Self-localization method based on non-circular signal combined weighted propagation operator and dimensionality reduction search

Abstract

The present invention discloses a self - localization method based on non - circular signal combined weighted propagation operator and dimensionality reduction search, including: establishing a non - circular signal model and a self - localization model, and receiving multi - radiation source signals. Using the elliptical covariance matrix of the received signals to expand the array aperture and calculating the covariance matrix. Block - processing the covariance matrix to obtain the propagation operator. Then, through dimensionality reduction processing, the non - circular phase search dimension is eliminated, and the three - dimensional search is transformed into a two - dimensional search problem. Next, the weight coefficients are calculated according to the different transmission signal powers of each radiation source. Finally, a cost function is constructed, and the position estimation result is obtained through spectral peak search. Compared with the traditional method, the present invention expands the array aperture by virtue of the non - circular signal characteristics, improves the self - localization accuracy, and at the same time significantly reduces the computational complexity by using the dimensionality reduction method.

Description

Technical Field

[0001] The present invention belongs to the technical field of passive positioning, and particularly relates to a self-positioning method based on non-circular signal combined weighted propagation operator and dimensionality reduction search. Background Art

[0002] The wide application of electronics and information technology has led to the continuous expansion of the application scope of unmanned systems. Among them, the autonomous positioning technology of unmanned systems is the basic core technology for unmanned systems to realize other functions. With the increasingly complex space electromagnetic environment, the current methods commonly used for the self-positioning of unmanned systems are easily affected, resulting in unsatisfactory positioning results.

[0003] Traditional passive positioning technologies use a two-step positioning method for positioning. However, due to problems such as intermediate parameter estimation errors, quadratic error propagation, approximate linearization processing of observation equations, and insufficient data association, it is difficult to obtain asymptotically optimal performance. Compared with the two-step positioning method, the direct positioning method avoids the errors in the intermediate estimation process and significantly improves the positioning accuracy.

[0004] In modern communication systems, amplitude modulation signals, binary phase shift keying signals, etc. all belong to non-circular signals. The elliptical covariance of non-circular signals can be used to expand the array aperture and improve the algorithm performance. Therefore, it has important theoretical significance and application value to effectively utilize existing non-circular radiation sources and implement self-positioning using a direct positioning algorithm. Summary of the Invention

[0005] The purpose of the present invention is to provide a self-positioning method based on non-circular signal combined weighted propagation operator and dimensionality reduction search for the deficiencies of the existing technology, which significantly reduces the computational complexity while using the non-circular characteristics to expand the array aperture;

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: A self-positioning method based on non-circular signal combined weighted propagation operator and dimensionality reduction search, including:

[0007] Step 1: Use a uniform linear array to collect data on non-circular signals emitted by multiple radiation sources to obtain received signals;

[0008] Step 2: Expand the received signals using the elliptical covariance matrix of the received signals and calculate its covariance matrix;

[0009] Step 3: Perform block processing on the covariance matrix in Step 2 to estimate the propagation operator;

[0010] Step 4: Obtain the noise subspace through the propagation operator, construct a three-dimensional search problem, and through dimensionality reduction processing, eliminate the phase search dimension of the non-circular signal, and transform the three-dimensional search problem into a two-dimensional search problem;

[0011] Step 5: Calculate the weights of each radiation source to the receiving array to obtain the weight coefficients;

[0012] Step 6: Construct a cost function using the two-dimensional search problem and the weight coefficients, and then obtain the position estimation value by performing a spectral peak search on the cost function.

[0013] Further, the received signal in Step 1 is:

[0014] x k (t) = b k a k (p)s k (t) + n k (t) k = 1, 2, …, K

[0015] where b k represents the power loss factor, a k (p) represents the noise-free baseband response to a unit plane wavefront, s k (t) represents the non-circular signal emitted from the k-th radiation source, and n(t) represents the Gaussian noise vector.

[0016] Further, the covariance matrix in Step 2 is:

[0017]

[0018] where z k (t) represents the extended array received signal, M represents the number of array elements placed, and L represents the number of snapshots.

[0019] Further, the signal for extending the array received signal is:

[0020]

[0021] where b k represents the power loss factor, a k (p) represents the noise-free baseband response to a unit plane wavefront, s k (t) represents the non-circular signal emitted from the k-th radiation source, n(t) represents the Gaussian noise vector, represents the non-circular phase of the k-th radiation source signal, (·) * represents the conjugate of the matrix.

[0022] Further, the propagation operator in Step 3 is:

[0023]

[0024] where G k is a 2M×1 dimensional matrix, H kIt is a matrix of 2M×(2M - 1) dimensions.

