A Three-Dimensional Parameter Estimation Method for Near-Field Sources in Space-Time Based on Parallel Factor Analysis

Abstract

The present invention relates to a three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition. The method includes: establishing a cross-array reception model, and establishing a three-dimensional rectangular coordinate system in the cross-array reception model. The cross-array reception model is composed of a uniform linear array located on the X-axis and a uniform linear array located on the Y-axis; assuming that there are K near-field targets, and the k-th near-field target S k incides on the cross-array with the electrical angle #imgabs0# and the distance r k The obtained distance estimation values #imgabs1# and #imgabs2# are subtracted to pair the parameters #imgabs3# and #imgabs4#. Based on the parallel factor decomposition technology, the present invention makes full use of the time-domain information and space-domain information of the signal, and obtains better performance while greatly reducing the computational complexity by means of an enhanced third-order structure. No such estimation algorithm has been proposed in the near-field background.

Description

Technical Field

[0001] The present invention relates to the technical field of near-field signal positioning, and in particular to a three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition. Background Art

[0002] Near-field signal positioning is widely used in fields such as radar, sonar, and wireless communication, and has received extensive attention in recent years. The initial near-field source positioning algorithms mainly improved the far-field source positioning algorithms and applied them to the near-field. For example, the MUSIC algorithm based on the near-field is simple to implement, but it involves multi-dimensional search and has a huge amount of calculation. In recent years, many scholars have used some dimensionality reduction techniques to reduce the multi-dimensional search to one-dimensional search, thereby improving the calculation efficiency, but the inherent high complexity of the spectral peak search still exists. Later, some algorithms based on compressive sensing were successively proposed, but their performance depends on the setting of certain parameters, and due to the existence of grids, the accuracy is limited to a certain extent. In the past two years, the algorithms based on optimization have attracted attention, but their computational complexity is even higher than that of the spectral peak search algorithms. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition, which can obtain automatically paired near-field two-dimensional electrical angles and distance parameters on the premise of a uniform cross-shaped array, and the entire parameter estimation process has low complexity and high parameter pairing accuracy.

[0004] The technical solution adopted by the present invention is a three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition, and the method includes the following steps:

[0005] S1. Establish a cross-shaped array receiving model, and establish a three-dimensional rectangular coordinate system in the cross-shaped array receiving model. The cross-shaped array receiving model is composed of a uniform linear array on the X-axis and a uniform linear array on the Y-axis; both the uniform linear arrays on the X-axis and the Y-axis include (2P + 1) array elements, and the array element at the coordinate origin is used as a reference array element, and the spacing between array elements is set to d = λ / 4, where λ is the wavelength of the incident signal;

[0006] S2. In the three-dimensional rectangular coordinate system, it is assumed that there are K near-field targets, and the k-th near-field target S k with an electrical angle and a distance r k incides on the cross-shaped array. Among them, k = 1, 2,..., K, and the received data model of the m-th array element on the X-axis is obtained as: where -P ≤ m ≤ P, P represents the number of unilateral array elements, s k (t) represents the incident signal of the k-th near-field target, and n m,0(t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , and τ xk (m) represents the propagation delay between the incident signal of the k-th near-field target in space arriving at the reference array element and arriving at any array element, and τ xk (m) ≈ ω xk m + φ xk m 2 , The received data model of the n-th array element located on the Y-axis is obtained as follows: where s k (t) represents the incident signal of the k-th near-field target, and n 0,n (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , and τ yk (n) represents the propagation delay between the incident signal of the k-th near-field target in space arriving at the reference array element and arriving at any array element, and τ yk (n) ≈ ω yk n + φ yk n 2 ,

[0007] S3. Based on the received data model of the m-th array element located on the X-axis obtained in step S2, the received data model of the array element at (-m - 1, -m) on the X-axis is obtained as follows: where represents the time-delay autocorrelation function of the k-th source; based on the received data model of the n-th array element located on the X-axis obtained in step S2, the received data model of the array element at (m + 1, m) on the X-axis is obtained as follows:

