A method for positioning a single-source of beidou indoors with the aid of an intelligent metasurface

Abstract

The application discloses an intelligent metasurface-assisted indoor Beidou single signal source positioning method, first constructs an intelligent metasurface-assisted indoor Beidou single signal source positioning system channel model, uses the intelligent metasurface to build a virtual line-of-sight link, then divides a far-field area of the intelligent metasurface into grids, changes a phase shift matrix of the intelligent metasurface so that the Beidou signal can be directionally reflected to different positions, and unknown target position estimation values are calculated by comprehensively evaluating positioning loss and received signal strength, finally, particle filtering is introduced to realize real-time optimization of dynamic positioning position estimation results, effectively solves the non-line-of-sight signal and the compatibility problem of the receiving terminal, and realizes low-cost, reliable and seamless positioning of an emergency area. Numerical simulation results show that the method can achieve meter-level to sub-meter-level positioning accuracy.

Description

Technical Field

[0001] This invention belongs to the field of indoor and outdoor seamless positioning technology, specifically relating to an intelligent metasurface-assisted indoor BeiDou single-signal source positioning method. Background Technology

[0002] Because satellite signals are inherently electromagnetic waves, they are naturally vulnerable, exhibiting weak signals, poor penetration, and susceptibility to interference. This makes it difficult to guarantee the availability and reliability of positioning services in emergency areas such as indoors, underground environments, and mountainous regions where GNSS signals are limited. Traditional solutions to this problem can be categorized into two main types: optimization from the satellite end and optimization from the ground receiver end.

[0003] For the satellite end, launching more satellites (such as large-scale deployment of low-Earth orbit satellites) improves satellite geometry and enhances global coverage and availability in obstructed environments. However, this approach is costly to deploy and prone to causing satellite orbit congestion. For the ground receiver end, on the one hand, receiver RF front-end design is optimized to improve weak signal reception capabilities. On the other hand, multiple sensors are integrated, such as inertial navigation (INS), ultra-wideband (UWB), and pseudosatellite technologies. Among them, UWB transmits information by sending and receiving high-frequency pulses between modules, possessing numerous advantages such as strong multipath resistance, high resolution, strong penetration, and low power consumption. However, its deployment cost is high due to environmental and cost constraints. Furthermore, UWB ranging results contain non-line-of-sight (NLOS) errors and systematic errors due to object obstruction and time delays, requiring estimation and compensation. Users also need to modify their receiving terminals to receive the signal. While pseudosatellites have high compatibility with terminal receivers, they require at least four signal transmitting base stations for networking, typically requiring time synchronization. The large size and weight of the equipment result in poor portability and mobility, complex and slow deployment, and susceptibility to multipath interference. Therefore, there is an urgent need to explore a new independent positioning paradigm—using intelligent metasurfaces to dynamically reconstruct satellite signal propagation paths, providing a solution from the satellite signal propagation segment without pre-existing infrastructure, and achieving reliable positioning in emergency areas at low cost.

[0004] Currently, metasurfaces are moving towards intelligence. Intelligent metasurfaces (RIS) can achieve real-time sensing and adaptive control by integrating various sensors, freeing them from dependence on human-operated electromagnetic functions. RIS also has great potential in improving channel capacity and signal coverage, and can provide strong guarantees for secure signal transmission. Based on the advantages of RIS in wireless communication systems, applying RIS to wireless positioning can generate reliable and high-precision position estimates at low cost and high energy efficiency, and some research results have been achieved in recent years. However, research on using metasurfaces to assist satellite communication and positioning is still in the initial exploratory stage, with only a few simulation verifications. These methods are too idealistic in constructing positioning scenarios and are only applicable to situations with at least 3 visible satellites. If the number of satellites in the LOS link is less than 3, the fixed position of the metasurface will lead to rank deficiency in the pseudorange equation, requiring the introduction of multiple metasurfaces for auxiliary positioning, which increases deployment costs. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses an intelligent metasurface-assisted indoor BeiDou single-signal-source positioning method. A corresponding channel model is established based on the scene characteristics of the positioning system, and BeiDou single-signal-source positioning is achieved through an optimal grid search method. Furthermore, to improve search efficiency, the relationship between the number of candidate grids and positioning accuracy is quantitatively studied during static positioning and applied to dynamic positioning calculations. A particle filtering algorithm is also incorporated to enhance dynamic positioning accuracy.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A smart metasurface-assisted indoor BeiDou single-signal-source positioning method includes the following steps:

[0008] Step 1: Establish the positioning system channel model;

[0009] Step 2: Divide the far-field three-dimensional region of the RIS on the side where the receiver is located into S grids;

[0010] Step 3: Enter the optimal grid search algorithm, set the RIS phase shift vector β to a random phase shift, and calculate the atomic channel F of the RIS-UE and the reconstructed signal y of each grid. constructed 。;

[0011] Step 4: Select the first n candidate grids with the smallest localization loss as the coarse localization result;

[0012] Step 5: Adjust the RIS phase shift vector so that the BeiDou signal beam is aligned with the n candidate grids in sequence, and calculate the corresponding received signal strength.

