A phase mismatch and pulse noise oriented ris-assisted mobile source angle-doppler joint estimation method

Abstract

The application belongs to the technical field of signal processing and wireless sensing, and discloses a RIS-aided mobile source angle-Doppler joint estimation method for phase mismatch and impulse noise, which comprises the following steps: acquiring a multi-time slot observation signal of a receiving end, and establishing an observation model containing two-dimensional arrival angle, Doppler frequency shift and RIS phase mismatch; adopting a Lawson robust loss to construct an adaptive weighting mechanism, performing atom tracking in a continuous angle-Doppler domain, and performing phase mismatch calibration according to a reconstructed incident signal, and alternately updating to convergence to obtain estimation of each source pitch angle, azimuth angle, Doppler frequency and phase mismatch. The application can suppress impulse noise outliers without pre-discretizing the angle and Doppler parameters, can simultaneously calibrate the RIS phase mismatch, and can realize robust joint estimation of the two-dimensional arrival angle and Doppler frequency of the mobile source.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and wireless sensing technology, specifically relating to a RIS-assisted joint estimation method for the angle-Doppler of a mobile source oriented towards phase mismatch and impulse noise. Background Technology

[0002] With the rapid development of wireless communication technology, the acquisition of direction of arrival (DOA) and motion status of mobile sources has received increasing attention. DOA reflects the spatial orientation of the source relative to the receiver or sensing node, while Doppler frequency reflects the relative radial motion between the source and the sensing node. Joint estimation of these two parameters provides fundamental information for target tracking, beam management, location prediction, and integrated communication and sensing. Traditional angle and Doppler estimation typically relies on multi-antenna arrays, multi-channel RF receiver links, or fixed array apertures, extracting parameters through phase differences between array elements and signal variations across multiple snapshots. In scenarios where direct links are obstructed, receiver deployment space is limited, or hardware costs are constrained, it is often difficult to balance coverage, estimation accuracy, and system complexity. Reconfigurable Intelligent Surfaces (RIS), composed of multiple tunable reflective elements, can controllably reflect propagating signals by changing the phase state of each reflective element. By using RIS to switch different reflection states across multiple time slots, observation data with different spatial coding characteristics can be obtained through a single receiver channel, thus providing new implementation conditions for angle and Doppler parameter estimation when direct links are blocked or hardware resources are limited. In existing RIS-assisted estimation methods, some methods use pre-discrete angles and Doppler search grids for matching or sparse reconstruction, which can easily lead to grid mismatch when the true parameter values ​​are located between grid points. Some methods only process stationary sources or single angle parameters, making it difficult to adapt to observation scenarios where the angle changes of moving sources are coupled with Doppler phase evolution. In actual RIS deployment and operation, the reflecting units are also affected by factors such as manufacturing tolerances, device aging, control circuit errors, temperature changes, and external environmental disturbances, causing the actual reflection phase of some units to deviate from the preset phase, resulting in inconsistencies between the observation model and the actual propagation process. If this phase mismatch is not identified and calibrated in time, it may lead to distortion of the source spatial response, parameter matching deviation, and reduced multi-target resolution. Meanwhile, mobile communication environments may experience non-stationary disturbances such as sudden electromagnetic interference, strong nearby signal leakage, and transient radiation from equipment switching. These disturbances typically only affect a small number of observation slots, but their amplitude may be significantly higher than conventional thermal noise. Existing parameter estimation methods based on the least squares criterion are easily dominated by such anomalous observations, leading to deviations in the estimation results of angle, Doppler frequency, and phase mismatch parameters. On the other hand, existing technologies often separate mobile source parameter estimation from RIS phase mismatch calibration, failing to fully consider the coupling relationship between the two in the observation model, making it difficult to maintain stable estimations when phase mismatch and impulse noise coexist. Therefore, it is necessary to study a technical solution that can jointly estimate the angle of the moving source and the Doppler parameters in real-world RIS phase mismatch and impulse noise environments. Summary of the Invention

[0003] This invention aims to address the shortcomings of existing technologies by proposing a RIS-assisted joint estimation method for the angle-Doppler frequency of a mobile source, addressing phase mismatch and impulse noise. This method utilizes Lawson loss to construct a robust weighted quadratic surrogate function, performs atomic tracking in the continuous angle-Doppler domain, and alternately updates the RIS phase mismatch through sparse calibration. This achieves joint estimation of the two-dimensional angle of arrival, Doppler frequency, and RIS phase mismatch of the mobile source, offering advantages such as strong robustness and high computational speed.