[0008] S4. The r -m-1,-m (τ) and r m+1,m (τ) obtained in step S3 are respectively arranged in vector form according to the array element positions m = -P, -P + 1,..., P - 1, that is: r1(τ) = [r p-1,p (τ), r p-2,p-1 (τ),..., r -1,0 (τ),..., r -p,-p+1 (τ)] T , r2(τ) = [r -p+1,-p (τ), r -p+2,-p+1 (τ),..., r 1,0 (τ),..., r p,p-1 (τ)] T , and their matrix form corresponds to: r2(τ) = BΦ x Ω xr s (τ); where B = [b(φ x1 ),..., b(φ xK )] r s (τ) = [r s1 (τ),..., r sK (τ)] T ;

[0009] S5. Take the vectors r1(τ) and r2(τ) obtained in step S4 and take L time delays respectively to form pseudo-snap data, obtaining two delay autocorrelation matrices R1 = [r1(1), r1(2),..., r1(L)] and R2 = [r2(1), r2(2),..., r2(L)], and represent R1 and R2 in matrix form as and R2 = BΦ x Ω x R s , where R s = [r s (1), r s (2),..., r s (L)], r s (l) = E{s(t + l)s * (t)} is the autocorrelation function of the signal;

[0010] S6. Define a (2×2p×L)-dimensional three-sided array X. Using the parallel factor model, slice X, and the dimension of each slice matrix is (2p×L). Then the matrices R1 and R2 obtained in step S5 are:

[0011] where U x = B, diag -1 (*) represents the row vector composed of the diagonal elements of the corresponding diagonal matrix;

[0012] S7. Perform COMFAC (Complex Parallel Factorization) on the three-sided array X defined in step S6 to obtain the estimated values of R x and U x : and Then the estimated parameters of the k-th signal and are: where angle() represents taking the phase angle, represents the i-th row and k-th estimated value of the matrix obtained by parallel factor decomposition;

[0013] S8. Similarly, according to steps S3 to S7, the estimated parameters of the k-th signal with respect to the Y-axis are obtained.

[0014] S9. According to the parameters and the estimated value of the distance is: The estimated value of the distance is:

[0015] S10. Subtract the two distance estimated values and obtained in S9 to achieve the pairing of the parameters and ;

[0016] S11. On the basis of the pairing completed in step S10, according to the expressions and the estimated value of the two-dimensional DOA is obtained and the estimated value of the distance is:

[0017] The beneficial effect of the present invention is as follows: By adopting the above three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition, which is based on the parallel factor decomposition technology, by fully utilizing the time-domain information and space-domain information of the signal, as well as the enhanced third-order structure, the performance of the estimation algorithm is effectively improved, the accuracy of parameter pairing is improved, and at the same time, the high computational complexity brought by similar multi-dimensional search is avoided; this method can obtain the automatically paired near-field two-dimensional electrical angles and distance parameters on the premise of a uniform cross-shaped array. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic diagram of the cross-shaped array receiving model in the three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition of the present invention;

[0019] Figure 2 is a schematic diagram of the pairing of the estimated parameters of three near-field sources obtained in the example of the specific implementation manner of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0020] The following further describes the invention with reference to the accompanying drawings and in conjunction with the specific implementation manner, so that those skilled in the art can implement it according to the description in the specification. The protection scope of the present invention is not limited to this specific implementation manner.

[0021] The present invention relates to a three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition, and this method includes the following steps:

[0022] S1. As shown in Figure 1 , a cross - array receiving model is established. A three - dimensional rectangular coordinate system is established in the cross - array receiving model. The cross - array receiving model is composed of a uniform linear array on the X - axis and a uniform linear array on the Y - axis. The uniform linear arrays on the X - axis and Y - axis both contain (2P + 1) array elements. The array element at the coordinate origin is used as the reference array element, and the spacing between array elements is set to d = λ / 4, where λ is the wavelength of the incident signal.

[0023] S2. In the three - dimensional rectangular coordinate system, it is assumed that there are K near - field targets. The k - th near - field target S k incides on the cross - array with the electrical angle and the distance r k . Among them, k = 1, 2, …, K. The received data model of the m - th array element on the X - axis is obtained as: where - P ≤ m ≤ P, P represents the number of unilateral array elements, s k (t) represents the incident signal of the k - th near - field target, n m,0 (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , τ xk (m) represents the propagation delay between the incident signal of the k - th near - field target in space reaching the reference array element and reaching any array element. τ xk (m) ≈ ω xk m + φ xk m 2 . The received data model of the n - th array element on the Y - axis is obtained as: where s k (t) represents the incident signal of the k - th near - field target, n 0,n (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , τ yk (n) represents the propagation delay between the incident signal of the k - th near - field target in space reaching the reference array element and reaching any array element. τ yk (n) ≈ ω yk n + φ yk n 2 .

