A joint amplitude and phase error estimation and direct positioning method based on mobile array

Abstract

The application discloses a kind of based on mobile array's joint amplitude-phase error estimation and direct positioning method, comprising: receiving radiation source signal by mobile array, again by the mobile transformation array position of array;New array receives radiation source signal again;Covariance matrix is calculated to the signal received by multiple array, and eigenvalue decomposition is carried out, to obtain multiple signal noise subspace;By noise subspace and steering vector reconstruction quadratic optimization problem, construct cost function, finally by grid search determine radiation source position, simultaneously obtain amplitude-phase error estimation value.The application breaks through the traditional direct positioning in the enclosure of radiation source position estimation precision limited by amplitude-phase error, and without auxiliary signal source and array element, also without iterative solution, can obtain high-precision radiation source position and amplitude-phase error joint estimation, with important application value.

Description

Technical Field

[0001] This invention relates to a method for jointly estimating the location of a radiation source and its amplitude and phase errors, and particularly to a method for jointly estimating amplitude and phase errors and directly locating the source based on a moving array. Background Technology

[0002] Array signal processing, as an important branch of modern signal processing, is a rapidly developing technological field in recent decades, widely used in military and civilian fields such as radar, sonar, and wireless communication. Passive localization is a key technology in array signal processing. Traditional passive localization techniques mostly employ a two-step estimation model: first, relevant measurements for localization are extracted from the target's radiated signal data, such as the angle of arrival, time of arrival, time difference of arrival, and signal strength; then, the target's position parameters are obtained from these observations. Direction Position Determination (DPD) technology differs from traditional two-step localization techniques. While using the received signal in two-step localization, it eliminates the need for estimating parameters such as the angle of arrival, allowing direct estimation of the target's position. DPD technology is based on the maximum likelihood principle, establishing a target cost function and determining the extreme points of the cost function through multi-dimensional grid search to obtain an estimate of the target's position.

[0003] The prevalence of array errors is a significant reason why passive positioning technology is difficult to apply in practical engineering. Generally, almost all direct positioning algorithms are based on the premise of precise knowledge of the array manifold. To achieve good algorithm estimation results, the array used in practice must be completely consistent with the standard array model in theoretical research. However, in practical applications, both device-specific factors and environmental factors can lead to array errors. When using an ideal array manifold for direct positioning, it is inevitable to obtain positioning results with large errors, or even invalid positioning results. Each array element in the sensor experiences a time delay in receiving the incoming wave, and this time delay is related to the incoming wave direction angle; the position is ultimately estimated using this time delay. Most array errors can be attributed to array amplitude and phase errors. Therefore, studying direct positioning algorithms under the condition of array amplitude and phase errors is of great significance for the practical application of passive positioning technology. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for joint amplitude and phase error estimation and direct positioning based on a moving array, so as to solve the technical problems mentioned in the background art. The method realizes array position switching based on the moving array, can correct amplitude and phase errors, realize joint estimation of array amplitude and phase errors and radiation source position, and improve the accuracy of direct positioning.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A joint amplitude and phase error estimation and direct positioning method based on a moving array, the method comprising the following steps:

[0007] Step S1: For a receiving array, acquire the radiation source signal received at the first position and calculate the covariance matrix of the signal. Then, obtain the corresponding noise subspace through eigenvalue decomposition. The receiving array consists of M array elements with a unit spacing d = λ / 2, where λ represents the wavelength.

[0008] Step S2: Move the receiving array multiple times, and perform the operation in step S1 once at each new position to obtain the corresponding noise subspace;

[0009] Step S3: Construct a quadratic optimization problem based on the noise subspace obtained from each movement, and then solve the quadratic optimization problem by constructing a cost function to obtain the estimated values ​​of the radiation source position and amplitude-phase error.

