A hankel low-rank restoration and robust phase ranging method for low-power bluetooth structured missing channel and interference

Abstract

The present application relates to a kind of low-power bluetooth structured Hankel low-rank recovery and robust phase ranging method for missing channel and interference, belong to low-power bluetooth phase ranging and indoor positioning technical field.The two-way complex response of initiation equipment and reflecting equipment on effective frequency point is obtained, second-order equivalent frequency domain channel is constructed and mapped to complete frequency grid;After initialization to missing frequency point, Hankel low-rank truncation and anti-Hankel reconstruction are carried out, fixed segmented credible weight is generated according to the structural residual of first recovery sequence and initial sequence, and observation value and recovery value are iteratively fused;The square root of recovered second-order equivalent channel is point by point, and branch is selected according to the continuity of adjacent frequency point, to obtain first-order equivalent frequency domain channel, and then estimate propagation delay and distance.The present application can complete fixed missing frequency point and suppress random interference frequency point simultaneously, improve channel recovery quality, phase continuity and ranging stability in multipath environment.

Description

Technical Field

[0001] This invention belongs to the field of Bluetooth Low Energy phase ranging and indoor positioning technology, and relates to a Hankel low-rank recovery and robust phase ranging method for Bluetooth Low Energy structured missing channels and interference. Background Technology

[0002] With the development of IoT terminals, mobile devices, warehouse asset management, indoor navigation, and proximity interaction technologies, low-cost, low-power wireless ranging technologies that can provide high ranging accuracy have attracted widespread attention. Bluetooth Low Energy (BLE) features high terminal penetration, mature radio frequency hardware, low power consumption, and easy deployment, making it suitable for building indoor positioning and proximity sensing systems.

[0003] Existing low-power Bluetooth ranging methods mainly include received signal strength indication (RSI) ranging, angle-of-arrival (AOA) positioning, and frequency domain ranging based on multi-frequency phase observation. RSI ranging relies on a propagation loss model and is susceptible to obstruction, human movement, and environmental changes. AOA positioning typically requires array antennas and multi-channel RF structures, resulting in high hardware costs and calibration complexity. Frequency domain ranging based on multi-frequency phase observation estimates propagation delay by utilizing phase changes at different frequencies, offering high potential ranging resolution, but it is sensitive to the number of frequency points, effective bandwidth, phase continuity, and abnormal frequency points.

[0004] In practical Bluetooth Low Energy systems, the ranging frequency grid typically cannot remain continuous and complete due to factors such as protocol configuration, broadcast channel occupancy, frequency scheduling, hardware sampling capabilities, and coexisting interference. On the one hand, some frequencies may be permanently missing according to the protocol or channel configuration, forming structured gaps with known locations and recurring occurrences. On the other hand, Wi-Fi, ZigBee devices, or other co-frequency devices may subject individual acquired frequencies to random interference, resulting in significant amplitude and phase deviations in the corresponding complex observations. Structured gaps reduce effective bandwidth and disrupt the continuity of the frequency domain sequence, while random interference may introduce erroneous observations into the recovery process. Both factors together cause delay spectrum peak shifts, an increase in false peaks, or unstable first-path identification.

[0005] Existing zero-filling, nearest-neighbor filling, linear interpolation, and spline interpolation methods primarily rely on local smoothness, failing to fully utilize the global structure of multipath channels formed by the superposition of a finite number of complex exponential components in the frequency domain. When multipath is strong or missing frequency points are continuously distributed, local interpolation is prone to amplitude and phase deviations. Dividing the effective frequency band into multiple sub-bands and performing spectral estimation separately can avoid some missing locations, but it reduces the effective bandwidth of each sub-band, and there is a lack of unified phase continuity constraints between different sub-bands. Atomic norm, sparse reconstruction, or semidefinite programming methods can utilize time-delay sparsity, but they are computationally intensive and parameter-sensitive; neural network-based recovery methods require training data and may be affected by environmental, equipment, and missing pattern variations.

[0006] The Hankel low-rank method can recover missing data by utilizing the low-rank or near-low-rank properties of the Hankel matrix corresponding to a finite complex exponential sequence. However, if all measured frequency points are considered completely reliable, random interference frequencies will be repeatedly written back in each iteration, contaminating the low-rank structure. If the frequency point weights are re-estimated in each iteration, the weights and the recovered results will change, which may cause iterative oscillations or convergence instability. In addition, the equivalent channel obtained by Bluetooth Low Energy bidirectional phase interaction usually contains a square form, and directly using it for one-way delay estimation may introduce delay scale inconsistencies and square root symbol jump problems.

[0007] Therefore, a ranging method is needed that can uniformly handle the structured missing frequency points and random interference frequency points of Bluetooth Low Energy, make full use of the low-rank structure of the multipath frequency domain channel, and stably recover the first-order equivalent channel from the bidirectional second-order equivalent channel. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a Hankel low-rank recovery and robust phase ranging method for low-power Bluetooth structured missing channels and interference.

[0009] To achieve the above objectives, the present invention provides the following technical solution: A Hankel low-rank recovery and robust phase ranging method for Bluetooth Low Energy structured missing channels and interference includes the following steps.

[0010] S1, the Bluetooth Low Energy initiating device and the reflecting device perform bidirectional signal interaction at multiple frequency points, acquire in-phase and quadrature (IQ) data or complex responses of the initiating device and the reflecting device at each effective frequency point, normalize the amplitude and phase of the complex responses at both ends and multiply them to obtain the second-order equivalent frequency domain channel observation sequence at the effective frequency point, and determine the structured missing frequency points based on the complete frequency point set and the effective frequency point set.

