CN112612018A - High-precision moving single-station direct positioning method based on arrival angle and Doppler frequency shift - Google Patents

Abstract

The invention discloses a high-precision movement single-station direct positioning method based on an arrival angle and Doppler frequency shift, which comprises the steps of firstly establishing a target source signal data receiving model containing the arrival angle and the Doppler frequency shift, and carrying out data acquisition on a target source; then, a time factor is constructed to expand the dimensionality of the received signal matrix; constructing a cost function for directly positioning the single moving station according to a target source data receiving model and data acquired by the single station for a target source and by combining the mean square error of the position of the target source; and finally, solving the radiation source position by utilizing an MVDR criterion according to the established target cost function. The invention can improve the positioning performance; for the scene needing to position a plurality of radiation sources, the number of the information sources is not required to be known in advance, and the positioning precision is effectively improved compared with a maximum likelihood method.

Description

High-precision motion single-station direct localization method based on angle of arrival and Doppler frequency shift

technical field

The invention belongs to the technical field of passive positioning, and in particular relates to a direct positioning method for a moving single station.

Background technique

The traditional passive positioning system generally adopts a two-step positioning mode, that is, the system first determines the parameters of the target source (such as the angle of arrival (Direction of Arrival, DOA), the time of arrival (TOA), and the time difference of arrival (Time Difference of Arrival). Arrival, TDOA), Doppler frequency difference (Frequency Difference of Arrival, FDOA), received signal strength, etc.) are estimated, and then by positioning and solving the acquired parameters, the location information of the target source is finally estimated. However, when using this two-step positioning method to locate the target source, it is necessary to collect a variety of data, and calculate the position of the target through the positioning equation, which separates the parameter estimation and the position calculation, and the calculation result is consistent with the actual target source. There is a large error between the positions, so the accuracy of passive positioning is not high enough, or even invalid.

In view of the shortcomings of the traditional two-step positioning model, in recent years, scholars have proposed a DirectPosition Determination (DPD) algorithm, which can locate the target radiation source in one step without pre-estimating parameters such as DOA and TDOA. Directly use the original array data to perform nonlinear estimation of the target position through maximum likelihood, subspace data fitting, etc. Because there is no need to estimate the target arrival parameters before estimating the target position, the loss of target information in the parameter estimation process is reduced, and the DPD algorithm has higher accuracy than the traditional two-step positioning method under low signal-to-noise ratio.

The traditional direct positioning method mostly uses a multi-station passive positioning system, which requires a large amount of communication data transmission between each station, which is very resource-intensive and the equipment is not easy to transplant. The direct positioning method of the moving single station is to intercept and measure the information emitted by the target source through a single moving observation station, and directly calculate the position information of the target source according to the received signal data. Compared with the multi-station passive positioning system, the motion single-station direct positioning system not only does not require a large amount of communication data transmission, but also has the advantages of simple structure and flexible equipment. Reconnaissance and many other civilian and military fields have broad prospects for development.

SUMMARY OF THE INVENTION

In order to overcome the deficiencies of the prior art, the present invention provides a high-precision moving single-station direct positioning method based on the angle of arrival and Doppler frequency shift. First, a target source signal data reception including the angle of arrival and Doppler frequency shift is established. model and collect data from the target source; then construct a time factor to expand the dimension of the received signal matrix; then according to the target source data receiving model and the data collected from the target source by a single station, combined with the mean square error of the target source location , construct the cost function for direct positioning of the moving single station; finally, according to the established objective cost function, the MVDR criterion is used to solve the radiation source position. The present invention can improve the positioning performance; for a scenario where multiple radiation sources need to be located, the number of sources does not need to be known in advance, and the positioning accuracy is effectively improved compared with the maximum likelihood method.

The technical scheme adopted by the present invention to solve its technical problem comprises the following steps:

Step 1: Assuming that the number of target radiation sources to be located in the space is Q, the motion receiving single station has M array elements, and K position points are selected on the motion trajectory of the motion receiving single station to receive the target radiation source signals respectively, The data reception model of the target radiation source signal received at the kth position is as follows:

a_k(p_q)的维度为M×1；d为运动接收单站阵元间距，θ_q为第q个目标辐射源信号的来向角，λ为目标辐射源信号波长，p_q为第q个目标辐射源的位置坐标；s_qk(·)为第q个目标辐射源信号入射到运动接收单站第k位置点处的信号包络；T_s为采样时间间隔，N为采样快拍数；n_k(n)为运动接收单站运动到第K个位置点时接收信号的噪声；Among them, b _qk is the path loss of the qth target radiation source signal reaching the kth position of the moving receiving single station; a _k (p _q ) is the array response of the moving receiving single station to the qth target radiation source,