[0025] Furthermore, the expression of the two-dimensional search problem in step 4 is:

[0026]

[0027] Among them, U n,k represents the noise subspace calculated from the received signal, e = [1, 0] T , D k (p) contains position information.

[0028] Furthermore, the weight coefficient in step 5 is:

[0029]

[0030] Among them, represents the estimated value of the power of the k-th signal source received by the array, is the estimated value of the noise power.

[0031] Furthermore, the cost function in step 6 is:

[0032]

[0033] Among them, w k represents the weight coefficient, e = [1, 0] T , U n represents the noise subspace calculated from the received signal, D k (p) contains position information.

[0034] Beneficial effects: Compared with the prior art, the direct positioning method adopted by the present invention does not require an intermediate parameter estimation process, avoiding errors caused by the intermediate process and effectively improving the positioning accuracy; it utilizes the elliptical covariance information of non-circular signals to expand the array aperture, and at the same time considers the heterogeneity of different radiation sources and assigns different weights, further improving the positioning accuracy; through dimensionality reduction processing, the non-circular phase search dimension is eliminated, significantly reducing the computational complexity. Description of the Drawings

[0035] Figure 1 is the flowchart of the self-positioning method based on non-circular signals combined with weighted propagation operator and dimensionality reduction search of the present invention.

[0036] Figure 2 is the positioning scenario diagram of the self-positioning method based on non-circular signals combined with weighted propagation operator and dimensionality reduction search of the present invention.

[0037] Figure 3 is the graph of the computational complexity (number of complex multiplications) of the present invention and other algorithms varying with the number of snapshots.

[0038] Figure 4 It is the comparison of the self - localization accuracy (RMSE) between the present invention and other algorithms under different signal - to - noise ratios.

[0039] Figure 5 It is the comparison of the self - localization accuracy (RMSE) between the present invention and other algorithms under different numbers of snapshots. Detailed implementation manners

[0040] The following further explains the present invention with reference to the accompanying drawings.

[0041] Symbol representation: In this article, bold uppercase letters, bold lowercase letters, and italic letters, such as A, a, and a, represent matrices, vectors, and scalars respectively. (·) T , (·) * , (·) H and (·) -1 represent the transpose, conjugate, conjugate transpose, and inverse operation of the matrix respectively.

[0042] The present invention provides a self - localization method based on the joint weighted propagation operator of non - circular signals and dimensionality - reduction search. As Figure 1 shown, it specifically includes the following steps:

[0043] Step 1: Construct a self - localization model as Figure 2 shown. The receiving array uses a uniform linear array to collect data of non - circular signals emitted by multiple radiation sources, and the received signal is obtained.

[0044] Suppose there are K incoherent narrow - band non - circular radiation sources in a certain space, and the positions are represented as u k = [v k , w k T , The position of the receiving station is represented as p = [x, y] T , and a uniform linear array with M array elements is placed to collect the source signals. Then the array - received signal at time t can be expressed as

[0045]

[0046] where represents the power loss factor, P k is the average transmission power of the k - th radiation source, P k ′ is the average power of the k - th radiation source received by the array, represents the array response vector, represents the noise - free baseband response to the unit plane wavefront, and the specific expression of a k (p) is

[0047] ​

[0048] where d represents the element spacing, with d = λ / 2, λ represents the signal wavelength, and s k (t) represents the non-circular signal emitted from the k-th radiation source, represents the Gaussian noise vector. It is assumed that the noise between elements is uncorrelated with each other and also uncorrelated with the radiation source signals.

[0049] This invention only considers strictly non-circular signals with a non-circularity rate of 1, which can be expressed as where represents the non-circular phase of the k-th radiation source signal, represents the signal amplitude of the k-th radiation source.

[0050] Step 2: Expand the received signal using the elliptical covariance matrix of the received signal and calculate its covariance matrix.

[0051] The array received signal is expanded to

[0052]

[0053] where can be regarded as the expanded direction matrix.

[0054] Collect data of L snapshots, and the sampled covariance matrix of the expanded received signal is

[0055]

[0056] Step 3: Perform block processing on the covariance matrix to estimate the Propagator Method (PM).

[0057] Assume that the expanded direction matrix A k is full rank, and it can be decomposed into

[0058]

[0059] In the formula, A k,1 consists of the first K rows of matrix A k , and A k,2 consists of the last 2M - K rows of matrix A k . When A k,1 is non-singular, there exists a propagation operator such that the following equation holds

[0060]

[0061] That is

[0062]

[0063] Define

[0064]

[0065]

[0066] According to the above two equations, we can obtain

[0067]

[0068] Thus, it can be known that Q n,k is orthogonal to A k , so Q n,k is included in the noise subspace. However, the columns of Q n,k are not mutually orthogonal. Orthogonalizing Q n,k can obtain the noise subspace projection operator.

