Single-anchor node super-resolution positioning method and apparatus, storage medium, and terminal

Abstract

The application discloses a single-anchor-node super-resolution positioning method and device, a storage medium and a terminal, and the single-anchor-node super-resolution positioning method comprises the following steps: a frequency control array-multiple-input multiple-output radar system signal model based on disturbance frequency is established; the influence of the disturbance frequency on positioning performance is analyzed, and a design criterion of the disturbance frequency sequence is obtained; an optimization problem is designed, and a super-resolution algorithm is proposed to realize parameter estimation of signal multipath and positioning of a user. Through frequency disturbance of signals between transmitting antennas of the frequency control array-multiple-input multiple-output system, the application releases the coupling between the transmitting angle and the signal propagation distance, so that super-resolution distance and transmitting angle estimation of multipath in the single-anchor-node positioning system become possible. The disturbance frequency design criterion proposed in the application can realize resolution of ambiguous multipath, and the super-resolution parameter estimation algorithm proposed in the application can realize super-resolution estimation of multipath parameters and accurate positioning of a user.

Description

Technical Field

[0001] This invention relates to a frequency design and positioning algorithm for a single-anchor node super-resolution positioning system, which belongs to the field of array signal processing technology. Background Technology

[0002] Traditional wireless positioning methods based on multiple anchor nodes consume significant communication resources, making single-anchor-node-based wireless positioning a hot research topic in recent years. To eliminate synchronization errors between the base station and the user, multipath parameters can be estimated, and the geometric relationships between multipath paths can be utilized to achieve synchronization-error-free user positioning. However, in real-world scenarios, bandwidth limitations often lead to distance ambiguity between multipath paths, making effective separation of multipath signals impossible and compromising the accuracy of parameter estimation.

[0003] Taking into account the user localization problem based on multipath single anchor nodes, the main challenges are as follows:

[0004] 1. When there is distance ambiguity between multipaths, it is difficult to achieve accurate parameter estimation of the paths;

[0005] 2. In traditional frequency-controlled array-multiple-input multiple-output systems, due to the coupling between the emission angle and the range, it is impossible to achieve super-resolution estimation of both separately in a single-anchor node positioning system;

[0006] 3. After introducing frequency perturbation, since different pulses have different frequency sequences, traditional parameter estimation methods are no longer applicable, and new algorithms need to be designed to solve for multipath parameters; Summary of the Invention

[0007] Objective of the Invention: To overcome the shortcomings of existing technologies, this invention provides a single-anchor node super-resolution positioning method, device, storage medium, and terminal. A super-resolution single-anchor node positioning system based on a frequency control array-multiple-input multiple-output (MIMO) architecture with frequency perturbation is proposed. This system can decouple the transmission angle and signal propagation distance in the MIMO architecture, enabling super-resolution parameter estimation of multipath when there is distance ambiguity between direct and indirect paths. This solves the problem that existing methods cannot accurately estimate multipath parameters under distance ambiguity. Furthermore, a solution algorithm suitable for this architecture is designed to estimate the multipath parameters.

[0008] Technical solution: To achieve the above objectives, the technical solution adopted by this invention is as follows:

[0009] This invention first provides a single-anchor node super-resolution positioning method, comprising the following steps:

[0010] Establish a signal model for a frequency-controlled array-multiple-input multiple-output radar system based on the perturbation frequency:

[0011]

[0012] Among them, Y n,p,q Y represents the output signal obtained after the signal received by the q-th antenna is matched and filtered by the signal at the p-th frequency in the n-th pulse. n,p,q For the receiver signal tensor In the context of the elements with coordinates [n, p, q], N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; a0 represents the amplitude of the received signal, r0 represents the distance between the user and the base station, and θ... A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 f represents the angle between the direct path between the base station and the user and the normal of the base station array. c The carrier frequency is represented by Δf, the frequency increment by Δf, the speed of light by c, and the distance between adjacent antennas of the transceiver array by d. n,p This represents the element in the nth row and pth column of the perturbation frequency sequence U;

[0013] Based on the established frequency-controlled array-multiple-input multiple-output radar system signal model based on the perturbation frequency, the user's range, velocity, and angle of arrival are obtained by super-resolution parameter estimation of the received signal tensor.