[0004] To achieve the above objectives, the present invention provides the following solution: A RIS-assisted joint angle-Doppler estimation method for moving sources, addressing phase mismatch and impulse noise, comprises the following steps: S1. Acquire the observation signals of the receiver in multiple time slots, and establish an observation model including two-dimensional angle of arrival, Doppler phase evolution and RIS phase mismatch based on the observation signals; S2. Reconstruct the predicted signal according to the observation model, determine the current observation residual based on the actual observation signal and the predicted signal, construct the Lawson robust loss function based on the current observation residual, and calculate the corresponding weighting coefficients based on the Lawson robust loss function; S3. Perform weighted atom tracing according to the weighting coefficients, select source atoms through coarse grid filtering and local refinement, and update the source complex amplitude and residuals using weighted least squares based on the selected source atoms; S4. Reconstruct the RIS incident signal based on the estimated parameters of the source atom, and establish a sparse reconstruction problem about the RIS phase mismatch vector based on the reconstructed RIS incident signal; S5. Estimate the sparse phase mismatch vector according to the sparse reconstruction problem, and perform mismatch unit support set identification, weighted least squares debiasing and unit mode projection according to the estimated sparse phase mismatch vector in sequence. S6. Recalculate the residuals and Lawson weights based on the updated phase mismatch, and repeat steps S3 to S5 until the preset convergence condition is met. Output the elevation angle, azimuth angle, Doppler frequency, and RIS phase mismatch estimation results for each mobile source.

[0005] Preferably, S1 includes: S11. Acquire observation signals from multiple mobile far-field narrowband sources after reflection by a RIS and received by a single-channel omnidirectional receiver in multiple consecutive time slots, wherein the RIS is a uniform planar array composed of multiple reflection units, and different phase control states are applied to each reflection unit of the RIS in each time slot. S12. Construct the spatial response and Doppler phase evolution of each of the mobile far-field narrowband sources after RIS reflection based on the elevation angle, azimuth angle, Doppler frequency and equivalent complex amplitude of each of the mobile far-field narrowband sources; S13. Construct a sparse RIS phase mismatch vector based on the deviation of the actual reflection phase of some reflection units of the RIS from the set phase; S14. The spatial response, the Doppler phase evolution, the phase control state of each time slot, the RIS phase mismatch vector, and the received noise together constitute the observation model.

[0006] Preferably, S2 includes: S21. Reconstruct the predicted signal according to the observation model, and determine the difference between the predicted signal and the actual observed signal as the current observation residual; S22. The residual cost is measured using the Lawson robust loss function based on the current observed residuals; S23. Obtain the weighted surrogate function based on the first-order Taylor expansion of the Lawson robust loss function, and calculate the adaptive weights based on the magnitude of the residuals in each time slot to obtain the weighting coefficients.

[0007] Preferably, S3 includes: S31. Construct candidate atoms in the continuous pitch angle, azimuth angle and Doppler frequency parameter domains, calculate the weighted matching score between each candidate atom and the current residual on the coarse search grid, and retain the candidate positions according to the weighted matching score; S32. Gradually narrow the search range and search step size within the local neighborhood of the retained candidate positions to obtain accurate continuous angles and Doppler parameters; S33. Add the selected source atoms to the source support set, and jointly update the complex amplitude of each selected source atom using a weighted least squares method based on the source support set; S34. Calculate the new residuals based on the updated reconstructed signals, and repeat S31-S33 until the source atom parameters corresponding to each moving source are obtained.

[0008] Preferably, S4 includes: S41. Based on the elevation angle, azimuth angle, Doppler frequency and complex amplitude of the selected source atoms, reconstruct the incident signal arriving at each reflection unit of the RIS in each time slot; S42. Combine the phase control state of each reflection unit in each time slot with the corresponding incident signal component to form a RIS phase mismatch sensing matrix; S43. Determine the phase mismatch residual based on the difference between the predicted received signal and the actual observed signal under the condition of ignoring RIS phase mismatch; S44. Construct the sparse reconstruction problem of the RIS phase mismatch vector based on the phase mismatch residual, the RIS phase mismatch sensing matrix, and the sparsity constraint.

[0009] Preferably, S5 includes: S51. The complex-valued fast iterative shrinking threshold algorithm is used to solve the sparse reconstruction problem of the RIS phase mismatch vector to obtain a temporary estimate of the RIS phase mismatch vector; S52. Identify the phase mismatched reflection units based on the temporary estimated modulus values ​​of each reflection unit, and form a mismatched unit support set; S53. A weighted least squares method is used to remove bias from the identified mismatched unit support set; S54. Project the debiased result onto the physical feasible set corresponding to the phase-type reflection error.

