A method for simultaneous localization and mapping assisted by UAV-RIS

Abstract

This invention relates to a method for simultaneous localization and mapping (SLAM) assisted by a UAV equipped with a reconfigurable smart surface (UAV-RIS), addressing the problems of parameter decoupling difficulties caused by cascaded channels and large amplitude-based localization and mapping errors due to signal strength distortion. The method includes: 1) constructing a nested parallel factor model of the received signal and performing tensor decomposition using a bilinear alternating least squares method to achieve joint channel parameter estimation and signal detection; 2) initializing and removing outliers using an amplitude-independent geometric inference method based on the estimated geometric parameters; and 3) optimizing the model using a weighted least squares method to determine user state and environmental characteristic parameters. This method reduces the impact of amplitude model mismatch and improves parameter estimation accuracy in complex channel environments, making it suitable for autonomous localization and mapping in low-altitude wireless networks.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and sensing technology, and in particular to a method for simultaneous localization and mapping (SLAM) assisted by a UAV equipped with a reconfigurable smart surface (UAV-RIS). Background Technology

[0002] The transition to 6G requires an integrated air-space-ground network to overcome limited ground coverage. In the air network, UAV-RIS can establish line-of-sight (LoS) links to alleviate coverage blind spots. Simultaneously, integrated communication and sensing (ISAC) technology enables concurrent data transmission and sensing. Therefore, snapshot-based wireless SLAM based on UAV-RIS has attracted widespread attention, providing a feasible technical path for autonomous navigation and communication in low-altitude wireless networks.

[0003] However, realizing such an integrated architecture faces significant challenges. The main challenge lies in the cascaded channel effect in the RIS auxiliary link, where multiplicative coupling channels make blind parameter decoupling difficult using traditional algorithms. Existing technologies propose using nested tensor models to embed the cascaded channels into an internal tensor structure in millimeter-wave and terahertz systems, thereby achieving channel matrix separation and parameter estimation. Although the tensor framework can provide high-precision channel parameter estimation, considering that ISAC needs to perform signal recovery under unknown channel conditions to maximize spectral efficiency, ensuring communication quality while maintaining high-precision parameter estimation remains a critical and challenging problem.

[0004] Furthermore, in terms of positioning and mapping, UAVs relying on Global Navigation Satellite Systems (GNSS) are susceptible to interference and signal interruptions in complex low-altitude environments, leading to the accumulation of positioning errors that propagate into the SLAM process and ultimately reduce mapping accuracy. Some literature proposes a robust snapshot-based wireless SLAM method, which uses a path loss model to distinguish between Loss of Position (LoS) and Non-Line-of-Sight (NLoS) based on signal amplitude. However, in dynamic low-altitude environments, received signal strength distortion caused by mobility and channel dynamics reduces the reliability of amplitude-based classification methods, leading to increased positioning errors and impacting mapping accuracy. Summary of the Invention

[0005] Purpose of the invention: This invention addresses the problems of difficulty in decoupling concatenated channel parameters and large positioning and mapping errors based on amplitude information in complex dynamic environments in existing technologies. It proposes a UAV-RIS-assisted SLAM method to improve positioning and mapping accuracy.

[0006] Technical solution: The UAV-RIS-assisted SLAM method of the present invention includes:

[0007] A nested parallel factor model of the received signal is constructed, and tensor decomposition is performed using the bilinear alternating least squares (BALS) method to achieve joint channel parameter estimation and signal detection.

[0008] Based on the estimated geometric parameters, an amplitude-independent geometric inference method is used for initialization and outlier removal;

[0009] The weighted least squares (WLS) method is used for optimization to determine user state and environmental characteristic parameters;

[0010] Furthermore, the construction of a nested parallel factor model of the received signal, and the tensor decomposition using the BALS method to achieve joint channel parameter estimation and signal detection, specifically includes:

[0011] An ISAC system comprising a base station, UAV-RIS, and mobile users is constructed. The UAV uses GNSS data to establish spatial coordinates, and the base station transmits ISAC signals that are reflected by the UAV-RIS to the mobile users. A multi-antenna transmission model for this system is established, where signals are received on multiple consecutive snapshots. The base station, UAV-RIS, and mobile users all employ uniform planar arrays. The distance from the base station to the RIS is... Subcarrier channel matrix Modeling as

[0012]

[0013] in, and These represent the number of antennas for the UAV-RIS and the base station, respectively. This indicates the number of paths from the base station to the RIS. Indicates complex gain. Indicates the sampling frequency. Indicates the total number of subcarriers. Indicates time delay. and These represent the array steering vectors at the UAV-RIS receiver and base station, respectively. and These represent the angle of arrival and the angle of departure, respectively, indicated by superscript. and These represent azimuth and elevation angles, respectively. This represents the matrix transpose operation.

[0014] Channel matrix from RIS to mobile users Modeling as

[0015]

[0016] in, This indicates the number of antennas on the mobile user terminal. This indicates the number of paths from the RIS to the mobile user. Indicates complex gain. Indicates time delay. and These represent the array steering vectors of the mobile user terminal and the UAV-RIS transmitter, respectively. and These represent the angle of arrival and the angle of departure, respectively.

[0017] On mobile devices, it will include Each time frame, spatial coding length is And the number of data streams is The received signal is constructed as a nested parallel factor tensor model. , represented as

[0018]

[0019] in, To combine the equivalent spatial dimensions after the receiver merger, Indicates the RIS phase shift frame number. The matrix representing the transmitted information symbols. Represents the space-time coding matrix. Represents the effective noise tensor. Represents a unit tensor. This represents the modal-3 expansion matrix defined by an internal tensor, which is defined as follows:

[0020]

[0021] in, This represents the RIS reflection phase shift matrix. and Let represent the channel tensor slice matrices combining the receive combiner and the transmit precoder, respectively. Its complete tensor form can be decomposed into a product containing the spatial array response factor matrix and the diagonal channel gain matrix, defined as...

[0022]

[0023]

[0024] in, and Each contains a transmit precoding matrix and receiving merge matrix The space factor matrix is ​​represented as ,in This represents the relevant arrival or departure angle variables. Similarly, a diagonal matrix is ​​defined. ,in Represents path delay variable, Represents the gain variable, matrix The List Represented as .

[0025] For the constructed external tensor model, a low-complexity BALS algorithm is employed, which performs alternating iterative fitting by minimizing the cost function, and jointly estimates the mode 3 expansion matrix and the information symbol matrix.

[0026]

[0027] in, This represents the square of the Frobenius norm. Using the first row of the known pilot sequence as a reference, the scale ambiguity generated during the alternating matrix decomposition is eliminated by multiplying by the corresponding diagonal calibration matrix.

[0028] Obtain the expansion matrix The internal core tensor was then reconstructed. The channel matrix is ​​obtained by minimizing the cost function. and ,Right now

[0029]

[0030] The extracted multi-subcarrier slice matrix is ​​reconstructed into a third-order channel tensor. and The trilinear least squares (TALS) algorithm is used for decoupling to extract the independent array response space factor matrix and the diagonal factor matrix containing delay and gain.

[0031] A truncated discrete Fourier transform (DFT) matrix with a Kronecker structure is used as a pre-encoder and merger to preserve the rotation invariance of the array subspace. An angular parameter estimation algorithm based on rotation-invariant subspace technology (ESPRIT) is employed to estimate the angular parameters from the decoupled spatial factor matrix.

[0032] Using the estimated factor matrix column vector and time delay steering vector Alignment characteristics are used to extract delay parameters through a one-dimensional search:

[0033]

[0034] in, The factor matrix containing time delay information represents the first factor. Column vectors The modulus of a complex scalar. The L2 norm of a vector. This represents the conjugate transpose operation. After reconstructing the angle and time delay correlation factor matrix and eliminating scale ambiguity, the estimated... Extracting gain .