The dimension of a _k (p _q ) is M×1; d is the distance between the moving receiving single-station array elements, θ _q is the origin angle of the qth target radiation source signal, λ is the wavelength of the target radiation source signal, and p _q is the th Position coordinates of the q target radiation sources; s _qk ( ) is the signal envelope of the q-th target radiation source signal incident at the k-th position of the moving receiving single station; T _s is the sampling time interval, and N is the sampling snapshot number; n _k (n) is the noise of the received signal when the moving receiving single station moves to the Kth position;

f _qk (p _q ) is the Doppler frequency shift of the q-th target radiation source relative to the k-th position of the moving receiving single station, and the expression is:

Among them, f _c is the carrier frequency of the target radiation source, v _k is the moving speed of the moving receiving single station reaching the k position point, p _k is the position coordinate of the moving receiving single station reaching the k position point, and c is the target radiation source signal the speed of transmission;

The time factor is superimposed on the data receiving model, and the data receiving model of formula (1) is extended to:

r _k (n)=B _k (b,p)s _k (n)+w _k (n) (3)

目标辐射源的位置坐标矩阵；B_k(b,p)＝[b_k(p₁),b_k(p₂),…,b_k(p_Q)]为扩展之后的阵列流型矩阵，其中

为引入多普勒频移之后的导向矢量，b_k(p_q)的维度为ML×1，B_k(b,p)维度大小为ML×Q，

Among them, r _k (n)=[x _k ^T (n),x _k ^T (n+1),...,x _k ^T (n+L-1)] ^T is the data receiving model after the time factor L is superimposed Result; w _k (n)=[n _k ^T (n),n _k ^T (n+1),…,n _k ^T (n+L-1)] ^T is the noise matrix, s _k (n)=[ s _1k (n),s _2k (n),…,s _Qk (n)] ^T is the signal envelope matrix,

The position coordinate matrix of the target radiation source; B _k (b,p)=[b _k (p ₁ ),b _k (p ₂ ),...,b _k (p _Q )] is the array flow pattern matrix after expansion, where

In order to introduce the steering vector after Doppler frequency shift, the dimension of b _k (p _q ) is ML×1, and the dimension of B _k (b,p) is ML×Q,

Step 2: Construct a cost function to locate the location of a single target radiation source:

in,

The least squares solution of s _k (n) that satisfies the above equation and reaches the minimum value is:

The cost function for locating the position of a single target radiation source is equivalent to:

Rewriting the above formula into matrix form, we have:

Introducing the signal data of the target radiation source received by K position points on the motion trajectory of the motion receiving single station, Equation (9) is equivalent to:

为协方差的块对角矩阵，

为运动接收单站到达k位置点处ML×ML维的采样协方差矩阵：where, B(b,p)=[B ₁ ^T (b,p)…B _K ^T (b,p)] ^T ,

is the block diagonal matrix of covariance,

is the sampling covariance matrix of ML × ML dimension at the k-position point of the moving receiving single station:

Step 3: Using the MVDR criterion, equations (7) and (10) are rewritten into the following forms:

Among them, w _opt (b, p) is the optimal weight vector, expressed as:

Among them, w(b,p) is the weight vector composed of the weight coefficients added to each array element of the motion receiving single station;

stw ^H (b,p)B(b,p)=1

Equation (14) is transformed into:

则Substituting equation (15) into equation (13), let

but

b为目标辐射源到运动接收单站K个位置的路径损耗矢量，代入式(16)，则：Let _Bk (b,p)= _Λk (p)b, where,

b is the path loss vector from the target radiation source to the K positions of the moving receiving single station. Substitute into equation (16), then:

In the formula, λ _min ( ) represents finding the minimum eigenvalue. According to the Hermitian property of the matrix of formula (17), formula (17) is rewritten as:

Then the p that satisfies the above formula to be the maximum value is the target radiation source position, and finally the target radiation source position expression is obtained:

Complete the location of the target radiation source.

Preferably, the target radiation source is a far-field narrowband signal.

Preferably, the M=8 and K=5.