[0010] Preferably, S6 includes: S61. Substitute the currently obtained RIS phase mismatch estimate into the observation model, reconstruct candidate atoms and reconstruct the received signal, and calculate the new observation residual; S62. Update the weights of the Lawson robust loss function based on the new residuals; S63. Repeat the source atom tracing, RIS incident signal reconstruction and sparse phase mismatch calibration process with the updated weights; S64. When the change in the objective function between two consecutive iterations is less than a preset threshold or the number of iterations reaches the maximum number, stop the iteration and output the elevation angle, azimuth angle, Doppler frequency and RIS phase mismatch estimation results of each mobile source.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The Lawson robust loss is used to adaptively weight the observation residuals, which can reduce the impact of impulse noise and large-amplitude anomaly observations, so that the method still has good estimation stability under low signal-to-noise ratio and impulse noise interference.

[0012] (2) Select and refine atoms in the continuous angle-Doppler domain to avoid parameter mismatch and resolution limitation caused by fixed search grid, and realize high-resolution joint estimation of moving source angle and Doppler frequency.

[0013] (3) The source parameter estimation and RIS phase mismatch calibration are iterated in a coordinated manner. The mismatch unit is identified and compensated by the current reconstructed incident signal, which reduces the spatial response distortion and false peaks caused by phase error. Fourth, time-varying RIS coding is used to construct multi-slot observation and complete joint sensing under single receiving channel conditions, which reduces the hardware complexity of the receiving link. Attached Figure Description

[0014] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a RIS-assisted mobile source observation system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the RIS phase mismatch calibration results according to an embodiment of the present invention; Figure 4 This is a comparative schematic diagram showing the variation of Doppler frequency estimation error with signal-to-noise ratio in an embodiment of the present invention; Figure 5 This is a comparative schematic diagram showing the change of pitch angle estimation error with signal-to-noise ratio in an embodiment of the present invention; Figure 6 This is a comparative schematic diagram showing the variation of azimuth estimation error with signal-to-noise ratio in an embodiment of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Example 1: In this embodiment, as Figure 1 As shown, a RIS-assisted joint angle-Doppler estimation method for moving sources, addressing phase mismatch and impulse noise, includes the following steps: S1. Acquire the observation signals from the receiver in multiple time slots, and establish an observation model based on the observation signals, including two-dimensional angle of arrival, Doppler phase evolution, and RIS phase mismatch.

[0019] S1 includes: S11. Acquiring observation signals from multiple mobile far-field narrowband sources reflected by a RIS and received by a single-channel omnidirectional receiver in multiple consecutive time slots, wherein the RIS consists of a uniform planar array of multiple reflecting elements, and different phase control states are applied to each reflecting element of the RIS in each time slot; S12. Constructing the spatial response and Doppler phase evolution of each mobile far-field narrowband source after reflection by the RIS based on the elevation angle, azimuth angle, Doppler frequency, and equivalent complex amplitude of each mobile far-field narrowband source; S13. Constructing a sparse RIS phase mismatch vector based on the deviation of the actual reflection phase of some reflecting elements of the RIS from the set phase; S14. Combining the spatial response, Doppler phase evolution, phase control states of each time slot, RIS phase mismatch vector, and received noise to form an observation model.

[0020] In this embodiment, as Figure 2 As shown, the constructed RIS-assisted mobile source observation system consists of K It consists of a far-field narrowband mobile signal source, a 2-bit RIS (Reflection Link System), and a single-channel omnidirectional receiver. The direct path from the signal source to the receiver is blocked, and the receiver obtains the signal via the RIS reflection link. The RIS is composed of... M The reflective elements are arranged in a uniform planar array, with its center serving as the origin of the coordinate system. The RIS aperture is located at... x - y Plane, normal direction is z Positive axis direction. Receiver in N Sampling is performed within each time slot, with an interval between adjacent sampling time slots being [missing information]. .

[0021] Record No. k The information source is in the first... n The elevation and azimuth angles incident on the RIS in each time slot are respectively and Its Doppler frequency is . No. m The position of each RIS unit is , wavelength is λ Pi is π π wave number is , j If the imaginary unit is used, then the RIS array steering vector The m Each component can be represented as: .

[0022] The phase control matrix of RIS is represented as follows: , , in, T Indicates transpose. Indicates the first n RIS phase control vector for each time slot Indicates all N The phase control matrix of the time-slot RIS. For a 2-bit RIS, Available from Choose from the options. Considering that only a small number of RIS cells experience phase mismatch, define a sparse mismatch vector. And let the actual RIS response matrix be: , in, Indicates the first M The mismatch coefficient of each RIS unit, For the constructed RIS mismatch matrix, This represents a unit diagonal matrix, and diag(·) is the diagonalization operator. For normal elements... For mismatched units, , This indicates the phase error of the unit.