[0010] Furthermore, in step S1, it is assumed that the receiving array is arranged along the y-axis, and there are K radiation sources in space, with the radiation source positions being p. k =[p xk ,p yk ,p zk ] T The K radiation source signals are all far-field narrowband signals with wavelength λ, and the location of the observation point is u1 = [u x1 ,u y1 ,u z1 ] T The exact location of the observation point is known;

[0011] When array amplitude and phase errors exist, the expression for the received radiation source signal is:

[0012] y1(t)=CA1s(t)+n1(t) (1)

[0013] In formula (1), s(t)=[s1(t),s2(t),…,s K (t)] T Let n1(t) be the signal vector, n1(t) be additive white Gaussian noise, and A1 = [a1(p1), a1(p2), ..., a1(p...]. K )] represents the direction matrix, a1(p k ) represents p k The array steering vector in the direction is represented as Where, d m k1(p) represents the position vector of the m-th array element relative to the reference element. kLet be the wavenumber vector at observation position u1, denoted as:

[0014] Furthermore, in step S1, the covariance matrix is ​​calculated based on the received radiation source signal, expressed as:

[0015]

[0016] In formula (2), J represents the number of snapshots of the data.

[0017] Furthermore, in step S1, the covariance matrix is ​​decomposed into eigenvalues, expressed as:

[0018]

[0019] In formula (3), and Let λ be the signal subspace and noise subspace obtained by eigendecomposition of the covariance matrix of the received signal at position 1. 1,i Let i = 1, ..., M be the M eigenvalues ​​of R1 and λ 1,1 ≥…≥λ 1,K >λ 1,K+1 =…=λ 1,M , and These are diagonal matrices consisting of K large eigenvalues ​​and MK small eigenvalues, respectively.

[0020] Furthermore, in step S2, when the l-th movement is performed, the noise subspace is... Assuming a total of L observations were made, the positions of the l observation points are denoted as u. l =[u xl ,u yl ,u zl ] T .

[0021] Furthermore, S3 specifically includes:

[0022] Step S301: Construct a quadratic optimization problem, expressed as:

[0023]

[0024] In formula (4), e1=[1,0,...,0] T c = [c1, c2, ..., c M [This refers to the amplitude and phase error.]

[0025] in, a represents the noise subspace obtained during the Lth observation; L (p) represents the steering vector of the receiving array during the Lth observation;

[0026] Step S302: Construct the cost function, the expression of which is:

[0027] Step S303: Calculate the partial derivative of the cost function: c=ξQ -1 (p)e1, where ξ is a constant, since Then we get ξ = 1 / e H Q -1 (p)e1;

[0028] Step S304: Obtain the estimated value of amplitude and phase error c:

[0029] Step S305: Substitute the estimated value of amplitude and phase error c into... The estimated location of the radiation source is expressed as:

[0030] .

[0031] The beneficial effects of this invention are:

[0032] This invention overcomes the limitations of existing direct positioning techniques in terms of amplitude and phase errors, enabling the acquisition of accurate position estimates and providing more accurate positioning performance. In the presence of amplitude and phase errors, this invention can estimate and correct the amplitude and phase errors without the need for auxiliary calibration of the signal source, auxiliary calibration of array elements, or iterative solutions, thus achieving high-resolution estimation. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating a joint amplitude and phase error estimation and direct positioning method based on a moving array provided in Embodiment 1;

[0034] Figure 2 This is a schematic diagram of a scenario for implementing a joint amplitude and phase error estimation and direct positioning method based on a moving array;

[0035] Figure 3 It is the scatter plot of the location provided in Example 1;

[0036] Figure 4 This is a comparison chart of the radiation source localization performance of the method in this embodiment and the direct localization method without amplitude and phase error correction at different signal-to-noise ratios;

[0037] Figure 5 This is a comparison chart of the estimation performance of the real and imaginary parts of the amplitude and phase error under different signal-to-noise ratios of the method in this embodiment. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1

[0040] See Figures 1-5 This embodiment provides a joint amplitude and phase error estimation and direct positioning method based on a moving array. The method includes the following steps:

[0041] Step S1: For a receiving array, acquire the radiation source signal received at the first position and calculate the covariance matrix of the signal. Then, obtain the corresponding noise subspace through eigenvalue decomposition. The receiving array consists of M array elements with a unit spacing d = λ / 2, where λ represents the wavelength.

