Direct positioning and tracking method for non-circular signals based on Taylor compensation under distributed monitoring stations

Abstract

The present invention provides a method for direct positioning and tracking of non-circular signals based on Taylor compensation at distributed monitoring stations, comprising the following steps: obtaining a received signal from a monitoring station; expanding the received signal, calculating a covariance matrix, and performing eigendecomposition on the covariance matrix; directly positioning and tracking the non-circular signal based on Taylor expansion to obtain the position of the signal source; and applying the least squares method to predict the position of the non-circular signal when the trajectories of multiple non-circular signals intersect. The present invention significantly reduces the complexity of the algorithm. In the deviation calculation, the orthogonality between the steering vector and the noise subspace of the received signal is fully utilized to calculate the deviation for tracking. The method has low algorithm complexity and good monitoring accuracy, and can still obtain good tracking and positioning results in poor environments. It avoids the data association problem when multiple signal sources exist, and considers the mutual influence problem when the signal source trajectories intersect, resolving the position ambiguity existing at that moment through the least squares method.

Description

Technical Field

[0001] The invention relates to a non-circular signal direct positioning and tracking method based on Taylor compensation in a distributed monitoring station, and belongs to the field of passive radar direct positioning and tracking. Background Art

[0002] With the rapid development of emerging industries such as 5G high-speed communications and the Internet of Things, the electromagnetic environment is becoming increasingly complex. Source localization technology plays a vital role in fields such as communications, navigation, and radio monitoring. However, due to the limited amount of source information available from a single source and large errors in direction-of-arrival estimation, positioning accuracy is low. Multi-array positioning can obtain richer source parameter information, significantly improving positioning performance. Furthermore, non-circular signals have a larger array aperture than traditional circular signals and have non-zero pseudo-covariance. Therefore, non-circular signals contain more information and can track a wider range of targets. Traditional tracking algorithms typically take a certain number of snapshots over a short time interval and assume that the source position remains unchanged within this small number of snapshots. By repeating these steps, the signal position is measured at each time instant, ultimately estimating the source's motion. Common algorithms include the two-step localization algorithm and the direct localization algorithm. The two-step algorithm is a common method for tracking source position and consists of two separate steps. First, the target source's position parameters, such as direction of arrival (DOA), Doppler shift, and time difference of arrival (TDOA), must be measured. These parameters can then be used to calculate the source position. However, the two-step positioning algorithm is suboptimal because the two steps are independent of each other and there is further transfer of errors. Compared with the two-step method, the direct method (DPD) has significant advantages because it can directly track the source by constructing a cost function. Since the construction of geometric relationships is avoided, the direct positioning method is more suitable for low signal-to-noise ratio situations and produces more accurate results. However, the above-mentioned algorithm simply repeats the position estimation at each moment, and the estimates between each moment are independent of each other. Therefore, using prior information to track the target position can further improve the tracking accuracy.

[0003] Secondly, circular signals and non-circular signals refer to signals with zero and non-zero elliptical covariance, respectively. Non-circular signals are often used in digital modulation schemes such as binary phase shift keying and amplitude shift keying. When a strict NC source is known to exist, previous work has shown that using the non-circular structure of the observed signal can improve the performance of traditional parameter estimation algorithms and resolve up to twice as many sources. Therefore, position tracking of non-circular signals has great research significance and application prospects. Summary of the Invention

[0004] Purpose of the invention: In view of the above existing technologies, a direct positioning and tracking method for non-circular signals based on Taylor compensation under distributed monitoring stations is proposed;

[0005] Technical solution:

[0006] The direct positioning and tracking method of non-circular signals based on Taylor compensation under distributed monitoring stations includes the following steps:

[0007] Step 1): obtaining a received signal from a monitoring station, wherein the received signal includes a non-circular signal and a noise signal;

[0008] Step 2): Expand the received signal, calculate the covariance matrix and perform eigendecomposition on the covariance matrix;

[0009] Step 3): Directly locate and track the non-circular signal based on Taylor expansion to obtain the position of the non-circular signal;

[0010] Step 4): When the trajectories of multiple non-circular signals intersect, the least squares method is applied to predict the position of the non-circular signal.

