A real-time positioning method based on adaptive weight coefficient space

Abstract

The application discloses a real-time positioning method based on adaptive weight coefficient space. The specific steps are as follows: an array signal receiving model is established; a spatial smoothing method based on a virtual subarray is applied to the array signal receiving model; a weight coefficient space is established according to a signal covariance matrix; angle estimation and position solution are carried out based on a subspace algorithm; a position error function is established according to a real position result and an estimated position result; and an adaptive adjustment feedback mechanism of the weight coefficient space is established according to the position error function. The application has the beneficial effects that the method starts from the definition of the weight coefficient space, estimates the position error by setting the position error function, compares the position error with an error threshold, dynamically adjusts the weight coefficient space parameters, realizes the self-adaptation of the weight coefficient space parameters, and can improve the indoor positioning precision.

Description

Technical Field

[0001] This invention relates to the field of indoor positioning technology, and specifically to a real-time positioning method based on adaptive weight coefficient space. Background Technology

[0002] In indoor positioning using Angle of Arrival (AOA) algorithms, angle estimation algorithms based on feature space decomposition have been continuously developed, such as multi-signal classification algorithms and signal estimation algorithms based on rotation factor invariance. These algorithms offer high resolution, but in multipath environments, coherent signals can confuse the estimation results, thus obscuring the positioning outcome. Therefore, spatial smoothing theory has been established, primarily for coherent signal decomposition to obtain more accurate location information. Traditional spatial smoothing techniques are categorized into forward spatial smoothing, backward spatial smoothing, and forward-backward spatial smoothing. While all three can decohere coherent signals to some extent, none can achieve parameter adaptation, failing to dynamically adjust parameters based on positioning results and evaluation. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings and defects of existing technologies by providing a real-time positioning method based on an adaptive weight coefficient space. This method starts by defining a weight coefficient space and estimates the position error by setting a position error function. By comparing the position error with an error threshold, the weight coefficient space parameters are dynamically adjusted, thereby achieving adaptive weight coefficient space parameters and improving indoor positioning accuracy.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: a real-time positioning method based on adaptive weight coefficient space, the specific steps of which are as follows: establishing an array signal receiving model; applying a spatial smoothing method based on a virtual subarray to the array signal receiving model; establishing a weight coefficient space based on the signal covariance matrix; performing angle estimation and position calculation based on the subspace algorithm; establishing a position error function based on the actual position result and the estimated position result; and establishing an adaptive adjustment feedback mechanism for the weight coefficient space based on the position error function.

[0005] Furthermore, the specific details of establishing the array signal reception model are as follows: Consider M far-field narrowband signals incident on a linear array in space. The array antenna consists of m array elements, where the number of array elements equals the number of channels. That is, the signal received by each array element is sent to the central processor through its respective transmission channel. Therefore, the signal can be represented using the following composite envelope form: Under the assumption of a narrowband far-field source, the following formula exists: The expression for the received signal of any array element can be written: Arrange the signals received by m array elements at a specific time into a column vector, and assume that the array elements are homogeneous and there are no factors such as channel inconsistency or mutual coupling. The vector expression of the signal received by any array element is as follows: X(t) = AS(t) + N(t).

[0006] Furthermore, the application of the spatial smoothing method based on virtual subarrays to the array signal receiving model specifically involves the following: In a linear array, the total number of array elements is m. Assuming that every n array elements are divided into a virtual subspace, the subspace matrix is ​​v = [1, 2, 3, ..., m-n+1]. Therefore, the received signal vector expression based on the virtual subspace is as follows: X v (t)=AU (v-1) S(t)+N v (t) can be expressed by the following formula: The signal covariance matrix based on the v-th subarray is expressed as follows: R′ V =AU (v-1) SU H(v-1) A H σ 2 I.