[0024] S3. According to the received data model of the m - th array element on the X - axis obtained in step S2, the received data model of the array element at (- m - 1, - m) on the X - axis is obtained as: where It represents the time-delay autocorrelation function of the k-th information source; according to the received data model of the n-th array element located on the X-axis obtained in step S2, the received data model of the array element at (m+1,m) on the X-axis is:

[0025] S4. Arrange r -m-1,-m (τ) and r m+1,m (τ) obtained in step S3 in vector form according to the array element positions m = -P, -P + 1,..., P - 1, that is: r1(τ) = [r p-1,p (τ), r p-2,p-1 (τ),..., r -1,0 (τ),..., r -p,-p+1 (τ)] T , r2(τ) = [r -p+1,-p (τ), r -p+2,-p+1 (τ),..., r 1,0 (τ),..., r p,p-1 (τ)] T , and its matrix form corresponds to: r2(τ) = BΦ x Ω x r s (τ); where B = [b(φ x1 ),..., b(φ xK )], r s (τ) = [r s1 (τ),..., r sK (τ)] T ;

[0026] S5. Take the L-time delays of the vectors r1(τ) and r2(τ) obtained in step S4 to form pseudo snapshot data, obtaining two time-delay autocorrelation matrices R1 = [r1(1), r1(2),..., r1(L)] and R2 = [r2(1), r2(2),..., r2(L)], and represent R1 and R2 in matrix form as and R2 = BΦ x Ω x R s , where R s = [r s (1), r s (2),..., r s (L)], r s (l) = E{s(t + l)s * (t)} is the autocorrelation function of the signal;

[0027] S6. Define a three-sided array X of dimension (2×2p×L), and use the parallel factor model to slice X. The dimension of each slice matrix is (2p×L). Then, the matrices R1 and R2 obtained in step S5 are as follows: where U x = B, diag -1 (*) represents the row vector composed of the diagonal elements of the corresponding diagonal matrix;

[0028] S7. Perform COMFAC (Complex Parallel Factor Analysis) on the three-sided array X defined in step S6 to obtain the estimated values of R x and U x : and Then, the estimated parameters of the k-th signal and are: where angle() represents taking the phase angle, represents the i-th row and k-th estimated value of the matrix obtained by parallel factor analysis;

[0029] S8. Similarly, according to steps S3 to S7, obtain the estimated parameters of the k-th signal about the Y-axis That is, just change the subscript x to y in all steps of S3 to S7, and the process is exactly the same;

[0030] S9. According to the parameters and obtain the estimated value of the distance as: The estimated value of the distance is:

[0031] S10. Since (ω xk , φ xk ) and (ω yk , φ yk ) are estimated independently in two steps, they do not match each other pairwise. However, from step S9, it can be seen that the two distances xk , φ xk ) and (ω yk , φ yk ) actually correspond to the same signal source. Although there are slight deviations in the estimation process, the parameters (ω and Actually correspond to the same signal source. Although there are slight deviations in the estimation process, the parameters (ω and By taking the difference between each pair of the distance sets xk , φ xk ) and (ω yk , φyk ) The correct pairing result. Because only when the pairing is correct, the distance values corresponding to the two sets of parameters are the closest. Therefore, the two distance estimates obtained in step S9 and are subtracted to achieve the pairing of the parameters and ;

[0032] S11. On the basis of the completion of the pairing in step S10, according to the expressions and the estimated value of the two-dimensional DOA is obtained, and the estimated value of the distance is:

[0033] The effectiveness of a three-dimensional parameter estimation method for near-field sources in space-time based on parallel factor decomposition proposed by the present invention is demonstrated by the following example.

[0034] Example: Suppose three independent near-field signals are incident on a cross array with 3 single-sided array elements at angles of (70°, 80°, 0.8λ), (100°, 110°, 1.2λ), and (120°, 150°, 2.0λ) respectively, that is, the total number of array elements included in the two uniform linear arrays is 7; the signal-to-noise ratio and the number of snapshots are set to 30 dB and 500 respectively, and pseudo-snapshots are used. The obtained results are as Figure 2 shown. From Figure 2 we can see that the estimated parameters of the three near-field sources can be correctly estimated and paired; therefore, the method proposed by the present invention is effective.