[0023] by Indicated by If is a diagonal matrix composed of diagonal elements, then the first... n The observation signal for each time slot can be written as: , in, Indicates the first n The observation signal in each time slot, Indicates the first k The equivalent complex amplitude of each information source, express M An identity matrix of order 1. This indicates system noise.

[0024] S2. Reconstruct the predicted signal based on the observation model, determine the current observation residual based on the actual observation signal and the predicted signal, construct the Lawson robust loss function based on the current observation residual, and calculate the corresponding weighting coefficients based on the Lawson robust loss function.

[0025] S2 includes: S21. Reconstructing the predicted signal based on the observation model, and determining the difference between the predicted signal and the actual observed signal as the current observation residual; S22. Measuring the residual cost using the Lawson robust loss function based on the current observation residual; S23. Obtaining the weighted surrogate function based on the first-order Taylor expansion of the Lawson robust loss function, and calculating the adaptive weights based on the magnitude of the residuals in each time slot to obtain the weighting coefficients.

[0026] In this embodiment, the source parameters, source complex amplitude, and RIS phase mismatch obtained in the current iteration are used to reconstruct the first... n Received signal per time slot And let the residual and residual power be respectively and Impulse noise will cause a small amount of The magnitude increases significantly, and if the traditional least squares criterion is directly applied, anomalous observations may dominate parameter updates.

[0027] To suppress the influence of anomalous residuals, the Lawson loss function is selected. Let s represent the non-negative residual power in any time slot. i In the next outer iteration i Indicates the outer iteration number, Indicates the first n The current residual power of each time slot, This represents the weight of the time slot. The Lawson loss and the weights obtained from its first-order Taylor expansion can be expressed as: , , , in, This represents the Lawson loss value. Indicates the first i Lawson weight matrix in the next iteration p Indicates shape parameters, Represents the scale parameter, and p satisfy , It is any positive number less than 0.01.

[0028] make If the constant term is independent of the parameter to be estimated, then the first-order Taylor upper bound of the Lawson loss is: , The above formula transforms the non-quadratic Lawson loss into a weighted least squares surrogate, with large abnormal residuals corresponding to smaller weights and normal observations corresponding to larger weights.

[0029] S3. Perform weighted atom tracing based on the weighting coefficients, select source atoms through coarse grid screening and local refinement, and update the source complex amplitude and residuals using weighted least squares based on the selected source atoms.

[0030] S3 includes: S31. Constructing candidate atoms in the continuous pitch, azimuth, and Doppler frequency parameter domains, calculating the weighted matching score between each candidate atom and the current residual on the coarse search grid, and retaining the candidate positions based on the weighted matching score; S32. Gradually narrowing the search range and search step size in the local neighborhood of the retained candidate positions to obtain accurate continuous angles and Doppler parameters; S33. Adding the selected source atoms to the source support set, and jointly updating the complex amplitude of each selected source atom using a weighted least squares method based on the source support set; S34. Calculating the new residual based on the updated reconstructed signal, and repeating S31-S33 until the source atom parameters corresponding to each moving source are obtained.

[0031] In this embodiment, the observation signals of all time slots are arranged in chronological order to form an observation vector. For a candidate angle-Doppler parameter set ,in , and Given candidate elevation angles, candidate azimuth angles, and candidate Doppler frequencies, construct their Doppler phase evolution vectors across all time slots. : .

[0032] The current RIS phase mismatch estimate is Under the conditions, Indicates the first i Mismatch estimation in the next outer iteration. Candidate source atoms are denoted as... , representing the predicted observation vector formed by a unit complex amplitude source across all observation time slots. We have: , in, This indicates element-wise multiplication. This atom simultaneously describes the spatial response of the candidate orientation, the time-slot phase evolution of the candidate Doppler frequency, the RIS encoding, and the current RIS phase mismatch.

[0033] make Indicates to be estimated K Angle-Doppler parameter set, This represents the corresponding complex magnitude vector. This indicates the preset continuous pitch, azimuth, and Doppler frequency search domain. Let represent the sparse regularization parameter of RIS phase mismatch. Then the joint optimization objective of the moving source parameters and RIS phase mismatch is: , , in, Indicates the first The atom in the first n Elements of each time slot. This objective simultaneously constrains the observation fitting error, the sparse representation of the moving source in the continuous angle-Doppler domain, and the sparsity of RIS phase mismatch.