[0035] Furthermore, the initialization and outlier removal based on the estimated geometric parameters using an amplitude-independent geometric inference method specifically includes:

[0036] UAV-RIS location Determined jointly by GNSS and estimated channel parameters, the base station is fully synchronized with the UAV-RIS system, and the complete geometric state variables of the mobile user are defined as follows: ,in For three-dimensional position coordinates, For the spatial orientation angle of mobile users, The receiver clock offset is used as the basis for establishing a physical measurement nonlinear mapping function. ,Right now

[0037]

[0038] in, At the speed of light, For the spatial orientation angle of UAV-RIS, to unify the expression, a displacement vector is defined: for the NLoS path ( The displacement vector is defined as follows: and At the same time, set indicator variables For Los path ( ),set up And indicator variables This ensures the correct path length while maintaining a consistent angle definition. Furthermore, the definition... This is the parameter measurement error covariance matrix transferred from the tensor decomposition stage to the SLAM stage.

[0039] Using the extracted angle parameters, a three-dimensional direction vector is defined in conjunction with the rotation matrix. and :

[0040]

[0041]

[0042] in, This is the counter-clockwise rotation matrix along the Z-axis. Define the relative position vector. By utilizing the vector cross product property to eliminate the unknown distance scalar, a unified geometric constraint residual equation applicable to both LosS and NLoS paths is derived, i.e.

[0043]

[0044] in, This represents a relative distance measurement that includes user clock skew. Used to evaluate geometric state The constraint residuals are calculated based on the geometric constraint residual equation, and the residual values ​​are used to remove outliers.

[0045] A strategy inspired by Random Sampling Consensus (RANSAC) is employed to iterate through and extract the smallest subset of parameters. Searching for a set of discrete angles within a preset range Given candidate orientation angles Then, the following cost function is constructed by minimizing the linear residuals to solve for the potential initial state:

[0046]

[0047] in, Indicates a fixed orientation angle Linear least squares cost function for conditional state variables and For subset The block constant matrix formed by stacking the direction vectors of each path according to the cross product relationship, and its sub-blocks are defined as follows: and , This indicates an antisymmetric matrix operator.

[0048] subset-based The solution yields the latent optimal estimated state. Feasibility tests are conducted, and only hypotheses satisfying either the LoS collinearity condition or the NLoS directional consistency condition are retained. The LoS collinearity condition is determined as follows:

[0049] and

[0050] in, For unit basis vectors, and This represents the cross product of the relative position estimation vector and the global direction vector. The relative position vector is estimated based on the potential state. This is the threshold for determining collinearity.

[0051] NLoS directional consistency condition is determined as follows:

[0052] and

[0053] in, This is a sign function used to extract the sign of the value within parentheses (i.e., it returns 1 when the value is positive, -1 when it is negative, and 0 when it is 0).

[0054] Substitute the solved states into the constraint residual equations to calculate the squared geometric residuals on all paths under the current assumption. By setting an interior point threshold Divide the path into sets of interior points. and external point set Calculate the total cost of the current assumption:

[0055]

[0056] in, Given the total cost of this assumed state across all paths, select the assumption that minimizes the total cost as the initial state of the system. The corresponding interior point set forms the optimization set. .

[0057] Furthermore, the optimization using the WLS method to determine user state and environmental characteristic parameters specifically includes:

[0058] Refine the user's orientation angle using local grid search And based on the reserved interior point set Constructing the WLS cost function:

[0059]

[0060] in, This represents the remaining conditional linear state after extracting the orientation angle. This represents the extracted squared gain. , , All of these represent geometric relation parameters derived from the global direction vector. This represents a third-order identity matrix.

[0061] By differentiating the cost function, we obtain the analytical closed-form solution for the refined mobile user state:

[0062]

[0063] Wherein, the weighted geometric matrix is The weighted mapping vector is The solution With refined orientation angle The vectors are merged and spliced ​​to form a full-state estimation vector for the mobile user that includes location, clock skew, and orientation angle. .

[0064] Fixed final solution full state vector The 3D location of each environmental landmark is independently estimated using the Gauss-Newton optimization algorithm:

[0065]

[0066] in, This represents the set of angle and time delay parameter measurements extracted from the tensor decomposition stage, indicated by the subscript in the lower right corner. This represents the squared Mahalanobis distance with weights equal to the inverse of the measurement error covariance matrix. Its function is to perform weighted optimization of each error based on the parameter uncertainty passed down from the tensor decomposition stage.