[0007] Furthermore, the establishment of the weight coefficient space based on the signal covariance matrix specifically involves: after the signal covariance matrix is ​​calculated, signal covariance matrices based on different subarrays are obtained, which can be represented as follows: R = [R′1, R′2, R′3, ..., R′...]. v Therefore, a weight coefficient space is established based on the signal covariance array, and its formula is as follows: K = K1, K2, K3, ..., K v Therefore, the covariance matrix is ​​recalculated from the weight coefficient space, as shown in the following formula:

[0008] Furthermore, the angle estimation and position calculation based on the subspace algorithm specifically involves: performing eigenvalue decomposition on the signal covariance matrix, which can be expressed by the following formula: Because the signal subspace and noise subspace composed of large eigenvectors in eigenvalue decomposition are equal, it can be represented as follows: Therefore, there exists a unique non-singular matrix W such that Furthermore, the above structure holds true for both subarrays in the signal subspace, and therefore can be represented as follows: Where Ω represents V S1 and V S2 Given the rotation-invariant relationship between these two subarrays, the signal subspace relationship between the two subarrays is as follows: V S2 =V S1 W -1 ΩW=VS1 Ψ, where if the rotation-invariant relation matrix Ψ can be obtained, the incident angle θ of the signal can be obtained. Based on the incident angle, the location information of the signal source can be obtained, as expressed by the following formula: x = Z * tan(θ).

[0009] Furthermore, the step of establishing the location error function based on the actual location result and the estimated location result specifically involves: assuming the actual distance between the information source and the base station is x. * Therefore, a position error function is established based on the actual distance and the estimated distance, as shown in the following formula:

[0010] Furthermore, the establishment of the adaptive adjustment feedback mechanism for the weight coefficient space based on the position error function specifically involves: determining whether the weight coefficient space parameters need to be adjusted based on the position error function; if the position error meets the error threshold requirement, there is no need to dynamically adjust the weight coefficient space parameters; if not, the weight coefficient space parameters need to be dynamically adjusted again for iterative calculation until the error threshold requirement is met.

[0011] After adopting the above technical solution, the beneficial effects of the present invention are as follows: the method starts from defining the weight coefficient space, and estimates the position error by setting the position error function. By comparing the position error with the error threshold, the weight coefficient space parameters are dynamically adjusted, which can realize the adaptive weight coefficient space parameters and improve the indoor positioning accuracy. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating the present invention.

[0014] Figure 2 This is a schematic diagram of the virtual subarray spatial smoothing in the algorithm of this invention. Detailed Implementation

[0015] See Figures 1-2 As shown, the technical solution adopted in this specific embodiment is as follows: The specific steps are as follows:

[0016] S1, Establish the array signal receiving model:

[0017] Consider M far-field narrowband signals incident on a linear array in space. The array antenna consists of m elements, where the number of elements equals the number of channels. That is, the signal received by each element is sent to the central processor via its respective transmission channel.

[0018] Therefore, the signal can be represented using the following composite envelope form: Among them, u i φ(t) is the amplitude of the received signal, φ(t) is the phase of the received signal, and w0 is the frequency of the received signal.

[0019] Under the assumption of a narrowband far-field source, the following formula exists:

[0020] The expression for the received signal of any array element can be written: Where i is an arbitrary array element, i = 1, 2, ..., m, g ij Let n represent the gain of the i-th array element on the j-th signal. i (t) represents the noise of the i-th array element at time t, τ ij This is expressed as the time delay of the j-th signal arriving at the i-th array element being equivalent to that of the reference array element.

[0021] 2) Arrange the signals received by m array elements at a specific time into a column vector, and assume that the array elements are homogeneous and there are no factors such as channel inconsistency or mutual coupling. The vector expression of the signal received by any array element is as follows: X(t) = AS(t) + N(t), where X(t) is an m×1 dimensional snapshot data vector, N(t) is an m×1 dimensional noise data vector, S(t) is an M×1 dimensional spatial signal vector, and A is an M×m dimensional signal steering vector matrix.

[0022] S2, Applying a spatial smoothing method based on virtual subarrays to the array signal reception model:

[0023] In a linear array, the total number of array elements is m. Assuming that every n array elements are divided into a virtual subspace, the subspace matrix is ​​v = [1, 2, 3, ..., m-n+1]. Therefore, the expression for the received signal vector based on the virtual subspace is as follows: X v (t)=AU (v-1) S(t)+N v (t), where U v It is the k-th power of an M×M diagonal matrix.

[0024] It can be expressed using the following formula:

[0025] The signal covariance matrix based on the v-th subarray is expressed as follows: R v =AU(v-1) SU H(v-1) A H +σ 2 I,

[0026] And it can be rewritten as: R′ V =AU (v-1) SU H(v-1) A H σ 2 I, where,σ 2 I represents the noise signal matrix.

[0027] S3, Establish the weight coefficient space based on the signal covariance matrix:

[0028] After the signal covariance matrix is ​​calculated, the signal covariance matrices based on different subarrays are obtained, which can be represented as follows: R = [R′1, R′2, R′3, ..., R′...]. v ], where v represents the subspace matrix and v = [1, 2, 3, ..., m-n+1].