[0034] In the i In the next outer iteration, the fixed and Then, the Lawson loss in the above equation is replaced with a weighted proxy of the first-order Taylor upper bound. Representing the L2 norm, we obtain the continuous atom tracing subproblem: , , The above equation is a non-convex continuous parameter optimization problem. In this embodiment, a weighted atom tracing method with coarse mesh screening, local refinement, and support set update is used to approximate the solution.

[0035] Arrange the current residuals into a residual vector according to the time slot sequence. This is the result of subtracting the currently reconstructed observation vector from the observed vector. Represents candidate parameter groups The normalized weighted matching score, in If we denote the conjugate transpose, then the matching score is: .

[0036] First, on a coarse grid of elevation, azimuth, and Doppler frequency, the matching score for each candidate atom is calculated according to the above formula, and candidate positions with higher scores are retained. Then, the search range and search step size are narrowed near the retained positions, performing at least one local refinement to obtain more accurate candidate elevation, azimuth, and Doppler frequencies in the continuous parameter domain. The angle and frequency step sizes of the coarse grid, as well as the number and step size of the local refinement, can be set according to computational resources and the required estimation accuracy.

[0037] Each refined candidate atom is selected and added to the source support set. . This is the set of indices of the currently selected source atoms. Construct an atom matrix with all atoms in the support set as columns. .make This represents the complex amplitude estimate of each atom within the support set. Represents a positive decimal to prevent instability during matrix inversion. Let represent the identity matrix of the same order as the number of columns in the atomic matrix. Then the complex magnitude can be updated using regularized weighted least squares as follows: .

[0038] Based on the updated atom matrix and complex amplitude, the received signal is reconstructed and the residual is updated. Further local cyclic refinement can be performed on each atom within the support set, followed by joint updates of the complex amplitude and residual. This process is repeated until the support set size reaches a preset number of sources, the maximum weighted matching score is lower than a preset threshold, or the residual decrease is lower than a preset threshold.

[0039] S4. Reconstruct the RIS incident signal based on the estimated parameters of the source atoms, and establish a sparse reconstruction problem about the RIS phase mismatch vector based on the reconstructed RIS incident signal.

[0040] S4 includes: S41. Reconstructing the incident signal arriving at each RIS reflection unit in each time slot based on the elevation angle, azimuth angle, Doppler frequency, and complex amplitude of the selected source atoms; S42. Combining the phase control state of each reflection unit in each time slot with the corresponding incident signal component to form the RIS phase mismatch sensing matrix; S43. Determining the phase mismatch residual based on the difference between the predicted received signal and the actual observed signal under the condition of ignoring RIS phase mismatch; S44. Constructing a sparse reconstruction problem of the RIS phase mismatch vector based on the phase mismatch residual, the RIS phase mismatch sensing matrix, and sparsity constraints.

[0041] In this embodiment, the incident signal at each reflection unit of the RIS is reconstructed in each time slot using the source support set, elevation angle, azimuth angle, Doppler frequency, and complex amplitude of each atom obtained in S3. n The reconstructed incident signal vector for each time slot is denoted as... , its first m element This indicates the first time slot. m The reconstructed incident signal at each reflecting unit. This represents the index of an atom within the supporting set. , , and They represent the first The elevation angle, azimuth angle, Doppler frequency, and complex amplitude of each selected atom are estimated, and the RIS incident signal is reconstructed as follows: .

[0042] Constructing the RIS phase mismatch sensing matrix Its rows correspond one-to-one with the observation time slots, and its columns correspond one-to-one with the RIS reflection units. express The n Line 1 m Column elements, let Indicates ignoring RIS phase mismatch. n Predicted received signal for each time slot, Indicates that it is composed of all The constructed predicted received signal vector, This represents the phase mismatch residual vector. Its construction relation is: , , , As can be seen from the above equation, the effect of phase mismatch on the received signal can be determined by... and The linear representation of the product, It can be used as an observable for recovering RIS phase mismatch.

[0043] S5. Estimate the sparse phase mismatch vector based on the sparse reconstruction problem, and perform mismatch unit support set identification, weighted least squares debiasing, and unit mode projection in sequence based on the estimated sparse phase mismatch vector.

[0044] S5 includes: S51. Solving the sparse reconstruction problem of the RIS phase mismatch vector using a complex-valued fast iterative shrinking threshold algorithm to obtain a temporary estimate of the RIS phase mismatch vector; S52. Identifying the reflection units that have phase mismatch based on the magnitude of the temporary estimate of each reflection unit, forming a mismatch unit support set; S53. Performing debiasing processing on the identified mismatch unit support set using a weighted least squares method; S54. Projecting the debiased result onto the physically feasible set corresponding to the phase-type reflection error.