[0013] Step 6: When the received signal strength is at its maximum, the corresponding grid is used as the final estimation result, and particle filtering is introduced to optimize the estimated value.

[0014] The specific steps are as follows:

[0015] Step 1. Establish the positioning system channel model.

[0016] The system channel is considered as a concatenated form of two sub-link channels, BS-RIS and RIS-UE, which are represented as follows:

[0017]

[0018] In the formula, H br and H ru Let δ represent the channel matrices of BS-RIS and RIS-UE, respectively. br and δ ru These represent the gains of the BS-RIS channel and the RIS-UE channel, respectively, where j is the imaginary unit, λ is the frequency of the BeiDou signal source, and d... br Let R be the known Euclidean distance from BS to RIS, and R be the unknown Euclidean distance from RIS to UE. The steering vector at the RIS array. It can be represented as:

[0019]

[0020] In the formula, d a and d e These represent the spacing between each unit in the horizontal and vertical directions, respectively, and M and N represent the number of rows and columns in the RIS array, respectively. θ represents the Kronecker product of a vector or matrix. x This represents the angle between the incident and reflected signals and the negative z-axis. This represents the angle between the projection of the incident or reflected signal onto the xoy plane and the positive x-axis.

[0021] Therefore, if the signal source transmits signal s, the signal received by the receiver is represented as:

[0022]

[0023] in, The adjustable phase shift vector of RIS can be represented as follows: n is a variable with variance σ 2 Random Gaussian noise with a mean of 0. The symbol T represents the transpose of the matrix, and ⊙ represents the Hadamard product of vectors.

[0024] Step 2. Divide the far-field three-dimensional region of the RIS on the side where the receiver is located into S grids.

[0025] The far-field region where the target is located is divided into grids, θ∈[0,π / 2]. The sampling interval is π / 50, R∈[2D] 2 / λ, R max The sampling interval is 0.25m, with a total of S grids. Among them, 2D... 2 / λ is the near-far field discrimination boundary. Since the upper bound of the far-field distance tends to infinity, R needs to be initially determined in order to improve search efficiency. max Under far-field conditions, beamforming is achieved through intelligent metasurface reflection. The transmission distance of the RIS-UE channel can be expressed as:

[0026]

[0027] Where δ1 and δ2 satisfy When θ r =θ, When the right side of the equation can reach its maximum value, then we have:

[0028]

[0029] Due to the power radiation pattern Often modeled as Therefore, the form is further reduced to the following formula:

[0030]

[0031] Where A represents the amplitude of the reflection coefficient of the RIS reflection unit. Based on the above derivation, the upper limit of the search for R is preliminarily determined.

[0032] Step 3. Set the RIS phase shift vector β to a random phase shift, and calculate the atomic channel F of the RIS-UE and the reconstructed signal y for each grid. constructed ;

[0033] First, define the atomic channel of RIS-UE. The channel from the RIS unit to each grid corresponds to each element therein. Define u as the selection vector; since there is only a single receiving target in this system, it has exactly one non-zero element, and ||u|| = 1. Based on this, the reconstructed signal for each grid can be written as:

[0034]

[0035] Step 4. Select the first n candidate grids with the smallest localization loss as the coarse localization result;

[0036] In the coarse localization stage, the L2 norm of the difference between the UE received signal and the reconstructed grid signal is defined as the localization loss, and the grid position with the smallest localization loss value is selected as the coarse localization result. The localization problem can be written in the following form:

[0037]

[0038] Since the difference in positioning loss between some grids may be very small, but the positions of these grids may not be close, in order to improve positioning accuracy, this algorithm selects n candidate grids i to enter the fine positioning algorithm during coarse positioning.

[0039] Step 5. Adjust the RIS phase shift vector so that the BeiDou signal beam is aligned with the n candidate grids in sequence, and calculate the corresponding received signal strength;

[0040] The phase shift vector β of the RIS is adjusted according to the position of the candidate grid so that the BeiDou signal transmitted by the BS can be sequentially aligned with the candidate grid position region. According to the beamforming principle, the reflection phase of each element of the RIS should satisfy the following at this time:

[0041]

[0042] Where, x k and y k Represents unit coordinates,

[0043]

[0044] Step 6. When the received signal strength is at its maximum, the corresponding grid is used as the final estimation result, and particle filtering is introduced to optimize the estimated value.