[0011] S2, the second-order equivalent frequency domain channel observation sequence is mapped to a complete frequency grid, and the structured missing frequency points are initialized to obtain an initial complete frequency domain sequence. Internal missing frequency points located between two valid frequency points are interpolated linearly, while edge missing frequency points located outside the coverage area of ​​valid frequency points are assigned values ​​using the nearest neighbor valid frequency point.

[0012] S3, embed the initial complete frequency domain sequence into a Hankel matrix, perform a first low-rank truncation on the Hankel matrix, and perform inverse Hankel reconstruction on the low-rank truncated Hankel matrix to obtain the first temporary recovery sequence.

[0013] S4. Calculate the structural anomaly score for each frequency point based on the structural residual between the initial complete frequency domain sequence and the first temporary recovery sequence. Generate segmented confidence weights for each frequency point based on the structural anomaly scores, and determine these segmented confidence weights as fixed confidence weights for subsequent low-rank recovery iterations. Frequency points with missing structure correspond to low confidence weights; effective frequency points with lower structural anomaly scores correspond to high confidence weights; effective frequency points with structural anomaly scores between two thresholds correspond to intermediate confidence weights that decrease with the degree of anomaly; and effective frequency points with higher structural anomaly scores correspond to low confidence weights.

[0014] S5. According to the fixed credible weight, the second-order equivalent frequency domain channel observation value and the corresponding temporary recovery value on the effective frequency point are weighted and updated. The temporary recovery value on the structured missing frequency point is used as the update value of the corresponding frequency point. The Hankel matrix construction, low-rank truncation, inverse Hankel reconstruction and weighted update are repeatedly executed until the preset convergence condition is met, and the recovered complete second-order equivalent frequency domain channel sequence is obtained.

[0015] S6. Perform complex square root operation on the complete second-order equivalent frequency domain channel sequence for each frequency point. In the two square root candidate branches corresponding to each frequency point, select the square root branch according to the continuity between adjacent frequency points to obtain the first-order equivalent frequency domain channel sequence.

[0016] S7. The first-order equivalent frequency domain channel sequence is input into the distance estimator to obtain the propagation delay estimate, and the distance estimate between the initiating device and the reflecting device is obtained based on the propagation delay estimate. The distance estimator employs an Inverse Fast Fourier Transform (IFFT) delay peak estimator or a Multiple Signal Classification (MUSIC) high-resolution spectrum estimator.

[0017] The present invention also provides a low-power Bluetooth structured missing channel recovery and robust phase ranging device, including a bidirectional data acquisition module, a second-order equivalent channel construction module, a frequency point mapping and initialization module, a Hankel low-rank recovery module, an anomaly weight generation module, a frequency point weighted update module, a square root branch selection module, and a distance estimation module. The output of the bidirectional data acquisition module is connected to the second-order equivalent channel construction module, and the output of the second-order equivalent channel construction module is connected to the frequency point mapping and initialization module. The Hankel low-rank recovery module receives the initial complete frequency domain sequence output by the frequency point mapping and initialization module and outputs a temporary recovery sequence. The anomaly weight generation module receives the initial complete frequency domain sequence and the first temporary recovery sequence and outputs fixed reliable weights. The frequency point weighted update module receives the second-order equivalent frequency domain channel observation sequence, the temporary recovery sequence, and the fixed reliable weights, and feeds back the updated complete frequency domain sequence to the Hankel low-rank recovery module. The square root branch selection module receives the converged complete second-order equivalent frequency domain channel sequence and outputs a first-order equivalent frequency domain channel sequence. The distance estimation module outputs the propagation delay estimate and the distance estimate based on the first-order equivalent frequency domain channel sequence.

[0018] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described Hankel low-rank recovery and robust phase ranging method.

[0019] Compared with the prior art, the present invention has at least the following beneficial effects.

[0020] (1) The complex responses at both ends of the bidirectional phase ranging link are normalized and multiplied, and the initial phase terms of the opposite local oscillators are used to cancel each other out, thereby constructing a second-order equivalent frequency domain channel suitable for unified recovery processing and reducing the impact of the initial phase difference at both ends on subsequent ranging.

[0021] (2) Embedding the second-order equivalent frequency domain channel into the Hankel matrix and using the low-rank or near-low-rank structure formed by the superposition of finite complex exponents of the multipath channel to recover the full frequency band of the missing structured frequency points. Compared with interpolation between adjacent frequency points or dividing the frequency band into multiple sub-bands, it can make fuller use of the complete frequency span and global channel structure.

[0022] (3) Only after the first low-rank reconstruction, segmented reliable weights are generated based on the structural residuals, and the segmented reliable weights are used in subsequent iterations. This allows normal observations, suspicious observations, and missing positions to participate in the update to different degrees, which can suppress the repeated writing back of random interference frequency points and avoid the oscillation caused by the repeated changes of weights with iteration.

[0023] (4) Perform a complex square root operation on the frequency point of the recovered second-order equivalent frequency domain channel, and select positive and negative square root branches according to the continuity of adjacent frequency points. This can suppress the phase jump caused by the multi-valuedness of the square root, and make the recovered first-order equivalent frequency domain channel suitable for inputting different types of back-end delay estimators.

[0024] (5) No neural network needs to be pre-trained, and no large-scale positive definite programming needs to be solved. It can be completed by singular value decomposition, anti-diagonal averaging and point-by-point weighting, which makes it easy to implement in low-power Bluetooth controllers, host processors, embedded processors or host computers.