Claims

1. A three-dimensional parameter estimation method for spatio-temporal near-field sources based on parallel factor decomposition, characterized in that: The method includes the following steps: S1. Establish a cross - array reception model, and establish a three - dimensional rectangular coordinate system in the cross - array reception model. The cross - array reception model is composed of a uniform linear array on the X - axis and a uniform linear array on the Y - axis. The uniform linear arrays on the X - axis and Y - axis both contain (2P + 1) array elements. The array element located at the coordinate origin is used as a reference array element, and the spacing between array elements is set to d = λ / 4, where λ is the wavelength of the incident signal. S2. In a three-dimensional rectangular coordinate system, assume there are K near-field targets, and the k-th near-field target S k with the electrical angle and the distance r k incides on a cross array. Here, k = 1, 2, …, K, and the received data model of the m-th element located on the X-axis is obtained as follows: where -P ≤ m ≤ P, P represents the number of unilateral elements, s k (t) represents the incident signal of the k-th near-field target, n m,0 (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , τ xk (m) represents the propagation delay between the incident signal of the k-th near-field target in space arriving at the reference element and arriving at any element, τ xk (m) ≈ ω xk m + φ xk m 2 , The received data model of the n-th element located on the Y-axis is obtained as follows: where s k (t) represents the incident signal of the k-th near-field target, n 0,n (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , τ yk (n) represents the propagation delay between the incident signal of the k-th near-field target in space arriving at the reference element and arriving at any element, τ yk (n) ≈ ω yk n + φ yk n 2 , S3. Based on the received data model of the m-th array element on the X-axis obtained in step S2, the received data model of the array element at (-m - 1, -m) on the X-axis is: where represents the time-delay autocorrelation function of the k-th signal source; based on the received data model of the n-th array element on the X-axis obtained in step S2, the received data model of the array element at (m + 1, m) on the X-axis is: S4. Arrange \(r\) obtained in step S3 -m-1,-m (τ) and \(r\) m+1,m (τ) into vector forms according to the array element positions \(m = -P, -P + 1,\cdots, P - 1\), respectively, that is: \(r_1(τ)=[r p-1,p (τ), r p-2,p-1 (τ),\cdots, r -1,0 (τ),\cdots, r -p,-p+1 (τ)] T , \(r_2(τ)=[r -p+1,-p (τ), r -p+2,-p+1 (τ),\cdots, r 1,0 (τ),\cdots, r p,p-1 (τ)] T , and their matrix forms correspondingly are: r_2(τ)=BΦ x Ω x r s (τ); where \(B = [b(φ x1 ),\cdots, b(φ xK )]\), r s (τ)=[r s1 (τ),\cdots, r sK (τ)] T ; S5. Take the vectors r1(τ) and r2(τ) obtained in step S4 with L time delays respectively to form pseudo-snapshots data, obtaining two time-delay autocorrelation matrices R1 = [r1(1), r1(2),..., r1(L)] and R2 = [r2(1), r2(2),..., r2(L)], and represent R1 and R2 in matrix form as and R2 = BΦ x Ω x R s , where R s = [r s (1), r s (2),..., r s (L)], r s (l) = E{s(t + l)s * (t)} is the autocorrelation function of the signal; S6. Define a (2×2p×L) - dimensional three - plane array X. Using the parallel factor model, slice X. The dimension of each slice matrix is (2p×L). Then the matrices R1 and R2 obtained in step S5 are as follows: where U x = B, diag -1 (*) denotes the row vector formed by the diagonal elements of the corresponding diagonal matrix; Perform COMFAC (Complex Parallel Factorization) on the three-sided array X defined in step S6 to obtain the estimates of R x and U x : and Then, the estimated parameters of the k-th signal and are: where angle() represents taking the phase angle, represents the i-th row and k-th estimated value of the matrix obtained by parallel factor decomposition; S8. Similarly, according to steps S3 to S7, the estimated parameters of the k-th signal with respect to the Y-axis are obtained. S9. Obtain according to the parameters and to get the estimated value of the distance as: The estimated value of the distance is: S10. Subtract the two distance estimation values obtained in S9 and to pair the parameters and ; S11. On the basis of the completion of the pairing in step S10, according to the expressions and obtain the estimated value of the two-dimensional DOA and obtain the distance The estimated value of is:

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