[0045] The received signal strength only reaches its maximum value when the receiver is located at that grid point. Therefore, the final location is estimated by sequentially calculating the receiver signal strength values ​​corresponding to the BeiDou signal reflected to different candidate grid points, as shown in the following formula:

[0046]

[0047] in, For the final estimated location, and β i These represent the channel parameters and phase shift vector corresponding to each grid cell, respectively. To reduce the positioning error caused by insufficient candidate grid cells, particle filtering is introduced to smooth the positioning result trajectory. The number of particles is initialized to N, and the weight of each particle is set to 1 / N. The particle weights are recursively calculated based on importance sampling to obtain:

[0048]

[0049] in, Let d be the weight of particle i at time k. mea-esti σ represents the Euclidean distance between the grid search observations and the particle filter estimates. mea-noise The standard deviation of the observed noise.

[0050] A system resampling strategy is adopted, taking the particle weight vector as input. By generating uniformly distributed sampling positions and mapping indices based on the cumulative distribution determined by the particle weights, weighted sampling is achieved. The weighted sample set is then used to obtain the estimated value at time k.

[0051]

[0052] in, To normalize particle weights, For the particle state vector, Estimate the state vector for the target. At this point, let... Output the final target localization result at time k.

[0053] The beneficial effects of this invention are as follows:

[0054] This invention proposes an intelligent metasurface-assisted indoor BeiDou single-signal source positioning method. Addressing the problem of severely limited GNSS signals in indoor, underground, and mountainous emergency areas, this method leverages the advantages of metasurfaces—low cost, ease of deployment, and effective wireless channel configuration—to alter the BeiDou signal channel environment along the propagation path, effectively establishing a virtual line-of-sight link. Optimal grid search enables BeiDou single-signal source positioning. Simulation results demonstrate that the proposed algorithm achieves meter-level to sub-meter-level positioning accuracy in both angle search and three-parameter search (angle + distance). Attached Figure Description

[0055] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0056] Figure 2 This is a comparison chart of the positioning errors of the optimal grid search algorithm and the one using particle filter estimation. Detailed Implementation

[0057] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0058] As shown in the figure, the specific steps of the intelligent metasurface-assisted indoor BeiDou single-signal-source positioning method of the present invention are as follows:

[0059] Step 1. Establish the positioning system channel model.

[0060] The system channel can be viewed as a cascaded form of two sub-link channels, BS-RIS and RIS-UE, which are represented as follows:

[0061]

[0062] In the formula, H br and H ruLet δ represent the channel matrices of BS-RIS and RIS-UE, respectively. br and δ ru These represent the gains of the BS-RIS channel and the RIS-UE channel, respectively, where j is the imaginary unit, λ is the frequency of the BeiDou signal source, and d... br Let R be the known Euclidean distance from BS to RIS, and R be the unknown Euclidean distance from RIS to UE. The steering vector at the RIS array. It can be represented as:

[0063]

[0064] In the formula, d a and d e These represent the spacing between each unit in the horizontal and vertical directions, respectively, and M and N represent the number of rows and columns in the RIS array, respectively. θ represents the Kronecker product of a vector or matrix. x This represents the angle between the incident and reflected signals and the negative z-axis. This represents the angle between the projection of the incident or reflected signal onto the xoy plane and the positive x-axis.

[0065] Therefore, if the signal source transmits signal s, the signal received by the receiver can be expressed as:

[0066]

[0067] in, The adjustable phase shift vector of RIS can be represented as follows: n is a variable with variance σ 2 Random Gaussian noise with a mean of 0. The symbol T represents the transpose of the matrix, and ⊙ represents the Hadamard product of vectors.

[0068] Step 2. Divide the far-field three-dimensional region of the RIS on the side where the receiver is located into S grids.

[0069] The far-field region where the target is located is divided into grids, θ∈[0,π / 2]. The sampling interval is π / 50, R∈[2D] 2 / λ, R max The sampling interval is 0.25m, with a total of S grids. Among them, 2D... 2 / λ is the near-far field discrimination boundary. Since the upper bound of the far-field distance tends to infinity, R needs to be initially determined in order to improve search efficiency. max Under far-field conditions, beamforming is achieved through intelligent metasurface reflection. The transmission distance of the RIS-UE channel can be expressed as:

[0070]

[0071] Where δ1 and δ2 satisfy When θ r =θ, When the right side of the equation reaches its maximum value, then:

[0072]

[0073] Due to the power radiation pattern Often modeled as Therefore, the form is further reduced to the following formula:

[0074]

[0075] Where A represents the amplitude of the reflection coefficient of the RIS reflection unit. Based on the above derivation, the upper limit of the search for R is preliminarily determined.