[0025] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0026] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 A schematic diagram of data acquisition for a low-power Bluetooth phase ranging system; Figure 2 A schematic diagram of Hankel matrix embedding for a frequency domain sequence; Figure 3 This is a schematic diagram of low-rank truncation of the Hankel matrix; Figure 4 A schematic diagram of the inverse Hankel reconstruction of a low-rank Hankel matrix; Figure 5 This is an overall flowchart of the Hankel low-rank recovery and robust phase ranging method of the present invention; Figure 6 This is a comparison chart of the mean absolute error of ranging under different Rician factors for different missing frequency processing methods when using the multipath Saleh-Valenzuela model. Figure 6 (a) shows the results of different processing methods applied to the inverse fast Fourier transform delay peak estimator. Figure 6 (b) shows the results of different processing methods used to access the high-resolution spectrum estimator for multiple signal classification. Detailed Implementation

[0027] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0028] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0029] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0030] Implementation Method 1: Bidirectional Phase Data Acquisition and Second-Order Equivalent Channel Construction like Figure 1 As shown, a Bluetooth Low Energy phase ranging system includes at least one initiating device and one reflecting device. The initiating device and the reflecting device perform bidirectional signal interaction according to a preset frequency point sequence, and obtain in-phase and quadrature data at each effective frequency point. By combining the in-phase and quadrature components into a complex number, the corresponding complex responses at both ends can be obtained.

[0031] The first in the complete frequency grid Each frequency point is denoted as During a single two-way ranging interaction, it is assumed that the propagation channel approximately satisfies reciprocity, the local oscillators at both ends maintain phase continuity during transmit / receive switching and phase acquisition, and the initial phase difference between the two ends has opposite signs in the two transmission directions. The reflecting device and the initiating device in the... The complex responses obtained at each frequency point are expressed as follows:

[0032]

[0033] in, For the reflecting device in the first Complex responses obtained at each frequency point For the initiating device in the Complex responses obtained at each frequency point and These are the RF link amplitude and phase calibration factors for the reflecting and initiating devices, respectively. For the two devices in the first The initial phase difference of the local oscillator at each frequency point For the first The first-order equivalent frequency domain channel response at each frequency point and These are the noise and hardware error terms for the two devices, respectively. It is the imaginary unit.

[0034] Normalize the amplitude and phase of the complex responses at both ends and multiply them to obtain the first... Second-order equivalent frequency domain channel observations at each effective frequency point:

[0035] because The initial phase difference between the two local oscillators cancels out in the product. This is true if the higher-order noise product is ignored or incorporated into the equivalent noise term. Approximate correspondence In practice, the amplitude and phase calibration factor can be obtained from the equipment factory calibration, online loopback calibration, or reference link calibration; when the calibration factor is already included in the underlying output, the complex responses at both ends after calibration can be directly multiplied.

[0036] For including The first-order equivalent frequency domain channel of the propagation path is expressed as:

[0037] in, For the number of propagation paths, For the first Complex gain of each propagation path For the first The propagation delay of each propagation path. The second-order equivalent frequency domain channel can be expressed as:

[0038] Therefore, the second-order equivalent frequency domain channel is still a superposition of a finite number of complex exponential components. The Hankel matrix constructed from this frequency domain sequence has a low-rank or approximately low-rank structure, providing a structural basis for subsequent recovery of missing frequency points.

[0039] Implementation Method 2: Complete Frequency Grid Mapping and Missing Frequency Point Initialization The complete frequency set and the effective frequency set are represented as follows:

[0040]

[0041] in, This represents the total number of frequency points in the complete frequency grid. Determined by the Bluetooth Low Energy channel configuration table, frequency index table, sampling control logic, or data validity flag. Belongs to Not belonging The frequency points are those with missing structure. For frequency points that were directly removed during the acquisition phase due to significant interference, they can also be included in the... Frequency points that were not pre-removed but had unknown interference were identified through subsequent structural anomaly scores.

[0042] To uniformly represent observation relationships, a validity mask is defined. :

[0043] The missing observation model for the second-order equivalent frequency domain channel is:

[0044] in, This is the equivalent error term formed by the multiplication of bidirectional complex responses, RF link errors, and environmental noise. For Since there are no reliable observations, the corresponding frequency values ​​need to be obtained by Hankel low-rank recovery.

[0045] The valid observations are mapped to a complete frequency grid arranged in ascending frequency order, and missing locations are initialized. The initial complete frequency domain sequence is represented as follows:

[0046] The interpolation coefficients corresponding to the internal missing frequency points are:

[0047] and:

[0048]

[0049]

[0050] in, For the first Initial values ​​for each frequency point Less than Maximum effective frequency index, greater than The minimum effective frequency index, In order to be with the first The index of the effective frequency point with the smallest distance between each frequency point. Internal linear interpolation is used to maintain the amplitude and phase variation trend between two effective frequency points, and edge nearest neighbor assignment is used to avoid amplitude divergence or non-physical phase abrupt changes caused by extrapolation beyond the effective frequency point range. The initialization only provides the initial values ​​for the low-rank iterations and is not used as the final recovery result.