[0069]

[0070] where U n,k represents the noise subspace calculated from the received signal. Similarly, there exists an invertible matrix T such that Q s,k T = A k , then the obtained signal subspace is

[0071]

[0072] For perform block processing where G k is a 2M×1 dimensional matrix, composed of the first column of ; H k is a 2M×(2M - 1) dimensional matrix, composed of the last 2M - 1 columns of .

[0073] Therefore, the propagation operator can be calculated as

[0074] Step 4: Obtain the noise subspace through the propagation operator, construct a three-dimensional search problem, and through dimensionality reduction processing, eliminate the non-circular phase search dimension, and transform the three-dimensional search problem into a two-dimensional search problem.

[0075] Define Performing spectral search on is a three-dimensional search problem with high computational complexity.

[0076] Performing matrix decomposition on obtains

[0077]

[0078] where Contains non-circular phase information, D k (p) Contains position information and uses to eliminate the trivial solution, where e = [1, 0] T , U n,k represents the noise subspace calculated from the received signal.

[0079] According to the Lagrange multiplier method, construct the following formula

[0080]

[0081] where α is the Lagrange multiplier.

[0082] Take the partial derivative of with respect to and set it to zero and substitute into it, we can get

[0083]

[0084] and substitute it into to obtain the cost function of the dimensionality-reduced PM self-localization algorithm. The cost function of the dimensionality-reduced PM self-localization algorithm is a two-dimensional search problem, and the cost function of the dimensionality-reduced PM self-localization algorithm is

[0085]

[0086] Step 5: Calculate the weights of each radiation source to the receiving array to obtain the weight coefficients.

[0087] Assume that the noise power remains unchanged. The power received by the array from different radiation sources depends on the source signal power P k and the power loss factor b k .

[0088] The covariance matrix can be decomposed into The eigenvalues of the covariance matrix can be expressed as

[0089]

[0090] where are the K larger non-zero eigenvalues of R s and characterize the power P w of the received signal. represents the noise power, and the estimated value of the noise power can be calculated from the 2M - K smaller eigenvalues, that is

[0091]

[0092] According to the estimated value of the noise power, the estimated value of the power received by the array from the k-th source can be obtained as

[0093]

[0094] The weight coefficient of the k-th source is obtained as

[0095] Step 6: Construct a cost function by using the two-dimensional search problem and the weight coefficient, and then obtain the position estimation value by performing a spectral peak search on the cost function.

[0096] Among them, the cost function is specifically a weighted dimensionality-reduced PM cost function, and the weighted dimensionality-reduced PM cost function is

[0097]

[0098] Perform a spectral peak search on it, and the maximum value point is the position estimation value of the observation station itself.

[0099] In the method of the present invention, the complexity of calculating the covariance matrix is The complexity of calculating the propagation operator is The complexity of the dimensionality-reduced search is

[0100] The total complexity of the traditional Subspace Data Fusion (SDF) method is:

[0101]

[0102] The total complexity of the non-circular signal three-dimensional PM algorithm is:

[0103]

[0104] where α x and α y , respectively represent the number of search grids in the x direction, y direction, and non-circular phase.

[0105] From Figure 3 it can be seen that the method of the present invention does not require three-dimensional spectral search, and the computational complexity is much smaller than that of the NC-3D-PM algorithm.

[0106] The performance estimation criterion of the present invention is that the root mean square error (RMSE) is defined as:

[0107]

[0108] where MC represents the number of Monte Carlo simulation experiments; represents the estimated value of the target position in the i-th Monte Carlo trial.

[0109] Figure 4This is a performance comparison graph of the method of the present invention and other algorithms with respect to the change in signal-to-noise ratio. The simulation conditions are as follows: there are 3 non-circular radiation sources, their non-circular phases are (10°, 30°, 50°) respectively, and their positions are [(100m, 900m), (500m, 300m), (700m, 700m)], the uniform linear array M = 5, the number of snapshots is 100, and the simulation is carried out 500 times. From Figure 4 It can be seen that under different signal-to-noise ratio conditions, compared with other algorithms, the method of the present invention has achieved higher self-localization accuracy, and with the improvement of the signal-to-noise ratio conditions, the performance will be significantly improved.

[0110] Figure 5 This is a performance comparison graph of the method of the present invention and other algorithms with respect to the change in the number of snapshots. The simulation conditions are as follows: there are 3 non-circular radiation sources, their non-circular phases are (10°, 30°, 50°) respectively, and their positions are [(100m, 900m), (500m, 300m), (700m, 700m)], the uniform linear array M = 5, the signal-to-noise ratio is 5dB, and the simulation is carried out 800 times. From Figure 5 It can be seen that the present invention has achieved higher positioning accuracy.