[0076] Step 3. Set the RIS phase shift vector β to a random phase shift, and calculate the atomic channel F of the RIS-UE and the reconstructed signal y for each grid. constructed ;

[0077] First, define the atomic channel of RIS-UE. The channel from the RIS unit to each grid corresponds to each element therein. Define u as the selection vector; since there is only a single receiving target in this system, it has exactly one non-zero element, and ||u|| = 1. Based on this, the reconstructed signal for each grid can be written as:

[0078]

[0079] Step 4. Select the first n candidate grids with the smallest localization loss as the coarse localization result;

[0080] In the coarse localization stage, the L2 norm of the difference between the UE received signal and the reconstructed grid signal is defined as the localization loss, and the grid position with the smallest localization loss value is selected as the coarse localization result. The localization problem can be written in the following form:

[0081]

[0082] Since the difference in positioning loss between some grids may be very small, but the positions of these grids may not be close, in order to improve the positioning accuracy, this algorithm selects n candidate grids i to enter the fine positioning algorithm during coarse positioning.

[0083] Step 5. Adjust the RIS phase shift vector so that the BeiDou signal beam is aligned with the n candidate grids in sequence, and calculate the corresponding received signal strength;

[0084] The phase shift vector β of the RIS is adjusted according to the position of the candidate grid so that the BeiDou signal transmitted by the BS can be sequentially aligned with the candidate grid position region. According to the beamforming principle, the reflection phase of each element of the RIS should satisfy the following at this time:

[0085]

[0086] Where, x k and y k Represents unit coordinates,

[0087] Step 6. When the received signal strength is at its maximum, the corresponding grid is used as the final estimation result, and particle filtering is introduced to optimize the estimated value.

[0088] The received signal strength only reaches its maximum value when the receiver is located at that grid point. Therefore, the final location is estimated by sequentially calculating the receiver signal strength values ​​corresponding to the BeiDou signal reflected to different candidate grid points, as shown in the following formula:

[0089]

[0090] in, For the final estimated location, and β i These represent the channel parameters and phase shift vector corresponding to each grid cell, respectively. To reduce the positioning error caused by insufficient candidate grid cells, particle filtering is introduced to smooth the positioning result trajectory. The number of particles is initialized to N, and the weight of each particle is set to 1 / N. The particle weights are recursively calculated based on importance sampling to obtain:

[0091]

[0092] in, Let d be the weight of particle i at time k. mea-esti σ represents the Euclidean distance between the grid search observations and the particle filter estimates. mea-noise The standard deviation of the observed noise.

[0093] A system resampling strategy is adopted, taking the particle weight vector as input. By generating uniformly distributed sampling positions and mapping indices based on the cumulative distribution determined by the particle weights, weighted sampling is achieved. The weighted sample set is then used to obtain the estimated value at time k.

[0094]

[0095] in, To normalize particle weights, For the particle state vector, Estimate the state vector for the target. At this point, let... Output the final target localization result at time k.

[0096] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A smart metasurface-assisted indoor BeiDou single-signal source positioning method, characterized in that, include: Step 1: Establish the positioning system channel model; Step 2: Divide the far-field three-dimensional region of the RIS on the side where the receiver is located into S grids; Step 3: Enter the optimal grid search algorithm: Set the RIS phase shift vector β to a random phase shift, calculate the atomic channel F of the RIS-UE and the reconstructed signal y of each grid. constructed ; Step 4: Select the first n candidate grids with the smallest localization loss as the coarse localization result; Step 5: Adjust the RIS phase shift vector so that the BeiDou signal beam is aligned with the n candidate grids in sequence, and calculate the corresponding received signal strength; Step 6: The grid corresponding to the maximum received signal strength is used as the final estimation result, and particle filtering is introduced to optimize the estimated value; the details are as follows: The received signal strength only reaches its maximum value when the receiver is located at that grid point. Therefore, the final location is estimated by sequentially calculating the receiver signal strength values ​​corresponding to the BeiDou signal reflected to different candidate grid points, as shown in the following formula: ； in, For the final estimated location, and Let represent the channel parameters and phase shift vector corresponding to each grid cell, respectively. To reduce the positioning error caused by insufficient candidate grid cells, particle filtering is introduced to smooth the positioning result trajectory. The number of particles is initialized to N, and the weight of each particle is set to 1 / N. The particle weights are recursively sampled according to importance to obtain: ； in, Let be the weight of particle i at time k. The Euclidean distance between the grid search observations and the particle filter estimates; The standard deviation of the observed noise; A system resampling strategy is adopted, taking the particle weight vector as input. By generating uniformly distributed sampling positions and mapping indices based on the cumulative distribution determined by the particle weights, weighted sampling is achieved. The weighted sample set is then used to obtain the estimated value at time k. ； in, To normalize particle weights, For the particle state vector, Estimate the state vector for the target; at this point, let Output the final target localization result at time k.