[0051] Implementation Method 3: Hankel Matrix Construction, Low-Rank Truncation, and Inverse Hankel Reconstruction like Figure 2 As shown, the length is The current complete frequency domain sequence Embed the Hankel matrix in the same way as its anti-diagonal elements. The elements of the Hankel matrix in the second-lowest-rank recovery iteration are represented as follows:

[0052] in:

[0053]

[0054]

[0055] Let be the row number of the Hankel matrix. Let be the number of columns in the Hankel matrix. To make the two dimensions of the matrix relatively balanced, it is possible to... Set to near an integer, and determine accordingly. As long as the conditions are met. Both can form Hankel matrices for low-rank recovery.

[0056] like Figure 3 As shown, singular value decomposition is performed on the Hankel matrix:

[0057] in, It is a left singular vector matrix. It is a right singular vector matrix. For singular value matrices, superscript This represents the conjugate transpose. Singular values ​​are arranged in descending order:

[0058] Before keeping From the singular values ​​and their corresponding left and right singular vectors, we obtain the low-rank Hankel matrix:

[0059] The low-rank Hankel matrix can also be represented as:

[0060] in, To truncate the rank of the lower rank, and The first There are two singular vectors: a left singular vector and a right singular vector. The truncation rank is used to control the regularization strength of low-rank recovery and is not necessarily equal to the number of physical propagation paths. In a set of implementation parameters suitable for Bluetooth Low Energy lacking structured scenarios, the truncation rank is set to... In other implementations, the truncation rank can be predetermined based on the number of effective frequency points, signal-to-noise ratio, or singular cumulative energy.

[0061] like Figure 4 As shown, since the singular value truncated matrix does not necessarily strictly satisfy the Hankel structure where the elements on the same antidiagonal are equal, the elements on the same antidiagonal of the low-rank matrix are averaged to recover the one-dimensional frequency domain sequence. The set of anti-diagonal element indices corresponding to each frequency point is represented as follows:

[0062] The temporary recovery sequence obtained by inverse Hankel reconstruction is represented as follows:

[0063] in, In order to be with the first The set of anti-diagonal element indices corresponding to each frequency point The number of elements in the set. According to the first The low-rank Hankel matrix reconstruction obtained in the nth iteration Temporary recovery value for each frequency point.

[0064] Implementation Method 4: Initial Structural Anomaly Detection and Fixed Credibility Weight Generation This invention divides the low-rank recovery process into an initial anomaly detection stage and a fixed-weight recovery stage. The initial anomaly detection stage is based solely on the initial complete frequency domain sequence. and the first temporary recovery sequence Generate reliable weights, which will not change with iterations after generation.

[0065] Since the variation of adjacent frequency points in a normal frequency domain channel is constrained by a finite complex exponential structure, while the frequency points affected by interference will form local abrupt changes in adjacent differences, the residual of the differential structure of adjacent frequency points is defined as follows:

[0066] in, , For the first The structural residual at the differential position of the nth adjacent frequency point. (This is in contrast to the nth...) The set of adjacent difference positions corresponding to each frequency point is represented as follows:

[0067] No. The structural anomaly fraction for each frequency point is represented as:

[0068] The background residual energy is represented as:

[0069] To adapt anomaly detection to different received amplitudes and noise levels, the structural anomaly score is normalized:

[0070] in, For the first Structural anomaly score at each frequency point For background residual energy, To prevent positive stable parameters with a denominator of zero, For the first Normalized structural anomaly scores for each frequency point.

[0071] Generate segmented confidence weights based on normalized structural anomaly scores:

[0072] in, For the first Segmented reliable weights for each frequency point The first abnormal score threshold, Let be the second anomaly score threshold, and satisfy:

[0073] In one implementation, the normalized outlier score is set based on the background residual energy. , and When the outlier score of a valid frequency point is not higher than the background level, the observation value of that frequency point is retained; when the outlier score is between two thresholds, the proportion of observation values ​​is gradually reduced as the degree of outlier increases; when the outlier score reaches the second threshold, the frequency point is treated as an unreliable frequency point. For structured missing frequency points, the settings are directly set. .

[0074] Since the weights are generated solely from the first low-rank reconstruction result, the confidence level of observations in subsequent iterations remains unchanged, thus preventing changes in the restored values ​​from adversely altering the weights and causing iterative oscillations. Fixed weights also ensure that normal frequencies, questionable frequencies, and missing frequencies maintain consistent data fusion rules across all iterations.

[0075] Implementation Method 5: Fixed Trusted Weight Iteration and Convergence Judgment After generating fixed confidence weights, the current complete frequency domain sequence is reconstructed into a Hankel matrix. Singular value decomposition, low-rank truncation, and inverse Hankel reconstruction are then repeatedly performed, and valid observations and temporary recovered values ​​are fused according to the fixed confidence weights. The update rule in the second-lowest-rank recovery iteration is:

[0076] in, For the updated number Each frequency point value For the first Second-order equivalent frequency domain channel observations at each effective frequency point To fix the credibility weight, This is the temporary recovery value obtained from this low-rank truncation and anti-Hankel reconstruction.

[0077] when When, the update results use the original observations; when When the update result is a weighted combination of the original observations and the low-rank restored values, the update result is a weighted combination of the original observations and the low-rank restored values; when In this case, the update result uses a low-rank recovery value. Therefore, fixed missing frequencies can be filled in by the low-rank structure, and the impact of random interference frequencies on the update result is reduced or eliminated depending on the degree of anomaly.

[0078] The relative change between two adjacent iterations is expressed as:

[0079] in, This represents the relative change between two consecutive iterations. For positive stable parameters, It is a norm 2. Iteration stops when the following expression is satisfied:

[0080] in, A preset convergence threshold is set. To limit the computational cost in the worst-case scenario, a preset maximum number of iterations is also set. When the number of iterations reaches Stop iteration when iteration stops. The complete frequency domain sequence obtained at the point of stopping iteration is denoted as the recovered complete second-order equivalent frequency domain channel sequence. .

