, the number M of the array elements of the transmitting array is 8, and the number M of uncalibrated amplitude-phase coefficients among the array elements of the transmitting array is M _c Is 4, each of

Suppose that the far field has two mutually independent target signal sources respectively positioned at theta ₁ ＝-15°,θ ₂ 20 deg. is equal to. In all experiments, the noise was assumed to be zero-mean white gaussian noise and the fast beat number was 400.

Conditions of the experiment

The simulation results of the angle estimation of the target angle for 200 times when the signal-to-noise ratio is from-10 dB to 10dB are shown in the figure 2 and the figure 3.

Analysis of experiments

As can be seen from fig. 2, the present invention can accurately estimate the true DOA value and its performance is slightly better than the original RARE method.

As can be seen from fig. 3, the time used by the present invention is significantly less than the time used by the original RARE.

The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.

Claims

1. A method for calibrating amplitude-phase errors and estimating direction of arrival based on rank loss root finding is characterized by comprising the following steps:

step 1: after the radar signals received by the receiving system are subjected to matched filtering, the output at the receiver is represented as x (t); x (t) refers to output data of the uniform linear array obtained at the receiver at the time t; the expression of x (t) is:

x(t)＝ΓAs(t)+n(t)，

wherein:

gamma is amplitude phase error matrix, A is array flow pattern matrix,

s (t) represents an N-dimensional incident signal vector at the time t, and N (t) represents an M-dimensional zero-mean Gaussian white noise vector at the time t;

the amplitude-phase error matrix gamma is defined as a matrix diag { tau ₁ ,τ ₂ ,...,τ _M M represents the number of array elements, diag {. cndot } represents a diagonal matrix, and the diagonal element in the diagonal matrix is tau ₁ ,τ ₂ ,...,τ _M Amplitude-phase error coefficient tau _m ＝ρ _m exp(jδ _m ),m＝1,2,...M，ρ _m And delta _m Respectively representing the amplitude error and the phase error of the m-th array element; assume a total of MIn the array element there is M _c The array elements are not calibrated, and the serial number of the array elements is recorded as {1,2 _c And the amplitude and phase error coefficients of other array elements are recorded as tau _m ＝1,m∈{M _c +1,M _c +2,...,M}；

And 2, step: solving covariance matrix R of matrix x (t), and decomposing eigenvalue to obtain noise subspace matrix E _N ；

And step 3: using a noise subspace matrix E _N Constructing a matrix U; the specific implementation comprises the following steps:

using a noise subspace matrix E _N Construction matrix

U is then divided into four sub-matrices, namely:

U ₁ is of dimension M _c ×M _c ，U ₂ Is of dimension M _c ×(M-M _c )，U ₃ Is (M-M) _c )×M _c ，U ₄ Is (M-M) _c )×(M-M _c ) (ii) a M denotes the number of array elements, M _c Representing the number of unaligned array elements;

and 4, step 4: a polynomial f (x) about a variable x is constructed by using U, and f (x) is made 0, and N roots with a mode closest to 1 are obtained

The specific implementation comprises the following steps:

order to

Construct a (2M-2M) _c -1) x 1-dimensional vector v, its i-th element v _i Defined as the sum of all elements on the kth diagonal of the matrix S; constructing a polynomial for the variable x:

let function f (x) be 0, find the N roots whose modulus is closest to 1

v _n Is the nth element of the vector v;

and 5: by using

And obtaining N DOA estimated values.

2. The method for amplitude-phase error calibration and direction of arrival estimation based on rank-loss root finding as claimed in claim 1, wherein the array flow pattern matrix A is defined as [ a (θ) ₁ ),a(θ ₂ ),...,a(θ _N )]Where N is the number of incident signals, θ _n N, which represents the nth true DOA value,

wherein j represents an imaginary number, and wherein,

3. The method for amplitude-phase error calibration and direction-of-arrival estimation based on rank-loss root finding as claimed in claim 1, wherein the step 2 is implemented by:

and (3) solving a covariance matrix of the array data by using the array output data:

R＝E{x(t)x ^H (t)}＝ΓAR _S A ^H Γ ^H +σ ² I _M

Wherein Λ _S Is a diagonal matrix of N large eigenvalues of the covariance matrix, E _S Is the feature vector corresponding thereto; lambda _N A diagonal matrix formed by the other M-N small eigenvalues, and an eigenvector corresponding to the diagonal matrix is E _N Referred to as a noise subspace matrix.

4. The method as claimed in claim 1, wherein the step 5 utilizes the method of amplitude-phase error calibration and direction of arrival estimation based on rank-loss root-finding

The estimated values of N DOAs are obtained as follows:

wherein:

represent

Phase angle of (a), theta _n The value range is

d represents the array element spacing, and λ represents the wavelength of the electromagnetic wave.