[0014] The present invention also provides a single-anchor node super-resolution positioning device, including a processor and a memory; the memory stores a program or instructions, which are loaded and executed by the processor to implement the single-anchor node super-resolution positioning steps provided above.

[0015] The present invention also provides a computer-readable storage medium storing a program or instructions that, when executed by a processor, implement the steps of the single-anchor node super-resolution positioning provided.

[0016] The present invention also provides a signal receiving terminal, which uses the single-anchor node super-resolution positioning provided above to locate the user.

[0017] A frequency-controlled array-multiple-input multiple-output radar system signal model based on perturbation frequency is established, making it possible to super-resolution estimate of the emission angle and propagation distance in a single-anchor node positioning system.

[0018] The impact of scrambling frequencies on positioning performance was analyzed, and design criteria for scrambling frequency sequences were derived.

[0019] The design optimization problem proposes a super-resolution algorithm to achieve parameter estimation of signal ambiguity path and user positioning.

[0020] Establish a signal model between the user and the base station based on a frequency-controlled array-multiple-input multiple-output radar system with perturbation frequency, and the receiver signal tensor. The element with coordinates [n, p, q] in the middle is defined as Y. n,p,q , Y represents a complex tensor with three dimensions N, P, and Q. n,p,q The output signal obtained after the signal received by the q-th antenna is matched and filtered by the signal at the p-th frequency in the n-th pulse is defined as follows:

[0021]

[0022] N represents the number of pulses, P represents the number of transmitting antennas, Q represents the number of receiving antennas; r0 represents the distance between the user and the base station, θ A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 f represents the angle between the direct path between the base station and the user and the normal of the base station array. c U represents the carrier frequency, Δf represents the frequency increment, and U n,p The element in the nth row and pth column of the perturbation frequency sequence U represents the transmit frequency index of the pth antenna in the nth pulse; d represents the spacing between adjacent antennas of the transceiver array; and c represents the speed of light. and The phase difference between them is:

[0023]

[0024] In the traditional frequency-controlled array-multiple-input multiple-output radar model, U n,p =p, which makes the phase difference equivalent to:

[0025]

[0026] This will result in θ A,0 There is a strong coupling between θ and r0, making super-resolution estimation of both impossible. Therefore, by designing a perturbation frequency sequence U, θ can be decoupled. A,0 The strong coupling between r0 and r0 makes super-resolution estimation of both possible.

[0027] The impact of perturbation frequency on positioning performance is analyzed and design criteria for perturbation frequency sequences are derived. Based on the Cramer-Rao bound analysis, the impact of perturbation frequency sequences on positioning performance is proposed and design criteria for the perturbation frequency sequences are derived.

[0028] The parameter s0 required for direct path positioning is:

[0029] s0=[r0θ A,0 θ B,0 ]

[0030] The Fisher information matrix for the required parameters is represented as follows: Its element in row i and column j is defined as:

[0031]

[0032] Wherein, F(s) 0,i ,s 0,j Let be the element in the i-th row and j-th column of the Fisher information matrix F, and s 0,i This represents the i-th parameter in s0; Indicates taking the real part, Indicates noise power. Y represents n,p,q For s 0,i Find the partial derivative, (·) H This indicates the conjugate transpose. This indicates that the summation of q in the term to be summed is performed from 0 to Q-1.

[0033] The Cramer-Rao bound for parameter estimation in s is denoted as CRLB, where for s 0,i The Cramer-Rao boundary estimate is defined as It is represented as:

[0034]

[0035] Among them, [F -1 ] i,i Let represent the i-th diagonal element of the inverse matrix F; by minimizing the Cramer-Rao bound of the parameter estimates in s, the design criterion is obtained as follows: To improve the accuracy of parameter estimates in s, the design of the perturbation frequency sequence U should satisfy maximizing f(U), which is defined as:

[0036]

[0037] The design optimization problem proposes a super-resolution algorithm to estimate the parameters of the signal ambiguity path and locate the user, including:

[0038] Based on the established model, super-resolution parameters such as user distance, velocity, and angle of arrival are estimated. When there is distance ambiguity between direct and indirect paths, the received signal tensor can be expressed as:

[0039]

[0040] The parameters of the direct and indirect paths are estimated based on the received signal tensor Y. When there is ambiguity between the direct and indirect paths, super-resolution estimation of parameters such as the distance, transmission angle, and angle of arrival of the two paths is still required. The parameter to be estimated is x = [r0θ]. A,0 θ B,0 r1θ A,1 θ B,1 ] TWhere r0 represents the direct path distance, r1 represents the indirect path distance, and θ A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. B,1 This represents the angle between the non-direct path between the base station and the user and the normal of the base station array. Let represent the outer product of tensors. The parameter estimation problem can be written as:

[0041]

[0042] in, This represents the signal coefficients to be estimated. By analyzing the correlation of each parameter, we can determine θ. B,0 ,θ B,1 Independent of other parameters, it can be directly solved using a multi-signal classification algorithm. Other parameters are solved using an improved version of the Newton-orthogonal matching pursuit method. Original signal tensor After expanding along the second dimension, it forms a two-dimensional matrix. It can be represented as:

[0043]

[0044] Defined as:

[0045]

[0046] Defined as:

[0047]

[0048] Where x=[r0θ A,0 r1θ A,1 ] T Let represent the vector of parameters to be estimated. The objective function in the original optimization problem can be expressed as:

[0049]

[0050] A coarse estimate of the parameters is first obtained using the orthogonal matching pursuit method. The signal coefficients are estimated using least squares as follows:

[0051]

[0052] The coarse estimate is further refined using Newton's method, with the first derivative matrix... With the second derivative matrix Defined as:

[0053]

[0054] By iterating using Newton's method, the final parameter estimate of x can be obtained. Each iteration is represented as follows:

[0055]

[0056] in Indicates the input The parameter estimation results after iterative updates. The parameter estimates obtained through iterative optimization can then be used to refine the relationship between r0 and θ. A,0 The user's location can be uniquely determined using these two parameters.

[0057] The present invention also provides a signal receiving terminal that uses the super-resolution single anchor node positioning system and estimation method described above for user positioning.

[0058] The frequency design, positioning algorithm, and terminal of the single-anchor node super-resolution positioning system provided by this invention have the following advantages compared with the prior art:

[0059] 1. Introducing frequency disturbances into the signals between the transmitting antennas of the frequency-controlled array-multiple-input multiple-output system makes super-resolution estimation of the transmission angle and propagation distance possible in a single-anchor node positioning system.

[0060] 2. Analyze the impact of scrambling frequency on positioning performance and obtain design criteria for scrambling frequency sequences. Solve the problem that the traditional frequency control array-multiple input multiple output system cannot estimate the parameters of the emission angle and distance in a single anchor node positioning system due to the coupling between the emission angle and the distance.

[0061] 3. The proposed algorithm is suitable for multipath parameter estimation after the introduction of frequency perturbation, and can achieve super-resolution performance and accurate user positioning. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the super-resolution single anchor node positioning system provided by the present invention.

[0063] Figure 2 The flowchart shows the super-resolution single anchor node positioning system and estimation method provided by the present invention.

[0064] Figure 3 This diagram illustrates the error localization probability of the proposed system under the ideal frequency sequence, based on the proposed frequency sequence design criteria.

[0065] Figure 4This diagram illustrates the error localization probability of the proposed system under a non-ideal frequency sequence, based on the proposed frequency sequence design criteria. Detailed Implementation

[0066] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0067] A single-anchor node super-resolution localization method, such as Figure 1 As shown, it includes the following steps:

[0068] Step 1: Establish a signal model between the user and the base station in a frequency-controlled array-multiple-input multiple-output radar system based on the perturbation frequency, and the receiver signal tensor. The element with coordinates [n, p, q] in the middle is defined as Y. n,p,q , Y represents a complex tensor with three dimensions N, P, and Q. n,p,q This indicates that the signal received by the q-th antenna passes through the transmission frequency (f) of the p-th antenna in the n-th pulse. c +u n,p The output signal obtained after matched filtering of the signal Δf is defined as follows:

[0069]

[0070] Where N represents the number of pulses, P represents the number of transmitting antennas, Q represents the number of receiving antennas; r0 represents the distance between the user and the base station, and θ A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 f represents the angle between the direct path between the base station and the user and the normal of the base station array. c U represents the carrier frequency, Δf represents the frequency increment, and U n,p The element in the nth row and pth column of the perturbation frequency sequence U represents the transmit frequency index of the pth antenna in the nth pulse; d represents the spacing between adjacent antennas of the transceiver array; and c represents the speed of light.