[0011] Preferably, in step 1),

[0012] Assume that there are K far-field narrowband non-circular signals in space that are incoherent and impact L monitoring stations, where each monitoring station is equipped with a uniform linear array. Assume that the position of the non-circular signal at time t is p k,t =(x k,t ,y k,t ) T (k=1,2,…,K), the lth observation station is located at u l =(x l ,y l ) T (l=1,2,…,L), and assume that all monitoring stations are time synchronized;

[0013] Then the received signal of the lth monitoring station is expressed as:

[0014] X l (t) = A l (t)s l (t)+n l (t) (1)

[0015] A l (t) is the steering matrix, expressed as:

[0016] A l (t)=[a l,1 (t),a l,2 (t),…,a l,K (t)] (2)

[0017] Steering vector a l,k (t) is expressed as:

[0018]

[0019] in represents the angle information in the received signal, λ represents the signal wavelength of the received signal, M is the number of array elements configured in the uniform linear array in the monitoring station, and d represents the array element spacing;

[0020] Signal Matrix l (t) is:

[0021] s l (t)=[s l,1 (t),s l,2 (t),…,s l,K (t)] T (4)

[0022] The kth non-circular signal s is received by the lth monitoring station at time t l,K (t) is:

[0023]

[0024] represents the signal strength of non-circular signals, represents the non-circular phase of the kth non-circular signal; rewrite formula (4) as:

[0025]

[0026] The matrix Ω is:

[0027]

[0028]

[0029] is a real-valued matrix;

[0030] The received signal of the lth monitoring station is re-expressed as:

[0031]

[0032] n l (t) is zero-mean Gaussian white noise.

[0033] Preferably, in step 2):

[0034] Expand the received signal of the lth monitoring station to:

[0035]

[0036] Extended steering matrix B l (t) is:

[0037]

[0038] Extended steering vector b l,k (t) is:

[0039]

[0040] The Gaussian noise matrix is

[0041] The covariance matrix of the received signal is:

[0042]

[0043] Perform eigenvalue decomposition on the covariance matrix, expressed as:

[0044] R l (t)=[U l,S (t)U l,N (t)]Λ l (t)[U l,S (t)U l,N (t)] H (14)

[0045] Among them U l,S (t) and U l,N (t) are the signal subspace and noise subspace of the signal received by the l-th observation station at time t; Λ l (t) is a diagonal matrix consisting of eigenvalues;

[0046] According to the subspace information fusion algorithm, using the orthogonality of the extended steering vector and the noise subspace, the non-circular signal satisfies the following function:

[0047]

[0048] in are the independent variables in the function, representing the position of the non-circular signal and the non-circular phase of the non-circular signal, For is the extended steering vector of the independent variable; perform a three-dimensional spectrum peak search on Equation (15), and when the local minimum is obtained, the estimated value of the non-circular signal position is obtained

[0049] Preferably, in step 3):

[0050] The position of the kth non-circular signal at time t+1 satisfies the relationship with the position at time t:

[0051]

[0052] where ξ x,k,t+1 and ξ y,k,t+1are the corresponding deviations of the x-axis coordinate and the y-axis coordinate;

[0053] At the same time, the non-circular phase There is an error in the calculation of , so there is:

[0054]

[0055] Indicates the deviation of non-circular phases at adjacent moments;

[0056] The extended steering vector b at time t+1 l,k (t+1) performs a first-order Taylor expansion to obtain:

[0057]

[0058] Since there is orthogonality between the noise subspace of the signal and the extended steering vector, then:

[0059]

[0060] When there are multiple non-circular signals in the observation area, the orthogonality is expressed as:

[0061]

[0062] Define three deviation diagonal matrices:

[0063]

[0064]