Due to the adoption of a high-precision moving single-station direct positioning method based on the angle of arrival and Doppler frequency shift of the present invention, the following beneficial effects have been achieved:

1. The single-station direct positioning method is adopted, which solves the problem of large positioning error caused by the separation of parameter estimation and position calculation in the traditional two-step positioning method, and effectively utilizes the simple structure and flexible equipment of the single-station direct positioning system. Etc;

2. The signal arrival angle and Doppler frequency shift information are fully utilized, and the data received by a single station is further expanded, which improves the positioning performance;

3. The MVDR criterion is introduced to improve the maximum likelihood positioning solution, and the corresponding constraints on the received data are added, so that the accuracy of the maximum likelihood positioning solution when locating multiple sources is further improved.

Description of drawings

FIG. 1 is a schematic diagram of a physical scene of the method of the present invention.

FIG. 2 is a two-dimensional positioning result diagram according to an embodiment of the present invention. Among them, Figure 2.a) is the distribution diagram of the location settings of the radiation source and the motion observation station, Figure 2.b) is the top view of the positioning result, and Figures 2.c) and d) are the horizontal and vertical section views of the positioning result.

FIG. 3 is a schematic diagram of the relationship between the root mean square error of angle estimation and the signal-to-noise ratio according to an embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

A high-precision moving single-station direct positioning method based on the angle of arrival and Doppler frequency shift, comprising the following steps:

Step 1: Assuming that the number of target radiation sources to be located in the space is Q, the motion receiving single station has M array elements, and K position points are selected on the motion trajectory of the motion receiving single station to receive the target radiation source signals respectively, The data reception model of the target radiation source signal received at the kth position is as follows:

a_k(p_q)的维度为M×1；d为运动接收单站阵元间距，θ_q为第q个目标辐射源信号的来向角，λ为目标辐射源信号波长，p_q为第q个目标辐射源的位置坐标；s_qk(·)为第q个目标辐射源信号入射到运动接收单站第k位置点处的信号包络；T_s为采样时间间隔，N为采样快拍数；n_k(n)为运动接收单站运动到第K个位置点时接收信号的噪声；Among them, b _qk is the path loss of the qth target radiation source signal reaching the kth position of the moving receiving single station; a _k (p _q ) is the array response of the moving receiving single station to the qth target radiation source,

The dimension of a _k (p _q ) is M×1; d is the distance between the moving receiving single-station array elements, θ _q is the origin angle of the qth target radiation source signal, λ is the wavelength of the target radiation source signal, and p _q is the th Position coordinates of the q target radiation sources; s _qk ( ) is the signal envelope of the q-th target radiation source signal incident at the k-th position of the moving receiving single station; T _s is the sampling time interval, and N is the sampling snapshot number; n _k (n) is the noise of the received signal when the moving receiving single station moves to the Kth position;

f _qk (p _q ) is the Doppler frequency shift of the q-th target radiation source relative to the k-th position of the moving receiving single station, and the expression is:

Among them, f _c is the carrier frequency of the target radiation source, v _k is the moving speed of the moving receiving single station reaching the k position point, p _k is the position coordinate of the moving receiving single station reaching the k position point, and c is the target radiation source signal the speed of transmission;

The time factor is superimposed on the data receiving model, and the data receiving model of formula (1) is extended to:

r _k (n)=B _k (b,p)s _k (n)+w _k (n) (3)

目标辐射源的位置坐标矩阵；B_k(b,p)＝[b_k(p₁),b_k(p₂),…,b_k(p_Q)]为扩展之后的阵列流型矩阵，其中

为引入多普勒频移之后的导向矢量，b_k(p_q)的维度为ML×1，B_k(b,p)维度大小为ML×Q，

Among them, r _k (n)=[x _k ^T (n),x _k ^T (n+1),...,x _k ^T (n+L-1)] ^T is the data receiving model after the time factor L is superimposed Result; w _k (n)=[n _k ^T (n),n _k ^T (n+1),…,n _k ^T (n+L-1)] ^T is the noise matrix, s _k (n)=[ s _1k (n),s _2k (n),…,s _Qk (n)] ^T is the signal envelope matrix,

The position coordinate matrix of the target radiation source; B _k (b,p)=[b _k (p ₁ ),b _k (p ₂ ),...,b _k (p _Q )] is the array flow pattern matrix after expansion, where

In order to introduce the steering vector after Doppler frequency shift, the dimension of b _k (p _q ) is ML×1, and the dimension of B _k (b,p) is ML×Q,