[0045] In this embodiment, a sparse regularization parameter introduced in the joint optimization objective is used. and with This represents the sum of the magnitudes of the vector elements. Based on the phase mismatch residual vector and the sensing matrix of S4, a weighted sparse reconstruction problem is constructed: , In the formula, This is the square root of the current weighting matrix. The first term in the above equation is used to fit the phase mismatch residual, and the second term is used to constrain the non-zero mismatch to be concentrated in a small number of reflection units.

[0046] The above equation is solved using a complex-valued fast iterative shrinkage threshold algorithm. The square root of the weighting matrix is ​​applied to both the phase mismatch sensing matrix and the phase mismatch residual vector to obtain the weighted sensing matrix. and weighted residual vector .by t Indicates the internal iteration number, with Indicates the first t Temporary mismatch estimation in the next internal iteration, with Indicates an acceleration auxiliary variable, to Indicates the iteration step size, in Indicates the threshold is For the complex-valued soft threshold operator, the update formula for the temporary mismatch estimate is: , , .

[0047] For any complex number z and positive threshold The complex-valued soft threshold operator is: , make To avoid positive decimals divided by zero, the iteration step size can be set as follows: .

[0048] by Indicates the first t The acceleration parameters for the next internal iteration are initially set to one. The acceleration parameters and auxiliary variables are then updated as follows: , , Each internal iteration first updates the temporary mismatch estimate along the decreasing direction of the weighted fitting error, then performs complex soft threshold shrinkage according to the complex soft threshold operator formula, and accelerates the process according to the acceleration parameter and auxiliary variable update formula, until the change in the mismatch vector between two adjacent internal iterations is less than the preset threshold or the preset maximum number of internal iterations is reached.

[0049] Based on the magnitude of the mismatch in each reflector element in the temporary mismatch estimate, a preset relative threshold is used to identify reflectors experiencing phase mismatch, forming a support set of mismatched elements. Let... This represents the temporary mismatch estimate obtained at the end of the internal iteration. The support set of the identified mismatch units, The relative threshold represents the condition that satisfies the following conditions. .make Indicates from Selecting support sets The submatrix obtained from the corresponding columns, This represents the mismatch estimate after bias correction. The support set identification and bias correction process is as follows: , , , In the formula, This represents the maximum value of the modulus of the elements in the vector. The first part represents the temporary mismatch estimate. m One element, To support the collection The supplement, The vector is zero. The above equation removes sparse constraints on the identified mismatched support set and performs a new weighted least squares estimation, thereby eliminating the underestimation of amplitude caused by soft threshold contraction.

[0050] Finally, a unit modulus projection is performed on the mismatch after debiasing. The phase angle of a complex number is represented by... Indicates the first m After phase mismatch estimation for each corrected reflector element, the projection relationship is as follows: , , This process ensures that the phase mismatch estimation meets the physical constraints of the actual RIS reflector unit.

[0051] S6. Recalculate the residuals and Lawson weights based on the updated phase mismatch, and repeat steps S3 to S5 until the preset convergence condition is met. Output the elevation angle, azimuth angle, Doppler frequency, and RIS phase mismatch estimation results for each mobile source.

[0052] S6 includes: S61. Substituting the currently obtained RIS phase mismatch estimate into the observation model, reconstructing candidate atoms and reconstructing the received signal, and calculating the new observation residual; S62. Updating the weights of the Lawson robust loss function based on the new residual; S63. Repeating the source atom tracking, RIS incident signal reconstruction, and sparse phase mismatch calibration process with the updated weights; S64. Stopping the iteration when the change in the objective function between two adjacent iterations is less than a preset threshold or the number of iterations reaches the maximum number, and outputting the elevation angle, azimuth angle, Doppler frequency, and RIS phase mismatch estimation results of each moving source.

[0053] In this embodiment, the RIS phase mismatch estimate obtained in S5 is substituted into the... n In the formula for the observed signal in each time slot, candidate source atoms are reconstructed and the received signal is reconstructed to obtain a new observation residual. Then, the Lawson weights are updated according to S2. Based on the updated weights and RIS phase mismatch, the weighted continuous atom tracking in S3, the RIS incident signal reconstruction in S4, and the sparse phase mismatch calibration in S5 are repeated.

[0054] The iteration stops when the number of outer iterations reaches the preset maximum. The output includes the elevation angle, azimuth angle, and Doppler frequency of each moving signal source, as well as the RIS phase mismatch vector.