[0065]

[0066] According to formulas (12), (18), and (20), we can obtain formula (24):

[0067]

[0068] Among them, O (2M-K)×K Represents a 2M-K×K dimensional zero matrix; partial derivative matrix Defined as:

[0069]

[0070] Then the partial derivative matrix ξ x (t+1),ξ y (t+1), Calculated as:

[0071]

[0072] in

[0073]

[0074]

[0075] The offset is therefore calculated;

[0076] At time t+1, the estimation of the position of the non-circular signal is and estimation of non-circular phase Accordingly, we get:

[0077]

[0078] The results are then iterated to achieve position tracking of multiple non-circular signals within the observation area.

[0079] Preferably, in step 4), when the motion trajectories of multiple non-circular signals intersect at time t+e, it is assumed that the position estimation values ​​of the non-circular signals at time m before this time are respectively Apply the least squares method to Fitting is performed and the position of the non-circular signal at the next moment is predicted at the same time.

[0080] Preferably, a threshold is set. When the position of the non-circular signal is greater than the threshold, steps 1)-3) are used to track the position of the non-circular signal. When the position of the non-circular signal is less than the threshold, the prediction results of the least squares method in steps 1)-4) are used to track the position of the non-circular signal.

[0081] Beneficial effects:

[0082] The present invention further optimizes source tracking by calculating compensation, providing a new approach for position tracking. Compared with the existing technology, the present invention has the following technical effects:

[0083] ① By expanding the first-order steering vector and utilizing the prior information of the previous moment, the tracking problem is transformed into a compensation problem, which greatly reduces the complexity of the algorithm. In the deviation calculation, the orthogonality between the steering vector and the noise subspace of the received signal is fully utilized to calculate the deviation to achieve tracking.

[0084] ② It has low algorithm complexity and good monitoring accuracy, and can still obtain good tracking and positioning results in poor environments;

[0085] ③ It avoids the data association problem when multiple sources exist, considers the mutual influence problem when the source trajectories intersect, and solves the position ambiguity at that moment through the least squares method. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is the positioning scene model of the present invention;

[0087] Figure 2 It is a schematic diagram of the array structure configured in the monitoring station of the present invention;

[0088] Figure 3 This is the position tracking diagram of the proposed algorithm under multiple information sources;

[0089] Figure 4 This is the tracking diagram of the proposed algorithm when the source trajectories cross;

[0090] Figure 5 It is a comparison of the tracking accuracy (RMSE) of the present invention and other algorithms under different signal-to-noise ratios;

[0091] Figure 6 It is a comparison of the tracking accuracy (RMSE) of the present invention and other algorithms under different snapshot numbers;

[0092] Figure 7 This is a comparison of the tracking accuracy (RMSE) of the present invention and other algorithms at different tracking times. DETAILED DESCRIPTION

[0093] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0094] Symbols indicate: In the present invention, (·) T ,(·) H (·) -1 and(·) * They represent transpose, conjugate transpose, inverse, and conjugate operations respectively. Bold capital letters represent matrices, and bold lowercase letters represent vectors. represents the Kronecker product, ⊙ represents the Khatri-Rao product, vec(·) represents vectorized operation, diag(·) represents diagonal operation on matrix or vector, ||·||1, ||·||2, ||·|| F They represent 1-norm, 2-norm and F-norm respectively.

[0095] This paper designs a direct positioning and tracking method for non-circular signals based on Taylor expansion in a distributed monitoring station environment. This method establishes monitoring stations with known locations, each using a uniform linear array as the signal receiving array. Within the tracking range, there are K moving sources, each emitting a non-circular signal. By performing a conjugate expansion on the non-circular signal reception form, a more informative non-circular signal reception form is obtained. The position of each source at the initial moment is calculated using a traditional direct position determination (DPD) algorithm. Taylor expansion is then used to transform the traditional tracking problem into a compensation problem. Based on the expanded direction matrix of the non-circular signal and the orthogonality between the noise subspace and the direction vector, a multi-subspace information fusion algorithm is used to calculate the position difference of the same source at adjacent moments, thereby achieving position tracking of the non-circular signal.