[0067] Compared with the prior art, the present invention has the following advantages: the present invention can jointly estimate the cascaded channel and communication signal of the system at the mobile user terminal, and effectively overcome the problem of amplitude model mismatch, and obtain highly robust SLAM performance in complex dynamic environments. Attached Figure Description

[0068] Figure 1 This is a flowchart of a UAV-RIS-assisted SLAM method according to the present invention;

[0069] Figure 2 This is a schematic diagram of the UAV-RIS assisted SLAM system of the present invention;

[0070] Figure 3 This is a comparison chart of the root mean square error (RMSE) performance of the present invention in channel parameter estimation with existing least squares (LS) and existing orthogonal matched pursuit (OMP) methods under different signal-to-noise ratios (SNR).

[0071] Figure 4 This is a comparison chart of the signal detection bit error rate (BER) performance of the present invention with existing LS methods and existing OMP methods under different SNRs;

[0072] Figure 5 This is a comparison chart of the SLAM estimation accuracy and path classification robustness of the present invention and existing robust snapshot SLAM methods at an SNR of 20dB. Detailed Implementation

[0073] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0074] Figure 2 This is a schematic diagram of the UAV-RIS assisted SLAM system of the present invention. Figure 2As shown, the system includes a base station, a UAV-RIS, and mobile users. The UAV establishes its spatial coordinates based on GNSS data. The mobile users receive ISAC signals transmitted by the base station reflected by the UAV-RIS.

[0075] Example 1

[0076] Figure 3 and Figure 4 This is a simulation diagram comparing the performance of the present invention with existing LS and OMP methods. System parameters are set as follows: 16 time frames, 16 spatial coding lengths, 16 RIS phase-shift frames, 16 data streams, a reserved spatial dimension of 9 after receiver processing with the merging matrix, a carrier frequency of 28 GHz, and 64QAM modulation. The total number of subcarriers is 256, of which 32 are used for SLAM. The base station is configured with an 8×8 array, mobile users with a 4×4 array, and UAV-RIS with a 4×4 array. Figure 3 The changes in RMSE for various channel parameters under different SNR conditions are shown. As the SNR increases, the RMSE of each parameter tends to decrease. Compared with existing LS and OMP methods, the proposed method exhibits a lower overall RMSE, indicating better parameter estimation performance under complex cascaded channel conditions. The RMSE of the proposed method increases with the number of paths. Figure 4 The results show a comparison of the BER performance of different methods. The method of this invention performs signal detection while estimating parameters, and its BER performance is superior to the comparison methods.

[0077] Example 2

[0078] Figure 5 This paper compares the SLAM estimation accuracy and path classification performance of the method of this invention with existing methods under a signal-to-noise ratio of 20 dB. The simulation scenario is set as a cubic space with a side length of 20 m, containing 20 snapshot times. To verify the performance of the method in complex environments, an amplitude distortion scenario was constructed, in which the ground LosS path is strongly attenuated, while the air NLoS path has a relatively enhanced signal strength under the UAV-RIS gain. Figure 5 As shown, under the aforementioned amplitude distortion condition, existing methods, relying on signal amplitude for path classification, may misclassify some NLoS paths as LoS paths, resulting in significant mapping errors. In contrast, the method of this invention, based on geometric constraints for path discrimination, can effectively suppress misclassification. In 20 snapshots, the method of this invention correctly identified 15 LoS paths, with an overall positioning error of 0.0826 m and a mapping error of 0.0572 m, indicating that the method of this invention has good robustness in complex channel environments.