[0055] It is worth noting that this embodiment employs a joint estimation framework that coordinates continuous angle-Doppler atom tracking with RIS sparse phase mismatch calibration. This framework improves the robustness of estimation under impulse noise and RIS phase mismatch conditions while avoiding parameter mismatch and resolution limitations caused by fixed grids. Specifically, in the outer iteration, Lawson robust weights are constructed based on the current observation residuals, and the moving source angle-Doppler parameters and RIS phase mismatch are updated alternately. During the source parameter update process, efficient selection of candidate atoms is achieved through coarse grid screening, local continuous refinement, and weighted least squares joint updates. During the phase mismatch calibration process, a sparse reconstruction model is established using the reconstructed RIS incident signal. Through complex-valued fast iterative threshold shrinkage, support set identification, bias removal, and unity mode projection, a phase mismatch estimate that satisfies the actual physical constraints is obtained. Through the above-mentioned alternating iterative mechanism, this embodiment achieves stable joint estimation of the two-dimensional angle of arrival, Doppler frequency, and RIS phase mismatch of the moving source.

[0056] Example 2: To verify the effectiveness of the method of this invention, simulation experiments were conducted on the MATLAB R2023b platform. The experimental computer was configured with an Intel Core i7-12700 processor. The RIS used an 8×8 uniform planar array, with a total number of reflection units of [missing information]. M =64, the number of continuously acquired observation time slots isN =100, the number of mobile sources is fixed. K =2. Under the above parameter settings, the RIS phase mismatch calibration performance and the moving source angle-Doppler joint estimation performance of the present invention were verified.

[0057] Figure 3 The diagram shows the RIS phase mismatch calibration results under a signal-to-noise ratio of 10 dB according to an embodiment of the present invention. The horizontal axis represents the RIS cell index, and the vertical axis represents the phase mismatch amplitude of each cell. Red circles represent preset true mismatch values, and black crosses represent the estimation results of the present invention. For the few RIS cells that have mismatched, the estimated values ​​are generally close to the true values. For cells that have not mismatched, the estimation results remain near zero. This result shows that the present invention can effectively identify phase mismatched cells and accurately calibrate the phase mismatch amplitude.

[0058] Figure 4 , Figure 5 , Figure 6 The figures show comparative diagrams illustrating the changes in source elevation angle, azimuth angle, and Doppler frequency estimation errors as a function of signal-to-noise ratio (SNR) in embodiments of the present invention. The horizontal axis of each figure represents the SNR in dB, and the vertical axis represents the root mean square error (RMSE). The Doppler frequency error is expressed in Hz, while the azimuth and elevation angle errors are expressed in degrees (deg). Smaller error values ​​indicate more accurate estimations of the corresponding parameters. The comparison methods include the DNN-Robust-DANM method based on deep neural network reconstruction and robust decoupling atomic norm minimization, and the HWI-MMP-DANM method which recovers low-rank information through atomic norm and uses an improved matrix pencil method to estimate parameters. CRLB serves as a theoretical lower bound reference. As shown in the figures, the errors of all methods decrease with increasing SNR. The present invention exhibits lower errors in the three parameter dimensions of pitch angle, azimuth angle, and Doppler frequency compared to the comparative methods, and is closer to CRLB, indicating that the continuous atomic refinement and sparse phase mismatch calibration mechanism can improve the joint estimation accuracy and mismatch resistance. Table 1 further shows that the single-run time of the present invention is shorter than that of the two comparative methods, thus balancing parameter estimation performance and computational efficiency.

[0059] Table 1: .

[0060] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A RIS-assisted joint angle-Doppler estimation method for moving sources accommodating phase mismatch and impulse noise, characterized in that, Includes the following steps: S1. Acquire the observation signals of the receiver in multiple time slots, and establish an observation model including two-dimensional angle of arrival, Doppler phase evolution and RIS phase mismatch based on the observation signals; S2. Reconstruct the predicted signal according to the observation model, determine the current observation residual based on the actual observation signal and the predicted signal, construct the Lawson robust loss function based on the current observation residual, and calculate the corresponding weighting coefficients based on the Lawson robust loss function; S3. Perform weighted atom tracing according to the weighting coefficients, select source atoms through coarse grid filtering and local refinement, and update the source complex amplitude and residuals using weighted least squares based on the selected source atoms; S4. Reconstruct the RIS incident signal based on the estimated parameters of the source atom, and establish a sparse reconstruction problem about the RIS phase mismatch vector based on the reconstructed RIS incident signal; S5. Estimate the sparse phase mismatch vector according to the sparse reconstruction problem, and perform mismatch unit support set identification, weighted least squares debiasing and unit mode projection according to the estimated sparse phase mismatch vector in sequence. S6. Recalculate the residuals and Lawson weights based on the updated phase mismatch, and repeat steps S3 to S5 until the preset convergence condition is met. Output the elevation angle, azimuth angle, Doppler frequency, and RIS phase mismatch estimation results for each mobile source.