[0029] Therefore, a weight coefficient space is established based on the signal covariance array, and its formula is as follows: K = K1, K2, K3, ..., K v , where K v Let represent the spatial coefficients of the weight coefficients of the v-th subarray, and

[0030] Therefore, the covariance matrix is ​​recalculated from the weight coefficient space, as shown in the following formula: Among them, K T This indicates the transpose operation on the weight coefficient space K.

[0031] S4, Angle estimation and position calculation based on subspace algorithm:

[0032] The eigenvalue decomposition of the signal covariance matrix obtained in S3 can be expressed by the following formula: Among them, R S R is the signal subspace composed of the eigenvectors corresponding to the large eigenvalues. N The noise subspace composed of eigenvectors corresponding to small eigenvalues

[0033] Because the signal subspace and noise subspace composed of large eigenvectors in eigenvalue decomposition are equal, it can be represented as follows: Where span{*} represents generating a subspace.

[0034] Therefore, there exists a unique non-singular matrix W such that Furthermore, the above structure holds true for both subarrays in the signal subspace.

[0035] Therefore, it can be represented as follows: Where Ω represents V S1 and V S2 The rotation-invariant relationship between these two subarrays,

[0036] Therefore, the signal subspace relationship between the two subarrays is as follows: V S2 =V S1 W -1 ΩW=V S1 Ψ, where if the rotation-invariant relation matrix Ψ can be obtained, the incident angle θ of the signal can be obtained. Based on the incident angle, the location information of the signal source can be obtained, as expressed by the following formula: x = Z * tan(θ), where Z represents the known source height and x represents the calculated distance between the source and the base station.

[0037] S5. Establish a position error function based on the actual position result and the estimated position result:

[0038] Assume the actual distance between the information source and the base station is x. * Therefore, a position error function is established based on the actual distance and the estimated distance, as shown in the following formula: The value of F ranges from 0% to 100%.

[0039] S6, Establish a spatial adaptive adjustment feedback mechanism for weighting coefficients based on the position error function:

[0040] Determine whether the spatial parameters of the weighting coefficients need to be adjusted based on the location error function:

[0041] If the position error meets the error threshold requirement, there is no need to dynamically adjust the spatial parameters of the weighting coefficients.

[0042] If the requirements are not met, it is necessary to dynamically adjust the spatial parameters of the weighting coefficients and perform iterative calculations until the error threshold requirements are met.

[0043] The adjustment method is as follows:

[0044] The joint matrix is ​​constructed by combining the spatially smoothed signal covariance matrix and the corresponding weight coefficients, which can be expressed by the following formula: R′=[K1:R′1,K2:R′2,K3:R′3,……,K v :R′ V ],

[0045] Next, the joint matrix is ​​sorted in ascending order according to the covariance matrix, expressed by the following formula: R″=[K f :R′ min ..., K h :R' max ], where Kf and K h It is R min and R max The corresponding covariance matrix.

[0046] For the dynamic adjustment of the weight coefficient space, mainly for K h Adjustments are made based on the doubling and division methods, i.e., for K. h By continuously doubling the size of the range or decreasing it by a factor of two, a suitable interval is found. Finally, the optimal value is found within this interval, and the remaining parameters are adjusted accordingly to satisfy the desired result. That's all.

[0047] The working principle of this invention is as follows: First, an array signal receiving model is established based on the array signal characteristics. Then, spatial smoothing is applied to the signal covariance matrix based on the virtual subarray. Since the virtual subarrays have the same dimension, initial values ​​of the weight coefficient space with the same dimension are established based on the dimension of the virtual subarray and the spatially smoothed signal covariance matrix. The signal covariance matrix after spatial smoothing is weighted according to the weight coefficient space to obtain the signal covariance matrix after weight coefficient space processing. Next, angle estimation and position calculation are performed based on the subspace algorithm, such as using the rotation-invariant subspace (ESPRIT) algorithm for angle estimation. Then, a position error function is established based on the estimated position result and the actual position result, and it is evaluated whether the error reaches the set error threshold. If the error threshold result reaches the set error, the final position is determined. If the error threshold result does not reach the set error, the weight coefficient space is iteratively calculated by adjusting the parameter weights until the error threshold result reaches the set error.