[0081] In embedded implementations, only the preceding calculations are needed. The system can identify the main singular values ​​and their corresponding singular vectors, or employ iterative singular value decomposition to reduce storage and computational costs. When the complete frequency grid, effective frequency set, and fixed confidence weights remain unchanged within a single ranging cycle, the corresponding index mapping relationships can also be pre-stored.

[0082] Implementation Method Six: Continuous Square Root Branch Selection After recovery This represents a second-order equivalent frequency domain channel. The complex square root has two candidate values ​​with opposite signs. If each frequency independently selects the principal square root, sign flipping may occur between adjacent frequencies. Phase transition. To recover the phase-continuous first-order equivalent frequency domain channel, a continuous square root branch selection is performed for each frequency point.

[0083] First, regarding the first Find the principal square root of the second-order equivalent frequency domain channel response at each frequency point:

[0084] No. The two candidate branches for each frequency point are and The first-order equivalent frequency domain channel response of the first frequency point is initialized as follows:

[0085] for The branch symbol is determined according to the Euclidean distance from the previous frequency point result:

[0086] And determine the first First-order equivalent frequency domain channel response at each frequency point:

[0087] in, The square root of the principal value. For the first Branch symbols at each frequency point This represents the first-order equivalent frequency domain channel response obtained through continuous branch selection. Since the complete frequency grid is arranged in ascending frequency order, selecting the candidate branch with the smallest distance from the previous result at each frequency point maintains local amplitude-phase continuity. Selecting the opposite branch at the first frequency point only multiplies the entire sequence by [the factor needed for the first frequency point]. It will not change the propagation delay determined by the frequency change.

[0088] In the presence of low signal-to-noise ratio or local deep fading, the continuity distance can be extended to the distance between the extrapolated values ​​of the previous two or more frequency points, or amplitude variation constraints can be added to the distance term, but it still belongs to the implementation method of selecting the frequency domain continuity branch from the positive and negative square root candidate branches.

[0089] Implementation Method Seven: Propagation Delay and Distance Estimation The first-order equivalent frequency domain channel sequence, selected through continuous square root branching, is input into the distance estimator. The distance estimator can employ an inverse fast Fourier transform delay peak estimator or a multi-signal classification high-resolution spectrum estimator.

[0090] When the complete frequency grid is an equally spaced frequency grid, the inverse fast Fourier transform time delay peak estimator constructs the time delay spectrum according to the following formula:

[0091] in, Delay for candidate propagation The corresponding time delay spectrum value, For the first The frequency of each frequency point. The propagation delay estimate is obtained by finding spectral peaks within a preset time delay search interval:

[0092] For situations requiring improved time delay resolution, zero-padding can be applied to the frequency domain sequence, interpolation can be performed near the time delay peak, or the above formula can be calculated directly based on the candidate time delay.

[0093] When using a multi-signal classification high-resolution spectrum estimator, a channel matrix is ​​constructed based on the first-order equivalent frequency domain channel sequence, and singular value decomposition is performed. Singular vectors corresponding to the main path components are selected to form the signal subspace, and the remaining singular vectors form the noise subspace matrix. The time-delay steering vector is represented as:

[0094] in, The number of elements in the delay steering vector, indicated by the superscript. This indicates transpose. The time delay spectrum of multiple signal classification is represented as:

[0095] Among them, superscript This represents the conjugate transpose. The propagation delay estimate is expressed as:

[0096] Due to the selection of square root branches The estimated distance between devices for a single-way equivalent frequency domain channel is expressed as follows:

[0097] in, The speed of electromagnetic wave propagation. This is the distance estimate between the initiating device and the reflecting device. When the back-end estimator uses the first path as the ranging delay, it selects the first path peak value from multiple delay spectrum peaks that meets preset amplitude, time sequence, or continuous tracking conditions.

[0098] Implementation Method 8: Overall Algorithm Flow like Figure 5 As shown, a complete ranging process is executed in the following order.

[0099] First, in-phase orthogonal data from the initiating and reflecting devices at each effective frequency point are received, forming complex responses at both ends. The amplitude and phase of the complex responses at both ends are normalized and multiplied to obtain a second-order equivalent frequency domain channel observation sequence. Subsequently, the complete frequency point set and the effective frequency point set are read, the observation sequence is mapped to the complete frequency grid, and linear interpolation is performed on missing internal frequency points, while nearest neighbor assignment is performed on missing edge frequency points.

[0100] Secondly, a Hankel matrix is ​​constructed using the initialized complete frequency domain sequence. The first singular value decomposition and low-rank truncation are then performed, and the first temporary recovered sequence is obtained through inverse Hankel reconstruction. Based on the adjacent differences between the initial complete frequency domain sequence and the first temporary recovered sequence, the structural residual, anomaly score, and normalized anomaly score are calculated. Segmented confidence weights are then generated and fixed.

[0101] Then, in each subsequent iteration, Hankel matrix construction, low-rank truncation, and inverse Hankel reconstruction are performed, and each valid frequency point is updated according to a fixed confidence weight; missing frequencies points are directly restored using temporary values. The relative change between two adjacent iterations is calculated until the convergence threshold is met or the maximum number of iterations is reached.