[0096] When the cost function reaches its minimum value, the estimated value of the source position can be obtained.

[0097] 2. Direct Positioning and Tracking Method of Non-Circular Signals Based on Taylor Expansion

[0098] Considering that there is a moving non-circular signal transmitter in the observation area, the position difference of the transmitter at adjacent moments is a bounded value. Therefore, we can consider tracking the position of the non-circular signal by calculating the position difference of the non-circular signal at adjacent moments. The position of the kth non-circular signal at time t+1 and the position at time t satisfy the following relationship

[0099]

[0100] where ξ x,k,t+1 and ξ y,k,t+1 are the corresponding deviations of the x-axis coordinate and the y-axis coordinate respectively. At the same time, we also consider that the calculation of the non-circular phase at the initial moment is not completely accurate, so there is

[0101]

[0102] Represents the deviation of the non-circular phase at adjacent moments. Performing a first-order Taylor expansion on the extended steering vector at time t+1 yields

[0103]

[0104] Since there is orthogonality between the noise subspace of the signal and the extended steering vector,

[0105]

[0106] When there are multiple non-circular signals in the observation area, this orthogonality can be expressed as

[0107]

[0108] Define the following three deviation diagonal matrices

[0109]

[0110]

[0111]

[0112] According to formulas (12), (18), and (20), the deviation diagonal matrix satisfies

[0113]

[0114] The partial derivative matrix Defined as

[0115]

[0116] Then these partial derivative matrices can be calculated as

[0117]

[0118] in

[0119]

[0120]

[0121] Therefore, the offset can be calculated. At time t+1, the position of the signal source and the NC phase can be obtained accordingly, that is,

[0122]

[0123] The results are then iterated to achieve position tracking of multiple emitters. This approach avoids the data association process and directly calculates the position without establishing new geometric relationships. However, when the trajectories of the emitters intersect, the position estimate of the intersection is usually fuzzy, which is a problem that needs to be considered in position tracking. To solve this problem, we use the standard least squares (OLS) method. Assume that the position measurements of the signal source at the first m moments are The least squares method is applied to fit it and the position at the next moment is predicted at the same time.

[0124] A single threshold is set. When the distance between the source position and the target position is greater than the threshold, the Taylor expansion method is used to track the target position. When the distance is less than the threshold, the prediction result of the least squares method is used instead of the result of the Taylor expansion calculation. This effectively reduces the errors that occur during the tracking process.

[0125] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A direct positioning and tracking method for non-circular signals based on Taylor compensation at distributed monitoring stations, characterized in that: The following steps are involved: Step 1): obtaining a received signal from a monitoring station, wherein the received signal includes a non-circular signal and a noise signal; Step 2): Expand the received signal, calculate the covariance matrix and perform eigendecomposition on the covariance matrix; Step 3): Directly locate and track the non-circular signal based on Taylor expansion to obtain the position of the non-circular signal; Step 4): When the trajectories of multiple non-circular signals intersect, the least squares method is applied to predict the position of the non-circular signal.

2. The non-circular signal direct positioning and tracking method based on Taylor compensation at distributed monitoring stations according to claim 1, characterized in that: In step 1), Assume that there are K far-field narrowband non-circular signals in space that are incoherent and impact L monitoring stations, where each monitoring station is equipped with a uniform linear array. Assume that the position of the non-circular signal at time t is p k,t =(x k,t ,y k,t ) T (k=1,2,…,K), the lth observation station is located at u l =(x l ,y l ) T (l=1,2,…,L), and assume that all monitoring stations are time synchronized; Then the received signal of the lth monitoring station is expressed as: X l (t)=A l (t)s l (t)+n l (t) (1) A l (t) is the steering matrix, expressed as: A l (t)=[a l,1 (t),a l,2 (t),…,a l,K (t)] (2) Steering vector a l,k (t) is expressed as: in represents the angle information in the received signal, λ represents the signal wavelength of the received signal, M is the number of array elements configured in the uniform linear array in the monitoring station, and d represents the array element spacing; Signal Matrix l (t) is: s l (t)=[s l,1 (t),s l,2 (t),…,s l,K (t)] T (4) The kth non-circular signal s is received by the lth monitoring station at time t l,K (t) is: represents the signal strength of non-circular signals, represents the non-circular phase of the kth non-circular signal; Rewrite formula (4) as: The matrix Ω is: is a real-valued matrix; The received signal of the lth monitoring station is re-expressed as: n l (t) is zero-mean Gaussian white noise.