[0042] Specifically, in this embodiment, step S1 includes:

[0043] Assume the receiving array is arranged along the y-axis, and there are K radiation sources in space, with the positions of the radiation sources being p. k =[p xk ,p yk ,p zk ] T The K radiation source signals are all far-field narrowband signals with wavelength λ, and the location of the observation point is u1 = [u x1 ,u y1 ,u z1 ] T The exact location of the observation point is known;

[0044] When array amplitude and phase errors exist, the expression for the received radiation source signal is:

[0045] y1(t)=CA1s(t)+n1(t) (1)

[0046] In formula (1), s(t)=[s1(t),s2(t),…,s K (t)] T Let n1(t) be the signal vector, n1(t) be additive white Gaussian noise, and A1 = [a1(p1), a1(p2), ..., a1(p...]. K )] represents the direction matrix, a1(p k ) represents p kThe array steering vector in the direction is represented as Where, d m k1(p) represents the position vector of the m-th array element relative to the reference element. k Let be the wavenumber vector at observation position u1, denoted as:

[0047] Specifically, in this embodiment, the covariance matrix is ​​calculated based on the received radiation source signal, and the expression is as follows:

[0048]

[0049] In formula (2), J represents the number of snapshots of the data.

[0050] Specifically, in this embodiment, the covariance matrix is ​​eigenvalued, and the expression is as follows:

[0051]

[0052] In formula (3), and Let λ be the signal subspace and noise subspace obtained by eigendecomposition of the covariance matrix of the received signal at position 1. 1,i Let i = 1, ..., M be the M eigenvalues ​​of R1 and λ 1,1 ≥…≥λ 1,K >λ 1,K+1 =…=λ 1,M , and These are diagonal matrices consisting of K large eigenvalues ​​and MK small eigenvalues, respectively.

[0053] Step S2: Move the receiving array multiple times, and perform the operation in step S1 once at each new position to obtain the corresponding noise subspace;

[0054] Specifically, in this embodiment, when the l-th move is performed, the noise subspace is: Assuming a total of L observations were made, the positions of the l observation points are denoted as u. l =[u xl ,u yl ,u zl ] T .

[0055] Step S3: Construct a quadratic optimization problem based on the noise subspace obtained from each movement, and then solve the quadratic optimization problem by constructing a cost function to obtain the estimated values ​​of the radiation source position and amplitude-phase error.

[0056] Specifically, in this embodiment, based on the property that the signal subspace and noise subspace are orthogonal, it is known that only when the array's steering vector a1(p) is determined by the actual radiation source position parameter p k When constructed, the projection of the guide vector onto the noise subspace is zero.

[0057] Considering the existence of amplitude and phase errors, the MUSIC function now becomes:

[0058]

[0059] ...

[0061]

[0062] Where c = [c1, c2, ..., c M [This represents the amplitude and phase error.]

[0063] make This leads to a quadratic optimization problem.

[0064] More specifically, in this embodiment, step S3 specifically includes:

[0065] Step S301: Construct a quadratic optimization problem, expressed as:

[0066]

[0067] In formula (4), e1=[1,0,...,0] T c = [c1, c2, ..., c M [This refers to the amplitude and phase error.]

[0068] in, a represents the noise subspace obtained during the Lth observation; L (p) represents the steering vector of the receiving array during the Lth observation;

[0069] Step S302: Construct the cost function, the expression of which is:

[0070] Step S303: Take the partial derivative of the cost function: c=ξQ -1 (p)e1, where ξ is a constant, since Then we get ξ = 1 / e H Q -1 (p)e1;

[0071] Step S304: Obtain the estimated value of amplitude and phase error c:

[0072] Step S305: Substitute the estimated value of amplitude and phase error c into... The estimated location of the radiation source is expressed as:

[0073] .

[0074] To verify the effectiveness of the method in this embodiment, the following demonstration is performed using MATLAB simulation analysis. The performance estimation metric is the root mean square error (RMSE), defined as follows:

[0075]

[0076]

[0077] Where N represents the number of Monte Carlo simulations, p k This represents the actual location of the k-th radiation source. c represents the estimated position of the k-th signal in the nth simulation experiment. m This represents the true value of the m-th amplitude-phase error coefficient. This represents the estimated value of the m-th amplitude and phase error coefficient in the n-th simulation experiment.

[0078] like Figure 2 The diagram shown is a scenario diagram of the method implemented in this embodiment. The number of drones selected in the simulation is M=10, L=4, and K=2.

[0079] like Figure 3 The diagram shows the scatter plot of the positioning results using the method in this embodiment. In the simulation, the number of radiation sources K=2, located at (100, 700, 0)m and (500, 500, 0)m respectively, and the number of observation points L=4, located at (-500, 0, 500)m, (0, 300, 500)m, (1000, 0, 500)m, and (0, 700, 500)m respectively. The moving array is a linear array with M=10 elements, the array plane is perpendicular to the z-axis, the signal-to-noise ratio (SNR) is 10dB, and the number of snapshots is set to J=500. Simulation results show that the proposed method can effectively correct amplitude and phase errors and has good positioning performance.