[0102] Finally, the square root of the converged complete second-order equivalent frequency domain channel sequence is calculated point by point. The positive and negative square root branches are selected according to the continuity of adjacent frequency points to obtain the first-order equivalent frequency domain channel sequence. This sequence is then input into the inverse fast Fourier transform delay peak estimator or the multi-signal classification high-resolution spectrum estimator to output the propagation delay and distance estimation results.

[0103] Implementation Method Nine: Distance Measuring Device This embodiment provides a low-power Bluetooth structured missing channel recovery and robust phase ranging device. This device can be installed in an initiating device, a reflecting device, a host device communicatively connected to the initiating device, or a standalone edge processing device, and includes the following modules.

[0104] The bidirectional data acquisition module is used to acquire in-phase orthogonal data or complex responses of the initiating device and the reflecting device at each effective frequency point, and transmit the in-phase orthogonal data or complex responses to the second-order equivalent channel construction module.

[0105] The second-order equivalent channel construction module is used to perform amplitude-phase normalization and multiplication on the complex responses at both ends, and transmit the resulting second-order equivalent frequency domain channel observation sequence to the frequency point mapping and initialization module.

[0106] The frequency point mapping and initialization module is used to determine the structured missing frequency points based on the complete frequency point set and the effective frequency point set, map the second-order equivalent frequency domain channel observation sequence to the complete frequency grid, and generate the initial complete frequency domain sequence through internal linear interpolation and edge nearest neighbor assignment.

[0107] The Hankel low-rank recovery module is used to construct a Hankel matrix based on the current complete frequency domain sequence, perform singular value decomposition and low-rank truncation, and average the output temporary recovered sequence using the same antidiagonal elements.

[0108] The anomaly weight generation module has its input connected to the frequency point mapping and initialization module and the first recovery output of the Hankel low-rank recovery module, respectively. It is used to calculate the structural residual and structural anomaly score based on the initial complete frequency domain sequence and the first temporary recovery sequence, and output fixed reliable weights.

[0109] The frequency point weighted update module receives the second-order equivalent frequency domain channel observation sequence, the temporary recovery sequence, and the fixed trusted weights, respectively. It performs weighted updates on the valid observation values ​​and the temporary recovery values ​​according to the fixed trusted weights, uses the temporary recovery values ​​of missing frequency points as the update values, and feeds back the updated complete frequency domain sequence to the Hankel low-rank recovery module.

[0110] The square root branch selection module is connected to the convergence result output of the frequency point weighted update module. It is used to perform complex square root operations on the complete second-order equivalent frequency domain channel sequence point by point, and select the branch with the smaller distance from the previous frequency point result from the positive and negative square root candidate branches, and output the first-order equivalent frequency domain channel sequence.

[0111] The distance estimation module, connected to the output of the square root branch selection module, is used to construct a time delay spectrum based on the first-order equivalent frequency domain channel sequence, determine the propagation time delay estimate, and output the distance estimate.

[0112] The modules described above can be implemented by a processor executing program instructions from memory, or by a digital signal processor, a field-programmable gate array, an application-specific integrated circuit (ASIC), or a combination thereof. The division of these modules is to illustrate the data processing functions; in actual hardware, they can be integrated into the same processor or distributed between the Bluetooth Low Energy controller and the host processor.

[0113] Implementation Method 10: Computer-readable storage medium This embodiment provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the processor performs bidirectional data reading, second-order equivalent channel construction, complete frequency grid mapping, missing frequency point initialization, Hankel low-rank truncation, anti-Hankel reconstruction, fixed reliable weight generation, weighted iteration, continuous square root branch selection, and propagation delay and distance estimation.

[0114] The computer-readable storage medium includes non-volatile memory, flash memory, read-only memory, solid-state storage media, or other media capable of storing program instructions. The program instructions can be deployed in Bluetooth Low Energy terminals, positioning base stations, mobile terminals, edge computing devices, or servers.

[0115] Implementation Method Eleven: Description of Recovery Effect Figure 6 The multipath Saleh-Valenzuela model is used to construct channels under different Rician factors, and the ideal one-way response, zero-filling, nearest neighbor filling, internal linear interpolation and edge nearest neighbor interpolation, amplitude-phase uniform interpolation, and the recovery method of this invention are integrated into the back-end distance estimator. Figure 6 The horizontal axis represents the Rician factor, and the vertical axis represents the mean absolute error of the distance measurement.

[0116] Depend on Figure 6 As shown in (a), when the inverse fast Fourier transform delay peak estimator is used, the zero-filling method maintains a large ranging error under different Rican factors; as the proportion of direct paths increases, the ranging error of different processing methods generally decreases, and the recovery method of this invention is closer to the ideal single-pass response curve under most test conditions. Figure 6 As can be seen in (b), when connected to a high-resolution spectrum estimator for multiple signal classification, the recovery method of the present invention maintains a low error over a wide range of Rician factors, indicating that the recovered first-order equivalent frequency domain channel can be compatible with different back-end estimators.