3. The direct positioning and tracking method for non-circular signals based on Taylor compensation at distributed monitoring stations according to claim 2, characterized in that: In step 2): Expand the received signal of the lth monitoring station to: Extended steering matrix B l (t) is: Extended steering vector b l,k (t) is: The Gaussian noise matrix is The covariance matrix of the received signal is: Perform eigenvalue decomposition on the covariance matrix, expressed as: R l (t)=[U l,S (t)U l,N (t)]Λ l (t)[U l,S (t)U l,N (t)] H (14) Among them U l,S (t) and U l,N (t) are the signal subspace and noise subspace of the signal received by the l-th observation station at time t; Λ l (t) is a diagonal matrix consisting of eigenvalues; According to the subspace information fusion algorithm, using the orthogonality of the extended steering vector and the noise subspace, the non-circular signal satisfies the following function: where p, are the independent variables in the function, representing the position of the non-circular signal and the non-circular phase of the non-circular signal, For p, is the extended steering vector of the independent variable; perform a three-dimensional spectrum peak search on Equation (15), and when the local minimum is obtained, the estimated value of the non-circular signal position is obtained 4. The method for direct positioning and tracking of non-circular signals based on Taylor compensation at distributed monitoring stations according to claim 3, characterized in that: In step 3): The position of the kth non-circular signal at time t+1 satisfies the relationship with the position at time t: where ξ x,k,t+1 and ξ y,k,t+1 are the corresponding deviations of the x-axis coordinate and the y-axis coordinate; At the same time, the non-circular phase There is an error in the calculation of , so there is: Indicates the deviation of non-circular phases at adjacent moments; The extended steering vector b at time t+1 l,k (t+1) performs a first-order Taylor expansion to obtain: Since there is orthogonality between the noise subspace of the signal and the extended steering vector, then: When there are multiple non-circular signals in the observation area, the orthogonality is expressed as: Define three deviation diagonal matrices: According to formulas (12), (18), and (20), we can obtain formula (24): Among them, O (2M-K)×K Represents a 2M-K×K dimensional zero matrix; partial derivative matrix Defined as: Then the partial derivative matrix ξ x (t+1),ξ y (t+1), Calculated as: in The offset is therefore calculated; At time t+1, the estimation of the position of the non-circular signal is and estimation of non-circular phase Accordingly, we get: The results are then iterated to achieve position tracking of multiple non-circular signals within the observation area.

5. The method for direct positioning and tracking of non-circular signals based on Taylor compensation at distributed monitoring stations according to claim 4, characterized in that: In step 4), when the motion trajectories of multiple non-circular signals intersect at time t+e, it is assumed that the position estimates of the non-circular signals at time m before this moment are Apply the least squares method to Fitting is performed and the position of the non-circular signal at the next moment is predicted at the same time.

6. The method for direct positioning and tracking of non-circular signals based on Taylor compensation at distributed monitoring stations according to claim 5, characterized in that: Set a threshold. When the distance between the positions of the non-circular signals is greater than the threshold, use steps 1)-3) to track the position of the non-circular signals. When the distance between the positions of the non-circular signals is less than the threshold, use the prediction results of the least squares method in steps 1)-4) to track the position of the non-circular signals.

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