[0080] Figure 4 The figure shows a comparison of the radiation source location estimation performance of the method in this embodiment and the direct positioning algorithm without amplitude and phase error correction at different signal-to-noise ratios. The simulation results show that the method in this embodiment has high estimation accuracy and excellent correction effect for amplitude and phase errors.

[0081] Figure 5The simulation results show the amplitude and phase error estimation performance of the method in this embodiment under different signal-to-noise ratios. The simulation results demonstrate that the method in this embodiment can accurately estimate the real and imaginary parts of the amplitude and phase error.

[0082] In summary, this invention breaks through the limitation of amplitude and phase error in the accuracy of radiation source location estimation in traditional direct positioning. Moreover, it does not require auxiliary sources and array elements, nor does it require iterative solutions. It can obtain high-precision joint estimation of radiation source location and amplitude and phase error, and has important application value.

[0083] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0084] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for joint amplitude and phase error estimation and direct positioning based on a moving array, characterized in that, The method includes the following steps: Step S1: For a receiving array, acquire the radiation source signal received at the first position and calculate the covariance matrix of the signal. Then, obtain the corresponding noise subspace through eigenvalue decomposition. The receiving array consists of M array elements with a unit spacing d = λ / 2, where λ represents the wavelength. Step S2: Move the receiving array multiple times, and perform the operation in step S1 once at each new position to obtain the corresponding noise subspace; Step S3: Construct a quadratic optimization problem based on the noise subspace obtained from each movement, and then solve the quadratic optimization problem by constructing a cost function to obtain the estimated values ​​of the radiation source position and amplitude-phase error; In step S1, it is assumed that the receiving array is arranged along the y-axis, and there are K radiation sources in space, with the radiation source positions being p. k =[p xk ,p yk ,p zk ] T The K radiation source signals are all far-field narrowband signals with wavelength λ, and the location of the observation point is u1 = [u x1 ,u y1 ,u z1 ] T The exact location of the observation point is known; When array amplitude and phase errors exist, the expression for the received radiation source signal is: y1(t)=CA1s(t)+n1(t) (1) In formula (1), s(t)=[s1(t),s2(t),…,s K (t)] T Let n1(t) be the signal vector, n1(t) be additive white Gaussian noise, and A1 = [a1(p1), a1(p2), ..., a1(p...]. K )] represents the direction matrix, a1(p k ) represents p k The array steering vector in the direction is represented as Where, d m k1(p) represents the position vector of the m-th array element relative to the reference element. k Let be the wavenumber vector at observation position u1, denoted as: In step S1, the covariance matrix is ​​calculated based on the received radiation source signal, and its expression is: In formula (2), J represents the number of snapshots of the data; In step S1, the covariance matrix is ​​decomposed into eigenvalues, expressed as follows: In formula (3), and Let λ be the signal subspace and noise subspace obtained by eigendecomposition of the covariance matrix of the received signal at position 1. 1,i Let i = 1, ..., M be the M eigenvalues ​​of R1 and λ 1,1 ≥…≥λ 1,K >λ 1,K+1 =…=λ 1,M , and These are diagonal matrices consisting of K large eigenvalues ​​and MK small eigenvalues, respectively. In step S2, when the l-th move is performed, the noise subspace is: Assuming a total of L observations were made, the positions of the l observation points are denoted as u. l =[u xl ,u yl ,u zl ] T ; S3 specifically includes: Step S301: Construct a quadratic optimization problem, expressed as: In formula (4), e1=[1,0,...,0] T c = [c1, c2, ..., c M [This refers to the amplitude and phase error.] in, a represents the noise subspace obtained during the Lth observation; L (p) represents the steering vector of the receiving array during the Lth observation; Step S302: Construct the cost function, the expression of which is: Step S303: Calculate the partial derivative of the cost function: c=ξQ -1 (p)e1, where ξ is a constant, since Then we get ξ = 1 / e H Q -1 (p)e1; Step S304: Obtain the estimated value of amplitude and phase error c: Step S305: Substitute the estimated value of amplitude and phase error c into... The estimated location of the radiation source is expressed as: 。

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