[0048] The above description is only used to illustrate the technical solution of the present invention and is not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention, as long as they do not depart from the spirit and scope of the technical solution of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A real-time positioning method based on adaptive weight coefficient space, characterized in that: The specific steps are as follows: S1, Establish the array signal receiving model; S2, apply a spatial smoothing method based on virtual subarrays to the array signal receiving model; S3. Establish the weight coefficient space based on the signal covariance matrix. Specifically, after the signal covariance matrix is ​​calculated, the signal covariance matrices based on different subarrays are obtained, and these matrices are represented as follows: Where v represents the subspace matrix and ; Therefore, the weight coefficient space is established based on the signal covariance array, and its formula is as follows: in, Let represent the spatial coefficients of the weight coefficients of the v-th subarray, and ; The covariance matrix is ​​recalculated from the weight coefficient space, as shown in the following formula: ,in, This represents the transpose operation on the weight coefficient space K; S4, angle estimation and position calculation are performed based on the subspace algorithm, specifically by performing eigenvalue decomposition on the signal covariance matrix, expressed by the following formula: ,in, The signal subspace is composed of the eigenvectors corresponding to the large eigenvalues. The noise subspace is composed of the eigenvectors corresponding to the small eigenvalues; Because the signal subspace and noise subspace composed of large eigenvectors in eigenvalue decomposition are equal, it can be represented as follows: ,in Indicates the generation of a subspace; Therefore, there exists a unique non-singular matrix W such that Furthermore, the above structure holds true for both subarrays in the signal subspace; It can be represented as follows: ,in, express and The rotation-invariant relationship between these two subarrays; The signal subspace relationship between the two subarrays is as follows: Where, if the rotation-invariant relation matrix is ​​obtained Then the angle of incidence of the signal can be obtained. Based on the incident angle, the location information of the signal source can be obtained, as shown in the following formula: Where Z represents the known source height, and x represents the calculated distance between the source and the base station; S5, Establish a position error function based on the actual position result and the estimated position result; S6, establish a spatial adaptive adjustment feedback mechanism for weight coefficients based on the position error function.

2. The real-time positioning method based on adaptive weight coefficient space according to claim 1, characterized in that: Specifically, S1 is: 1) Consider M far-field narrowband signals incident on a linear array in space. The array antenna consists of m elements, where the number of elements equals the number of channels. That is, the signal received by each element is sent to the central processor through its respective transmission channel. Therefore, the signal is represented using the following composite envelope form: ,in, It is the amplitude of the received signal. It is the phase of the received signal. It is the frequency of the received signal; Under the assumption of a narrowband far-field source, the following formula exists: Write the expression for the received signal of any array element: Where i is any array element, , This is expressed as the gain of the i-th array element on the j-th signal. Let represent the noise of the i-th array element at time t. This means that the time delay of the j-th signal arriving at the i-th array element is equivalent to the time delay of the reference array element; 2) Arrange the signals received by m array elements at a specific time into a column vector, and assume that the array elements are isotropic and there are no channel inconsistencies or mutual coupling factors. The vector expression of the signal received by any array element is as follows: ,in, for 3D snapshot data vector, for 3D noisy data vector, for A is a 3D signal vector. 3D signal steering vector matrix.

3. The real-time positioning method based on adaptive weight coefficient space according to claim 2, characterized in that: In a linear array, the total number of array elements is m. Assuming that every n array elements are divided into a virtual subspace, then the subspace matrix is... ; Therefore, the expression for the received signal vector based on the virtual subspace is as follows: ,in, for The k-th power of a diagonal matrix; Expressed using the following formula: ; The signal covariance matrix based on the v-th subarray is expressed as follows: And it can be rewritten as: in, This represents the noise signal matrix.

4. The real-time positioning method based on adaptive weight coefficient space according to claim 3, characterized in that: Specifically, S5 assumes that the actual distance between the information source and the base station is... Therefore, a position error function is established based on the actual distance and the estimated distance, as shown in the following formula: Where F ranges from 0% to 100%.

5. The real-time positioning method based on adaptive weight coefficient space according to claim 4, characterized in that: Specifically, S6 involves determining whether the spatial parameters of the weighting coefficients need to be adjusted based on the position error function. If the position error meets the error threshold requirement, there is no need to dynamically adjust the spatial parameters of the weighting coefficients. If the requirements are not met, it is necessary to dynamically adjust the spatial parameters of the weighting coefficients and perform iterative calculations until the error threshold requirements are met.

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