Step 2: Construct a cost function to locate the location of a single target radiation source:

in,

The least squares solution of s _k (n) that satisfies the above equation and reaches the minimum value is:

The cost function for locating the position of a single target radiation source is equivalent to:

Rewriting the above formula into matrix form, we have:

Introducing the signal data of the target radiation source received by K position points on the motion trajectory of the motion receiving single station, Equation (9) is equivalent to:

为协方差的块对角矩阵，

为运动接收单站到达k位置点处ML×ML维的采样协方差矩阵：where, B(b,p)=[B ₁ ^T (b,p)…B _K ^T (b,p)] ^T ,

is the block diagonal matrix of covariance,

is the sampling covariance matrix of ML × ML dimension at the k-position point of the moving receiving single station:

Step 3: Using the MVDR criterion, equations (7) and (10) are rewritten into the following forms:

Among them, w _opt (b, p) is the optimal weight vector, expressed as:

Among them, w(b,p) is the weight vector composed of the weight coefficients added to each array element of the motion receiving single station;

stw ^H (b,p)B(b,p)=1

Equation (14) is transformed into:

则Substituting equation (15) into equation (13), let

but

b为目标辐射源到运动接收单站K个位置的路径损耗矢量，代入式(16)，则：Let _Bk (b,p)= _Λk (p)b, where,

b is the path loss vector from the target radiation source to the K positions of the moving receiving single station. Substitute into equation (16), then:

In the formula, λ _min ( ) represents finding the minimum eigenvalue. According to the Hermitian property of the matrix of formula (17), formula (17) is rewritten as:

Then the p that satisfies the above formula to be the maximum value is the target radiation source position, and finally the target radiation source position expression is obtained:

Complete the location of the target radiation source.

Preferably, the target radiation source is a far-field narrowband signal.

Preferably, the M=8 and K=5.

Specific examples:

1. Establish a target source signal data receiving model including the angle of arrival and Doppler frequency shift, and collect data from the target source. In order to effectively utilize the Doppler frequency shift information, a time factor is constructed to expand the dimension of the received signal matrix;

2. According to the target source data receiving model established in step 1 and the data collected by the single station on the target source, combined with the mean square error of the target source position, construct the cost function of the direct positioning of the moving single station;

3. According to the established objective cost function, use the MVDR criterion to solve the location of the radiation source.

Assuming that there are two far-field narrowband signals as the target radiation source, their two-dimensional position parameters are (x, y) = (-1.2km, 1.2km), (x, y) = (0km, 0km), and the motion receiving A single station is a uniform linear array with M=8 array elements, as shown in Figure 2.a). Assuming that the target radiation source is stationary, the moving receiving single station moves along the abscissa at a speed of 6km/h to receive data every 0.25h, and receives K=5 times of data in total. The specific physical scene is shown in Figure 1.

Set the SNR as 30dB, the number of snapshots as snap=100, and the time factor L=3. The positioning results are shown in Figure 2. Figure 2.a) is the distribution diagram of the location settings of the radiation source and the motion observation station, Figure 2. b) The top view of the positioning result, Fig. 2.c) and d) are the horizontal and vertical section views of the positioning result, as can be seen from the illustration, the method of the present invention can accurately locate the position of the radiation source and the resolution is high; Figure 3 is the RMSE curve of several positioning methods (Monte Carlo times: 500 times), including the method of the present invention, MVDR direct positioning based on the angle of arrival (see references: Rieken D W, Fuhrmann D R. Generalizing MUSIC and MVDR for multiple noncoherent arrays[J].IEEE Transactions on SignalProcessing,2004,52(9):2396-2406.), ML direct localization based on angle of arrival and Doppler, ML direct localization method based on angle of arrival (see reference: L.M.Kaplan ,Qiang Le and N.Molnar,"Maximumlikelihood methods for bearings-only target localization,"2001IEEEInternational Conference on Acoustics,Speech,and SignalProcessing.Proceedings(Cat.No.01CH37221),Salt Lake City,UT,USA,2001,pp. 3001-3004vol.5, doi:10.1109/ICASSP.2001.940281.). It can be seen from the figure that, compared with the direct positioning method using ML, the moving single-station direct positioning method proposed by the present invention has better positioning effect and higher positioning accuracy in the case of locating multiple target radiation sources; Compared with the MVDR direct positioning of the corners, the method of the present invention also improves the positioning accuracy to a certain extent by using the Doppler information. The above simulation situations illustrate the beneficial effects of the method of the present invention.