[0117] Figure 6This illustration demonstrates the synergistic effect of Hankel low-rank recovery, fixed confidence weights, and continuous square root branch selection under conditions of structured missing and multipath propagation. Actual ranging performance is also affected by frequency span, number of effective frequency points, signal-to-noise ratio, RF link calibration error, interference intensity, and environmental multipath distribution. The results shown do not constitute a limitation on the scope of this invention.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A Hankel low-rank recovery and robust phase ranging method for low-power Bluetooth structured missing channels and interference, characterized in that, include: S1, the initiating device and the reflecting device of Bluetooth Low Energy (BLE) perform bidirectional signal interaction at multiple frequency points, acquire in-phase orthogonal IQ data or complex responses of the initiating device and the reflecting device at each effective frequency point, normalize the amplitude and phase of the complex responses at both ends and multiply them to obtain the second-order equivalent frequency domain channel observation sequence at the effective frequency point, and determine the structured missing frequency points based on the complete frequency point set and the effective frequency point set; S2, map the second-order equivalent frequency domain channel observation sequence to the complete frequency grid, initialize the structured missing frequency points, and obtain the initial complete frequency domain sequence; S3, embed the initial complete frequency domain sequence into a Hankel matrix, perform a first low-rank truncation on the Hankel matrix, and perform inverse Hankel reconstruction on the low-rank truncation Hankel matrix to obtain the first temporary recovery sequence; S4. Calculate the structural anomaly score of each frequency point based on the structural residual between the initial complete frequency domain sequence and the first temporary recovery sequence, generate the segmented credible weight of each frequency point based on the structural anomaly score, and determine the segmented credible weight as the fixed credible weight used in subsequent low-rank recovery iterations. S5. According to the fixed credible weight, the second-order equivalent frequency domain channel observation value and the corresponding temporary recovery value on the effective frequency point are weighted and updated. The temporary recovery value on the structured missing frequency point is used as the update value of the corresponding frequency point. The Hankel matrix construction, low-rank truncation, inverse Hankel reconstruction and weighted update are repeatedly executed until the preset convergence condition is met, and the recovered complete second-order equivalent frequency domain channel sequence is obtained. S6, Perform complex square root operation on the complete second-order equivalent frequency domain channel sequence for each frequency point, and select the square root branch from the two square root candidate branches corresponding to each frequency point according to the continuity between adjacent frequency points to obtain the first-order equivalent frequency domain channel sequence. S7. Input the first-order equivalent frequency domain channel sequence into the distance estimator to obtain the propagation delay estimate, and obtain the distance estimate between the initiating device and the reflecting device based on the propagation delay estimate.

2. The Hankel low-rank recovery and robust phase ranging method according to claim 1, characterized in that, In the frequency points The complex response obtained by the reflecting device and the complex response obtained by the initiating device are respectively expressed as follows: The observed values ​​in the second-order equivalent frequency domain channel observation sequence are represented as follows: in, For the reflection device in the first Complex responses obtained at each frequency point For the initiating device in the Complex responses obtained at each frequency point This is the RF link amplitude and phase calibration factor for the reflecting device. This is the RF link amplitude and phase calibration factor for the initiating device. For the initiating device and the reflecting device in the first The initial phase difference of the local oscillator at each frequency point For the first The first-order equivalent frequency domain channel response at each frequency point This refers to the noise and hardware error terms corresponding to the reflecting device. The noise and hardware error terms corresponding to the initiating device. For the first Second-order equivalent frequency domain channel observations at each frequency point.

3. The Hankel low-rank recovery and robust phase ranging method according to claim 1, characterized in that, The complete frequency point set and the effective frequency point set are respectively represented as follows: The initial complete frequency domain sequence is determined according to the following formula: The interpolation coefficients are expressed as follows: in, For a complete set of frequency points, For the effective frequency set, This represents the total number of frequency points in the complete frequency grid. For the first Initial values ​​for each frequency point Less than Maximum effective frequency index, greater than The minimum effective frequency index, In order to be with the first The index of the effective frequency point with the smallest distance between frequency points. For the first The frequency point at the first The frequency point and the first Interpolation coefficients between frequency points.

4. The Hankel low-rank recovery and robust phase ranging method according to claim 1, characterized in that, In the In the next low-rank recovery iteration, a Hankel matrix is ​​constructed based on the current complete frequency domain sequence. The elements of the Hankel matrix are represented as follows: in, , , The singular value decomposition of the Hankel matrix is ​​expressed as: Before keeping From the singular values ​​and their corresponding left and right singular vectors, we obtain the low-rank Hankel matrix: The inverse Hankel reconstruction is performed by averaging the matrix elements on the same antidiagonal, resulting in a temporary recovered sequence: The set of anti-diagonal element indices is represented as follows: in, For the first The Hankel matrix constructed by the second-lowest rank recovery iteration. The Hankel matrix is ​​the first... Line 1 Column elements, For the first The second low-rank recovery iteration Each frequency point value Let n be the row number of the Hankel matrix. Let be the column number of the Hankel matrix. It is a left singular vector matrix. It is a right singular vector matrix. For singular value matrices, superscript This indicates the conjugate transpose. To truncate the rank of the lower rank, This is the low-rank truncated Hankel matrix. In order to be with the first The set of anti-diagonal element indices corresponding to each frequency point The number of elements in the anti-diagonal element index set. The first one obtained by anti-Hankel reconstruction Temporary recovery value for each frequency point.

5. The Hankel low-rank recovery and robust phase ranging method according to claim 1, characterized in that, The structural residual is determined based on the difference between adjacent frequency points of the initial complete frequency domain sequence and the first temporary recovery sequence, and the structural residual is expressed as: With the The set of adjacent difference positions corresponding to each frequency point is represented as follows: The structural anomaly scores for each frequency point are expressed as follows: The background residual energy is represented as: The normalized structural anomaly score is expressed as: The segmented credible weights are represented as follows: in, For the first Structural residuals at differential positions of adjacent frequency points The first anti-Hankel reconstruction obtained Temporary recovery value for each frequency point In order to be with the first The set of adjacent differential positions corresponding to each frequency point The number of elements in the set of adjacent difference positions. For the first Structural anomaly score at each frequency point For background residual energy, For positive stable parameters, For the first Normalized structural anomaly scores for each frequency point For the first Segmented reliable weights for each frequency point The first abnormal score threshold, The second anomaly score threshold is given, and it satisfies the following conditions: .