[0071] Consider the signal received by the q1-th antenna, which is then subjected to matched filtering of the signal transmitted at the p1-th antenna in the n1-th pulse to obtain the output signal. The output signal is obtained by matching and filtering the signal received by the q2th antenna with the transmission frequency of the p2th antenna in the n2th pulse. The phase difference between them is:

[0072]

[0073] in, and Let represent the elements in Y with coordinates [n1, p1, q1] and [n2, p2, q2] respectively; Δφ = represents and The phase difference between them; This represents the element in the n1th row and p1th column of the perturbation frequency sequence U. This represents the element in the n2th row and p2th column of the perturbation frequency sequence U.

[0074] In the traditional frequency-controlled array-multiple-input multiple-output radar model, U n,p =p, which makes the phase difference equivalent to:

[0075]

[0076] This will result in θ A,0 There is a strong coupling between θ and r0, making super-resolution estimation of both impossible. Therefore, by designing a perturbation frequency sequence U, θ can be decoupled. A,0 The strong coupling between r0 and r0 makes super-resolution estimation of both possible.

[0077] Step 2: Analyze the impact of the perturbation frequency on the positioning performance and obtain the design criteria for the perturbation frequency sequence. Based on the Cramer-Rao bound analysis, the impact of the perturbation frequency sequence on the positioning performance is proposed, and the design criteria for the perturbation frequency sequence are obtained.

[0078] The parameter s0 required for direct path positioning is:

[0079] s0=[r0θ A,0 θ B,0 ]

[0080] The Fisher information matrix for the required parameters is represented as follows: Its element in row i and column j is defined as:

[0081]

[0082] Wherein, F(s) 0,i ,s 0,j Let be the element in the i-th row and j-th column of the Fisher information matrix F, and s 0,i This represents the i-th parameter in s0; Indicates taking the real part, Indicates noise power. Y represents n,p,q For s 0,i Find the partial derivative, (·) H This indicates the conjugate transpose. This indicates that the summation of q in the term to be summed is performed from 0 to Q-1.

[0083] The Cramer-Rao bound for parameter estimation in s is denoted as CRLB, where for s 0,i The Cramer-Rao boundary estimate is defined as It is represented as:

[0084]

[0085] Among them, [F -1 ] i,i Let i represent the i-th diagonal element of the inverse matrix of matrix F;

[0086] By minimizing the Cramer-Rao bound of the estimated parameters in s, the design criterion is obtained as follows: To improve the accuracy of the parameter estimation in s, the design of the perturbation frequency sequence U should satisfy the maximization of f(U), which is defined as:

[0087]

[0088] Step 3: Design the optimization problem and propose a super-resolution algorithm to estimate the parameters of the ambiguous signal path and locate the user. When there is distance ambiguity between the direct and indirect paths, the received signal tensor Y can be expressed as:

[0089]

[0090] Where r0 represents the direct path distance, r1 represents the indirect path distance, and θ A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. B,1 This represents the angle between the non-direct path between the base station and the user and the normal of the base station array. Represents the outer product of tensors;

[0091] The parameters of the direct and indirect paths are estimated based on the received signal tensor Y. When there is ambiguity between the direct and indirect paths, super-resolution estimation of parameters such as the distance, transmission angle, and angle of arrival of the two paths is still required. The parameter to be estimated is x = [r0 θ]. A,0 θ B,0 r1 θ A,1 θ B,1 ] T Where r0 represents the direct path distance, r1 represents the indirect path distance, and θ A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. B,1 This represents the angle between the non-direct path between the base station and the user and the normal of the base station array. This parameter estimation problem can be written as:

[0092]

[0093] in, This represents the signal coefficients to be estimated. By analyzing the correlation of each parameter, we can determine θ. B,0 ,θ B,1 Independent of other parameters, it can be directly solved using a multi-signal classification algorithm. Other parameters are solved using an improved version of the Newton-orthogonal matching pursuit method. Original signal tensor After expanding along the second dimension, it forms a two-dimensional matrix. It can be represented as:

[0094]

[0095] Defined as:

[0096]

[0097] Defined as:

[0098]

[0099] Where x = [r0 θ] A,0 r1 θ A,1 ] T Let represent the vector of parameters to be estimated. The objective function in the original optimization problem can be expressed as:

[0100]

[0101] A coarse estimate of the parameters is first obtained using the orthogonal matching pursuit method. The signal coefficients are estimated using least squares as follows:

[0102]

[0103] The coarse estimate is further refined using Newton's method, with the first derivative matrix... With the second derivative matrix Defined as:

[0104]

[0105] By iterating using Newton's method, the final parameter estimate of x can be obtained. Each iteration is represented as follows:

[0106]

[0107] in, Indicates the input The parameter estimation results after iterative updates. The parameter estimates obtained through iterative optimization can then be used to refine the relationship between r0 and θ. A,0 The user's location can be uniquely determined using these two parameters.

[0108] The following is a verification example of the present invention, applied to a super-resolution single-anchor node positioning system with frequency disturbances, verifying that in the system designed in this invention, based on the proposed frequency design criteria and algorithm, user positioning can be achieved even when there is distance ambiguity between direct and indirect paths.

[0109] Table 1 Simulation Parameters

[0110] Number of transmitting antennas P 6 Number of receiving antennas Q 8 Pulse number N 5 Frequency increment Δf 1MHz

[0111] The simulation parameters are shown in Table 1, and the positioning error is as follows: Figure 3 , Figure 4 As shown, where Figure 3 The positioning error is obtained when the frequency sequence design satisfies that f(U) is large. Figure 4 The positioning error was obtained when the frequency sequence design satisfied a small f(U). The blue triangles represent the base station locations, and the orange circles represent the locations of scattering points forming non-direct paths. Each point in the image represents the probability that the positioning error is greater than 3m when the user is at that location. It can be seen that the probability of a positioning error greater than 3m is close to 0 in most locations. In contrast, the positioning error obtained when f(U) is small... Figure 4 The probability of positioning errors is higher than that in [the context of the previous sentence]. Figure 3 The positioning error was reduced. This proves the effectiveness of the designed frequency sequence design criteria and solves the problem that traditional frequency control array-multiple-input multiple-output systems cannot achieve user positioning in single-anchor node positioning systems due to the coupling between the emission angle and the distance.

[0112] Furthermore, taking a point (-30.5m, 10.2m) as an example, when the user is located at this point, the probability of a positioning error greater than 3m is close to 0. The direct path distance formed by the user's location is 40m, and the non-direct path distance is 57.8m. The distance difference between the two paths is 17.8m, which is less than the distance resolution of 25m at this time. This confirms that accurate positioning of the user can still be achieved when there is distance ambiguity between the two paths, indicating that the proposed system and algorithm have super-resolution capability for multipath propagation and high-precision positioning performance. It is precisely because of its ability to perform super-resolution estimation of emission angle and propagation distance in a single-anchor node positioning system.

[0113] This invention takes single-anchor node user positioning as an example, and verifies that the proposed single-anchor node super-resolution positioning system has the ability to achieve user positioning when there is distance ambiguity between direct and indirect paths. It solves the problem of emission angle and distance coupling in the traditional frequency control array-multiple-input multiple-output system in single-anchor node positioning system, and proves that the probability of positioning deviation can be reduced and the positioning accuracy can be improved based on the proposed frequency design criteria and algorithm.