2. The intelligent metasurface-assisted indoor BeiDou single-signal source positioning method as described in claim 1, characterized in that, Step 1 involves establishing the positioning system channel model; specifically as follows: The system channel is considered as a concatenated form of two sub-link channels, BS-RIS and RIS-UE, which are represented as follows: ； ； In the formula, and These represent the channel matrices of BS-RIS and RIS-UE, respectively. and These represent the gains of the BS-RIS channel and the RIS-UE channel, respectively, where j is the imaginary unit. The carrier wavelength of the BeiDou signal source. Given the known Euclidean distance from BS to RIS, The unknown distance from RIS to UE; the steering vector at the RIS array. Represented as: ； In the formula, , , , and These represent the spacing between each unit in the horizontal and vertical directions, respectively, and M and N represent the number of rows and columns in the RIS array, respectively. Represents the Kronecker product of a vector or matrix. This represents the angle between the incident and reflected signals and the negative z-axis. This represents the angle between the projection of the incident or reflected signal onto the xoy plane and the positive x-axis. Therefore, if the signal source transmits signal s, the signal received by the receiver is represented as: ； in, This represents the adjustable phase shift vector of RIS, where n is the variance. Random Gaussian noise with a mean of 0; the symbol T represents the transpose of the matrix, and the symbol ⊙ represents the Hadamard product of vectors.

3. The intelligent metasurface-assisted indoor BeiDou single-signal source positioning method as described in claim 2, characterized in that, Step 2 involves dividing the far-field three-dimensional region of the RIS on the side where the receiver is located into S grids; specifically as follows: The far-field region where the target is located is divided into grids. , The sampling interval is , The sampling interval is 0.25m, with a total of S grids; among which, This is the boundary between the near and far fields. Since the upper bound of the far field distance tends to infinity, it needs to be initially determined to improve search efficiency. Under far-field conditions, beamforming is achieved through intelligent metasurface intelligent reflection. The RIS-UE channel transmission distance is expressed as: ； in, and satisfy ;when , When the right side of the equation reaches its maximum value, then: ； Due to the power radiation pattern Often modeled as Therefore, the form is further reduced to the following formula: ； in, This represents the amplitude of the reflection coefficient of the RIS reflector unit; based on the above derivation, it is preliminarily determined that... The upper limit of the search.

4. The intelligent metasurface-assisted indoor BeiDou single-signal source positioning method as described in claim 3, characterized in that, Step 3 involves setting the RIS phase shift vector β to a random phase shift, calculating the atomic channel F of the RIS-UE, and the reconstructed signal y for each grid. constructed The details are as follows: First, define the atomic channel of RIS-UE. The channel from the RIS cell to each grid corresponds to each element therein; definition To select the vector, since there is only a single receiving target in this system, there is one and only one non-zero element, and Based on this, the reconstruction signal for each grid is written as: 。 5. The intelligent metasurface-assisted indoor BeiDou single-signal source positioning method as described in claim 1, characterized in that, Step 4 involves selecting the first n candidate grids with the smallest localization loss as the coarse localization result; specifically as follows: In the coarse localization stage, the L2 norm of the difference between the UE received signal and the grid reconstructed signal is defined as the localization loss, and the grid position with the smallest localization loss value is selected as the coarse localization result; the localization problem is written in the following form: ； During coarse localization, n candidate grids i are selected to enter the fine localization algorithm.

6. The intelligent metasurface-assisted indoor BeiDou single-signal source positioning method as described in claim 2, characterized in that, Step 5 involves adjusting the RIS phase shift vector so that the BeiDou signal beam is sequentially aligned with the n candidate grids, and then calculating the corresponding received signal strength; the details are as follows: The phase shift vector β of the RIS is adjusted according to the position of the candidate grid so that the BeiDou signal transmitted by the BS can be sequentially aligned with the candidate grid position region. According to the beamforming principle, the reflection phase of each element of the RIS should satisfy the following at this time: ； in, and Represents unit coordinates, , .

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