6. The Hankel low-rank recovery and robust phase ranging method according to claim 5, characterized in that, The segmented trusted weights are generated after the first low-rank truncation and anti-Hankel reconstruction, and these segmented trusted weights remain unchanged in subsequent low-rank recovery iterations. The complete frequency domain sequence in the second-lowest rank recovery iteration is updated according to the following formula: The relative change between two consecutive low-rank recovery iterations is expressed as: when Or the number of iterations reaches the preset maximum number of iterations. Stop the low-rank recovery iteration when the time comes, where, For the first After the second low-rank recovery iteration update Frequency domain channel values ​​at each frequency point For the first Second-order equivalent frequency domain channel observations at each effective frequency point These are fixed, reliable weights generated from the first temporary recovery sequence and remaining unchanged in subsequent low-rank recovery iterations. For the first Temporary recovery values ​​obtained from second-lower-rank truncation and inverse Hankel reconstruction This represents the relative change between two consecutive low-rank recovery iterations. For positive stable parameters, To preset the convergence threshold, This is the preset maximum number of iterations.

7. The Hankel low-rank recovery and robust phase ranging method according to claim 1, characterized in that, The first [element] in the recovered complete second-order equivalent frequency domain channel sequence Each frequency point value is denoted as For the first Perform complex square root operations on each frequency point value to obtain the principal square root: The first-order equivalent frequency domain channel response of the first frequency point is determined as follows: For the For each frequency point, the branch sign of the candidate square root branch is determined according to the following formula: And determine the first according to the following formula First-order equivalent frequency domain channel response at each frequency point: in, , For the first time after recovery Second-order equivalent frequency domain channel response at each frequency point The principal square root of the second-order equivalent frequency domain channel response is given. For the first The square root branch symbol of each frequency point The first one obtained through continuous branch selection The first-order equivalent frequency domain channel response at each frequency point.

8. The Hankel low-rank recovery and robust phase ranging method according to claim 1, characterized in that, The distance estimator includes an Inverse Fast Fourier Transform (IFFT) delay peak estimator or a Multi-Signal Classification (MUSIC) high-resolution spectrum estimator, wherein the IFFT delay peak estimator constructs the delay spectrum according to the following formula: The MUSIC high-resolution spectrum estimator constructs a channel matrix based on the first-order equivalent frequency domain channel sequence and performs singular value decomposition on the channel matrix to obtain the noise subspace matrix. And construct the time delay spectrum according to the following formula: The time delay steering vector is represented as: The propagation delay estimate and the distance estimate are respectively expressed as: in, For IFFT delay spectrum, For the MUSIC time delay spectrum, Due to the delay in search and propagation, For the first The frequency of each frequency point The noise subspace matrix, For delay steering vector, The number of elements in the delay steering vector, indicated by the superscript. Indicates conjugate transpose, superscript Indicates transpose. The time delay spectrum is obtained using the IFFT time delay peak estimator or the MUSIC high-resolution spectrum estimator. This is an estimate of the propagation delay. The speed of electromagnetic wave propagation. This is the estimated distance between the initiating device and the reflecting device.

9. A low-power Bluetooth structured missing channel recovery and robust phase ranging device, characterized in that, It includes a two-way data acquisition module, a second-order equivalent channel construction module, a frequency point mapping and initialization module, a Hankel low-rank recovery module, an anomaly weight generation module, a frequency point weighted update module, a square root branch selection module, and a distance estimation module; The bidirectional data acquisition module is used to acquire in-phase orthogonal data or complex responses of the initiating device and the reflecting device at each effective frequency point, and transmit the in-phase orthogonal data or complex responses to the second-order equivalent channel construction module. The second-order equivalent channel construction module is used to perform amplitude-phase normalization and multiplication on the complex responses at both ends, and transmits the resulting second-order equivalent frequency domain channel observation sequence to the frequency point mapping and initialization module. The frequency point mapping and initialization module is used to map the second-order equivalent frequency domain channel observation sequence to the complete frequency grid and generate an initial complete frequency domain sequence. The Hankel low-rank recovery module is used to construct a Hankel matrix based on the initial complete frequency domain sequence, perform low-rank truncation and inverse Hankel reconstruction in sequence, and output a temporary recovery sequence. The input of the abnormal weight generation module is connected to the first recovery output of the frequency point mapping and initialization module and the Hankel low-rank recovery module, respectively, and is used to generate fixed reliable weights based on the initial complete frequency domain sequence and the first temporary recovery sequence. The frequency point weighted update module receives the second-order equivalent frequency domain channel observation sequence, the temporary recovery sequence, and the fixed reliable weight, respectively, performs weighted update on each frequency point, and feeds back the updated complete frequency domain sequence to the Hankel low-rank recovery module for iterative processing. The square root branch selection module is connected to the output of the frequency point weighted update module and is used to perform complex square root operation and continuous branch selection on the complete second-order equivalent frequency domain channel sequence that meets the preset convergence conditions to obtain the first-order equivalent frequency domain channel sequence. The distance estimation module is connected to the output of the square root branch selection module and is used to determine the propagation delay estimate and distance estimate based on the first-order equivalent frequency domain channel sequence.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the Hankel low-rank recovery and robust phase ranging method according to any one of claims 1 to 8.

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