[0111] In summary, compared with the prior art, the direct positioning method adopted by the present invention does not require an intermediate parameter estimation process, avoids the errors caused by the intermediate process, and effectively improves the positioning accuracy. The elliptical covariance information of the non-circular signal is utilized to expand the array aperture, and different weights are assigned considering the heterogeneity of different radiation sources, further improving the positioning accuracy; the non-circular phase search dimension is eliminated through dimensionality reduction processing, significantly reducing the computational complexity.

[0112] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A self - localization method based on non - circular signals combined with weighted propagation operator and dimensionality - reduction search, characterized in that, Including: Step 1: Use a uniform linear array to collect data on non-circular signals emitted by multiple radiation sources to obtain received signals; Step 2: Expand the received signals using the elliptical covariance matrix of the received signals and calculate its covariance matrix; Step 3: Perform block processing on the covariance matrix in Step 2 to estimate the propagation operator; Step 4: Obtain the noise subspace through the propagation operator, construct a three-dimensional search problem, and through dimensionality reduction processing, eliminate the phase search dimension of the non-circular signal, transforming the three-dimensional search problem into a two-dimensional search problem; Step 5: Calculate the weights of each radiation source to the receiving array to obtain weight coefficients; Step 6: Use the two-dimensional search problem and the weight coefficients to construct a cost function, and then obtain the position estimate value by performing a spectral peak search on the cost function; The specific steps of step 3 include: assuming that the extended direction matrix A k is full rank, decompose it into where A k,1 is composed of the first K rows of matrix A k , and A k,2 is composed of the last 2M - K rows of matrix A k ; When A k,1 is non-singular, there exists a propagation operator such that the following equation holds That is Define According to the above two equations, it can be obtained that It can be seen from this that Q n,k is orthogonal to A k , so Q n,k is included in the noise subspace; However, Q n,k does not have columns that are mutually orthogonal. Orthogonalizing Q n,k yields the noise subspace projection operator, whose expression is: where U n,k represents the noise subspace calculated from the received signal; Similarly, there exists an invertible matrix T such that Q s,k T = A k , and the resulting signal subspace is Pair Perform block processing Among them, G k Is a 2M×1 dimensional matrix, composed of The first column of; H k Is a 2M×(2M - 1) dimensional matrix, composed of The last 2M - 1 columns of; Then the propagation operator is calculated as The weight coefficient in Step 5 is: Among them, represents the estimated value of the power of the k-th signal source received by the array, is the estimated value of the noise power.

2. The self - localization method based on non - circular signals combined with weighted propagation operator and dimensionality - reduction search according to claim 1, characterized in that, The received signal in Step 1 is: x k (t) = b k a k (p)s k (t) + n k (t)k = 1, 2, L, K Among them, b k represents the power loss factor, a k (p) represents the noise-free baseband response to a unit plane wavefront, s k (t) represents the non-circular signal emitted from the k-th radiation source, and n(t) represents the Gaussian noise vector.

3. The self - localization method based on non - circular signals combined with weighted propagation operator and dimensionality - reduction search according to claim 1, characterized in that, The covariance matrix in Step 2 is: Among them, z k (t) represents the received signal of the extended array, M represents the number of array elements placed, and L represents the number of snapshots.

4. The self - localization method based on non - circular signal combined weighted propagation operator and dimensionality - reduction search according to claim 3, characterized in that, The signal after expanding the array received signal is: where, b k represents the power loss factor, a k (p) represents the noise-free baseband response to a unit plane wavefront, s k (t) represents the non-circular signal emitted from the k-th radiation source, n(t) represents the Gaussian noise vector, represents the non-circular phase of the k-th radiation source signal, (·) * represents the conjugate of a matrix.

5. The self - localization method based on non - circular signal combined weighted propagation operator and dimensionality - reduction search according to claim 1, characterized in that, The propagation operator in Step 3 is: Among them, G k is a 2M×1 dimensional matrix, and H k is a 2M×(2M - 1) dimensional matrix.

6. The self - localization method based on non - circular signal combined weighted propagation operator and dimensionality - reduction search according to claim 1, characterized in that, The expression of the two-dimensional search problem in Step 4 is: Among them, U n,k represents the noise subspace calculated from the received signal, and e = [1, 0] T , D k (p) contains position information.

7. The self - localization method based on non - circular signal combined weighted propagation operator and dimensionality - reduction search according to claim 1, characterized in that, The cost function in Step 6 is: Among them, w k represents a weight coefficient, e = [1, 0] T , U n represents the noise subspace calculated from the received signal, D k (p) contains position information.

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