[0079] The above description is merely one specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be conceived by those skilled in the art within the technical scope disclosed in the present invention without creative effort should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A UAV-RIS-assisted simultaneous localization and mapping method, characterized in that... The method includes: A nested parallel factor model of the received signal is constructed, and tensor decomposition is performed using the bilinear alternating least squares (BALS) method to achieve joint channel parameter estimation and signal detection. Specifically, this includes: constructing an integrated sensing and communication (ISAC) system comprising a base station, UAV-RIS, and mobile users; establishing spatial coordinates for the UAV using GNSS data; the base station transmitting ISAC signals reflected by the UAV-RIS to the mobile users; establishing a multi-antenna transmission model for this system; the system receiving signals on multiple consecutive snapshots; and the base station, UAV-RIS, and mobile users all employing uniform planar arrays. The distance from the base station to the UAV-RIS is... Channel matrix of subcarriers The model is as follows: ， in, and These represent the number of antennas for the UAV-RIS and the base station, respectively. This indicates the number of paths from the base station to the RIS. Indicates complex gain. Indicates the sampling frequency. Indicates the total number of subcarriers. Indicates time delay. and These represent the array steering vectors at the UAV-RIS receiver and base station, respectively. and These represent the angle of arrival and the angle of departure, respectively, indicated by superscript. and These represent azimuth and elevation angles, respectively. This represents the matrix transpose operation, from UAV-RIS to the mobile user's... Channel matrix of subcarriers The model is as follows: ， in, This indicates the number of antennas on the mobile user terminal. This indicates the number of paths from the RIS to the mobile user. Indicates complex gain. Indicates time delay. and These represent the array steering vectors of the mobile user terminal and the UAV-RIS transmitter, respectively. and These represent the angle of arrival and the angle of departure, respectively. On mobile devices, this will include... Each time frame, spatial coding length is And the number of data streams is The received signal is constructed as a nested parallel factor tensor model. , represented as ， in, To combine the equivalent spatial dimensions after the receiver merger, Indicates the RIS phase shift frame number. Represents the transmission symbol matrix, Represents the spatiotemporal encoding matrix, Represents the effective noise tensor. Represents a unit tensor. This represents the modal-3 expansion matrix defined by an internal tensor, which is defined as follows: ， in, This represents the RIS reflection phase shift matrix. and Let represent the channel tensor slice matrices combining the precoder and the combiner, respectively. The complete tensor form can be decomposed into a product containing the spatial array response factor matrix and the diagonal channel gain matrix, defined as follows: ， ， in, and Each contains a transmit precoding matrix and receiving merge matrix The space factor matrix is ​​represented as ,in Representing the relevant arrival or departure angle variables, similarly, a diagonal matrix is ​​defined. ,in Representing the relevant path delay variable, the gain variable is... ,matrix The The column is specifically represented as For the constructed external tensor model, the low-complexity BALS algorithm is used, which performs alternating iterative fitting by minimizing the cost function, and jointly estimates the mode 3 expansion matrix and the transmission symbol matrix, i.e. ， in, The square of the Frobenius norm is represented by the first row of the known pilot sequence as a reference. The expansion matrix is ​​obtained by multiplying by the corresponding diagonal calibration matrix to eliminate scale ambiguity generated during the alternating matrix decomposition. The internal core tensor was then reconstructed. The channel matrix is ​​obtained by minimizing the cost function. and ,Right now ， The extracted multi-subcarrier slice matrix is ​​reconstructed into a third-order channel tensor. and The trilinear least squares (TALS) algorithm is used for decoupling, extracting independent array response spatial factor matrices and diagonal factor matrices containing time delay and gain. A truncated discrete Fourier transform (DFT) matrix with a Kronecker structure is used as a pre-encoder and combiner to preserve the rotation invariance of the array subspace. An ESPRIT algorithm based on rotation-invariant subspace estimation is employed to estimate angular parameters from the decoupled spatial factor matrices. The estimated factor matrix column vectors and the time delay steering vector are then used... The alignment characteristics are used to extract path delay parameters through a one-dimensional search: ， in, Represents the estimated factor matrix The Column vectors The modulus of a complex scalar. The L2 norm of a vector. This indicates a conjugate transpose operation, which reconstructs the angle and time delay correlation factor matrix and eliminates scale ambiguity, from the estimated... Extracting gain ; Based on the estimated geometric parameters, an amplitude-independent geometric