2. The RIS-assisted joint angle-Doppler estimation method for moving sources oriented towards phase mismatch and impulse noise as described in claim 1, characterized in that, S1 includes: S11. Acquire observation signals from multiple mobile far-field narrowband sources after reflection by a RIS and received by a single-channel omnidirectional receiver in multiple consecutive time slots, wherein the RIS is a uniform planar array composed of multiple reflection units, and different phase control states are applied to each reflection unit of the RIS in each time slot. S12. Construct the spatial response and Doppler phase evolution of each of the mobile far-field narrowband sources after RIS reflection based on the elevation angle, azimuth angle, Doppler frequency and equivalent complex amplitude of each of the mobile far-field narrowband sources; S13. Construct a sparse RIS phase mismatch vector based on the deviation of the actual reflection phase of some reflection units of the RIS from the set phase; S14. The spatial response, the Doppler phase evolution, the phase control state of each time slot, the RIS phase mismatch vector, and the received noise together constitute the observation model.

3. The RIS-assisted joint angle-Doppler estimation method for moving sources oriented towards phase mismatch and impulse noise as described in claim 1, characterized in that, S2 includes: S21. Reconstruct the predicted signal according to the observation model, and determine the difference between the predicted signal and the actual observed signal as the current observation residual; S22. The Lawson robust loss function is used to measure the residual cost based on the current observed residuals; S23. Obtain the weighted surrogate function based on the first-order Taylor expansion of the Lawson robust loss function, and calculate the adaptive weights based on the magnitude of the residuals in each time slot to obtain the weighting coefficients.

4. The RIS-assisted joint angle-Doppler estimation method for moving sources oriented towards phase mismatch and impulse noise as described in claim 1, characterized in that, S3 includes: S31. Construct candidate atoms in the continuous pitch angle, azimuth angle and Doppler frequency parameter domains, calculate the weighted matching score between each candidate atom and the current residual on the coarse search grid, and retain the candidate positions according to the weighted matching score; S32. Gradually narrow the search range and search step size within the local neighborhood of the retained candidate positions to obtain accurate continuous angles and Doppler parameters; S33. Add the selected source atoms to the source support set, and jointly update the complex amplitude of each selected source atom using a weighted least squares method based on the source support set; S34. Calculate the new residuals based on the updated reconstructed signals, and repeat S31-S33 until the source atom parameters corresponding to each moving source are obtained.

5. The RIS-assisted joint angle-Doppler estimation method for moving sources oriented towards phase mismatch and impulse noise as described in claim 4, characterized in that, S4 includes: S41. Based on the elevation angle, azimuth angle, Doppler frequency and complex amplitude of the selected source atoms, reconstruct the incident signal arriving at each reflection unit of the RIS in each time slot; S42. Combine the phase control state of each reflection unit in each time slot with the corresponding incident signal component to form a RIS phase mismatch sensing matrix; S43. Determine the phase mismatch residual based on the difference between the predicted received signal and the actual observed signal under the condition of ignoring RIS phase mismatch; S44. Construct the sparse reconstruction problem of the RIS phase mismatch vector based on the phase mismatch residual, the RIS phase mismatch sensing matrix, and the sparsity constraint.

6. The RIS-assisted joint angle-Doppler estimation method for moving sources oriented towards phase mismatch and impulse noise as described in claim 1, characterized in that, S5 includes: S51. The complex-valued fast iterative shrinking threshold algorithm is used to solve the sparse reconstruction problem of the RIS phase mismatch vector to obtain a temporary estimate of the RIS phase mismatch vector; S52. Identify the phase mismatched reflection units based on the temporary estimated modulus values ​​of each reflection unit, and form a mismatched unit support set; S53. A weighted least squares method is used to remove bias from the identified mismatched unit support set; S54. Project the debiased result onto the physical feasible set corresponding to the phase-type reflection error.

7. The RIS-assisted joint angle-Doppler estimation method for moving sources oriented towards phase mismatch and impulse noise as described in claim 1, characterized in that, S6 includes: S61. Substitute the currently obtained RIS phase mismatch estimate into the observation model, reconstruct candidate atoms and reconstruct the received signal, and calculate the new observation residual; S62. Update the weights of the Lawson robust loss function based on the new residuals; S63. Repeat the source atom tracing, RIS incident signal reconstruction and sparse phase mismatch calibration process with the updated weights; S64. When the change in the objective function between two consecutive iterations is less than a preset threshold or the number of iterations reaches the maximum number, stop the iteration and output the elevation angle, azimuth angle, Doppler frequency and RIS phase mismatch estimation results of each mobile source.

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