[0114] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A single-anchor node super-resolution positioning method, characterized in that, Includes the following steps: Establish a signal model for a frequency-controlled array-multiple-input multiple-output radar system based on the perturbation frequency: in, Indicates the first The signal received by the antenna is processed by the first antenna. The first pulse The output signal obtained after matching filtering of signals of each frequency. For the receiver signal tensor The median coordinate is elements, Indicates the number of pulses. Indicates the number of transmitting antennas. Indicates the number of receiving antennas; a 0 indicates the amplitude of the received signal. Indicates the distance between the user and the base station. This represents the angle between the direct path between the base station and the user and the normal of the user array. This represents the angle between the direct path between the base station and the user and the normal of the base station array. Indicates the carrier frequency. Indicates frequency increment; Represents the speed of light; Indicates the spacing between adjacent antennas of the transceiver array; Represents the perturbation frequency sequence The Okay, number Column elements; Based on the established frequency-controlled array-multiple-input multiple-output radar system signal model based on the perturbation frequency, the user's distance, speed and angle of arrival are obtained by super-resolution parameter estimation of the received signal tensor. Based on the established frequency-controlled array-multiple-input multiple-output radar system signal model based on the perturbation frequency, super-resolution parameter estimation is performed on the received signal tensor to obtain the user range and angle of arrival, including: The received signal tensor Y and the parameters to be estimated for the direct and indirect paths. They are respectively: in, This indicates that the tensor outer product is performed in the third dimension. Indicates the direct path distance. Indicates the distance of a non-direct route. This represents the angle between the direct path between the base station and the user and the normal of the user array. This represents the angle between the direct path between the base station and the user and the normal of the base station array. This indicates the angle between the non-direct path and the normal of the user array. This represents the angle between the non-direct path between the base station and the user and the normal of the base station array; and Represent the transmitting array manifold and the receiving array manifold, respectively; The Middle Line number The elements of a column are defined as follows: The Middle Each element is defined as: in, This indicates the angle between the signal direction and the array normal. Indicates the signal transmission distance; The parameter estimation problem is written as: in, Represents the signal coefficients to be estimated; The square of the Frobenius norm of the matrix is ​​given by . Solve using a multi-signal classification algorithm The estimated value ;right The estimation is then solved by improving the Newton-orthogonal matching pursuit method; the original signal tensor After expanding along the second dimension, it forms a two-dimensional matrix. , is represented as: Defined as: Defined as: in, This represents the vector of parameters to be estimated in the direct and indirect paths at this point. They represent The first, second, third, and fourth elements in the equation; the objective function in the original optimization problem is expressed as: A coarse estimate of the parameters is first obtained using the orthogonal matching pursuit method. And the signal coefficients are estimated by least squares. for: The coarse estimate is further refined using Newton's method, with the first derivative matrix... With the second derivative matrix Defined as: By iteratively applying Newton's method, the final result is obtained. Parameter estimation; each iteration is represented as: in, Indicates the input The parameter estimation results after iterative updates; the parameter estimates obtained through iterative optimization enable... The estimate.

2. The single-anchor node super-resolution positioning method according to claim 1, characterized in that, Perturbation frequency sequence According to Maximize to obtain, where Defined as: 。 3. The single-anchor node super-resolution positioning method according to claim 2, characterized in that, The perturbation frequency sequence The design of the criterion for the impact of perturbation frequency sequences on positioning performance, based on Cramer-Rao boundary analysis, includes: Parameters required for direct path positioning for: The Fisher information matrix for the required parameters is represented as follows: , its first Okay, number Column elements are defined as: in, The first element in Fisher's information matrix F Okay, number Column elements, express The first in One parameter; Indicates taking the real part, Indicates noise power. express right Find the partial derivative. This indicates the conjugate transpose. Indicate the terms to be summed from arrive Perform summation; right The Cramer-Rao bound for the intermediate parameter estimation is expressed as: Among them, The Cramer-Rao boundary estimate is defined as It is represented as: in, Representation matrix The inverse matrix of the first One diagonal element; By minimizing the The Cramer-Rao bounds estimated for each parameter yield the design criterion: perturbation frequency sequence. The design meets the needs of maximize.

4. A single-anchor node super-resolution positioning device, characterized in that, It includes a processor and a memory; the memory stores a program or instructions, which are loaded and executed by the processor to implement the steps of the single-anchor node super-resolution localization method as described in any one of claims 1 to 3.

5. A computer-readable storage medium, characterized in that, The readable storage medium stores a program or instructions that, when executed by a processor, implement the steps of the single-anchor node super-resolution positioning method as described in any one of claims 1 to 3.

6. A signal receiving terminal, characterized in that, The user is located using the single-anchor node super-resolution positioning method described in any one of claims 1-3.

Images