Claims (3)

1. A high-precision moving single-station direct positioning method based on an arrival angle and Doppler frequency shift is characterized by comprising the following steps:

step 1: assuming that the number of target radiation sources to be positioned in a space is Q, a moving receiving single station is provided with M array elements, K position points are selected on a moving track of the moving receiving single station to respectively receive target radiation source signals, and a data receiving model of the target radiation source signals received at the K position is as follows:

wherein, b_qkPath loss for the qth target radiation source signal to reach the kth position point of the motion receiving single station; a is_k(p_q) In response to the qth array of target radiation sources for the mobile receiving station,

a_k(p_q) Dimension of (d) is mx 1; d is the spacing of array elements of the single station for receiving motion, theta_qIs the angle of arrival of the q-th target radiation source signal, λ is the target radiation source signal wavelength, p_qPosition coordinates of a qth target radiation source; s_qk() a signal envelope for the q-th target radiation source signal incident at the kth location point of the single station of motion reception; t is_sIs the sampling time interval, and N is the sampling fast beat number; n is_k(n) is the noise of the received signal when the moving receiving single station moves to the Kth position point;

f_qk(p_q) For the Doppler shift of the qth target radiation source relative to the kth position point of the moving receiving single station, the expression is:

wherein f is_cIs the carrier frequency, v, of the target radiation source_kFor moving the receiving station to the speed of movement at the point k_kC is the propagation speed of the target radiation source signal for the position coordinate of the moving receiving single station reaching the k position point;

superposing a time factor on the data receiving model, and expanding the data receiving model of the formula (1) into:

r_k(n)＝B_k(b,p)s_k(n)+w_k(n) (3)

wherein r is_k(n)＝[x_k ^T(n),x_k ^T(n+1),,x_k ^T(n+L-1)]^TThe result is obtained after the data receiving model is subjected to time factor L superposition; w is a_k(n)＝[n_k ^T(n),n_k ^T(n+1),…,n_k ^T(n+L-1)]^TIs a noise matrix, s_k(n)＝[s_1k(n),s_2k(n),…,s_Qk(n)]^TIn the form of a matrix of the envelope of the signal,

a position coordinate matrix of the target radiation source; b is_k(b,p)＝[b_k(p₁),b_k(p₂),…,b_k(p_Q)]Is an array flow pattern matrix after expansion, wherein

To introduce a steering vector after Doppler shift, b_k(p_q) Has a dimension of ML x 1, B_kThe (b, p) dimension is ML x Q,

step 2: constructing a cost function for locating the position of a single target radiation source:

wherein,

s satisfying the above formula to a minimum value_kThe least squares solution of (n) is:

the cost function equivalence for locating a single target radiation source location is:

rewriting the above formula into a matrix form includes:

target radiation source signal data received by K position points on the motion trail of the motion receiving single station is introduced, and the formula (9) is equivalent to:

wherein B (B, p) ═ B₁ ^T(b,p)…B_K ^T(b,p)]^T，

Is a block-diagonal matrix of the covariance,

a sample covariance matrix for the ML × ML dimension at the k location point for the motion receiving single station:

and step 3: using the MVDR criterion, equations (7) and (10) are rewritten into the following forms, respectively:

wherein, w_opt(b, p) is an optimal weight vector, expressed as:

w (b, p) is a weight vector formed by weight coefficients added to each array element of the motion receiving single station;

s.t.w^H(b,p)B(b,p)＝1

equation (14) is transformed by the MVDR principle into:

substituting formula (15) for formula (13) to obtain

Then

Let B_k(b,p)＝Λ_k(p) b, wherein,

b is the path loss vector from the target radiation source to the moving receiving single station K positions, and an equation (16) is substituted, then:

in the formula, λ_min(. cndot.) represents the calculation of the minimum eigenvalue, and the hermitian property of the matrix of equation (17) is used to rewrite equation (17) as:

then p satisfying the above formula as the maximum value is the target radiation source position, and finally the target radiation source position expression is obtained:

and completing the positioning of the target radiation source.

2. The method of claim 1, wherein the target radiation source is a far-field narrow-band signal.

3. A high-precision mobile single-station direct positioning method based on angle of arrival and doppler shift according to claim 1, wherein M-8 and K-5.

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