inference method is used for initialization and outlier removal, specifically including: assuming the location of UAV-RIS. Determined jointly by GNSS and estimated channel parameters, the base station is fully synchronized with the UAV-RIS system, and the complete geometric state variables of the mobile user are defined as follows: ,in For three-dimensional position coordinates, For the spatial orientation angle of mobile users, To account for the receiver clock deviation, a physical measurement nonlinear mapping function is established based on this. ,Right now ， in, At the speed of light, For the spatial orientation angle of UAV-RIS, to unify the expression, a displacement vector is defined: for non-line-of-sight paths ( The displacement vector is defined as follows: and At the same time, set indicator variables For line-of-sight paths ( ),set up And indicator variables To ensure the correct path length while maintaining a consistent angle definition, in addition, the definition... To obtain the parameter measurement error covariance matrix transferred from the tensor decomposition stage to the simultaneous localization and mapping stage, a three-dimensional direction vector is defined using the extracted angle parameters and the rotation matrix. and : ， ， in, Let Z be the counterclockwise rotation matrix along the Z-axis, and define the relative position vector as follows: Based on geometric relationships, a unified geometric constraint residual equation applicable to both line-of-sight and non-line-of-sight paths is derived: ， in, This represents a relative distance scalar that includes the clock offset of mobile users. Used to evaluate geometric state The constrained residuals are calculated based on the geometric constraint residual equation, and the residual values ​​are used to remove outliers. A strategy inspired by Random Sampling Consensus (RANSAC) is adopted to iterate through and extract the smallest subset of parameters. Searching for a set of discrete angles within a preset range Given candidate orientation angles Then, the following cost function is constructed by minimizing the linear residuals to solve for the potential initial state: ， in, Indicates a fixed orientation angle Linear least squares cost function for conditional state variables and For subset The block constant matrix formed by stacking the direction vectors of each path according to the cross product relationship is defined as follows: and , This indicates an antisymmetric matrix operator, for subset-based... The solution yields the latent optimal estimated state. A feasibility test was conducted, and the condition of collinearity of line of sight was retained. and Or, satisfy the non-line-of-sight directional consistency condition. and The assumption, in which For unit basis vectors, and It is the cross product of the direction vector and the relative position vector. The relative position vector is estimated based on the potential state. The threshold for determining collinearity. This is a sign function used to extract the sign of the value within parentheses (i.e., returns 1 for positive, -1 for negative, and 0 for 0). The solved state is then substituted into the constraint residual equation to calculate the squared geometric residuals of the current assumption across all paths. By setting an interior point threshold Divide the path into sets of interior points. and external point set Calculate the total cost of the current assumption: ， in, Given the total cost of this assumed state across all paths, select the assumption that minimizes the total cost as the initial state of the system. The corresponding interior point set forms the optimization set. ; The weighted least squares (WLS) method is used for optimization to determine user state and environmental characteristic parameters, specifically including refining the user's orientation angle using local grid search. For the preserved interior point set The square of the obtained channel gain As reliability weights for each path, construct the WLS cost function: ， in, This represents the remaining conditional linear state after extracting the orientation angle. , , All of these represent the parameters of the geometric relation matrix derived from the global direction vector. Let denote the third-order identity matrix. By differentiating the cost function, we obtain the analytical closed-form solution for the refined mobile user state: ， in, and Representing the weighted geometric matrix and weighted mapping vector expanded using the direction vector matrix and reliability weights respectively, the solution yields a high-precision full-state estimation vector for the mobile user, including position, clock skew, and orientation angle. The final user state obtained by the fixed solution For each reflection path, the corresponding landmark location The three-dimensional coordinates of the landmark are estimated by minimizing the physical measurement mapping error using the Gauss-Newton optimization algorithm: ， in, This represents the set of angle and time delay parameter measurements extracted from the tensor decomposition stage, indicated by the subscript in the lower right corner. This represents the squared Mahalanobis distance with weights equal to the inverse of the measurement error covariance matrix. Its function is to perform weighted optimization of each error based on the parameter uncertainty passed down from the tensor decomposition stage.

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