A FTM correction non-line-of-sight ranging method based on matrix pencil CSI multi-path parameter estimation

Abstract

This invention proposes an FTM-corrected non-line-of-sight ranging method based on matrix-bundled CSI multipath parameter estimation. First, Channel State Information (CSI) data from WiFi devices is collected, an augmented matrix is ​​constructed, and singular value decomposition is performed to obtain a left singular matrix and singular value vectors. Second, the average power of the CSI is calculated and transformed to the logarithmic domain to determine the maximum number of candidate paths. Based on the singular value vectors, a Minimum Description Length (MDL) criterion is constructed to adaptively estimate the number of effective paths. Then, the propagation delay of each path is obtained using the matrix-bundled algorithm, a Vandermonde matrix is ​​constructed, and the received power of each path is estimated using the least squares method. Finally, the power ratio of the direct path is calculated as a reliability factor. If it is below a threshold, the second strongest path is selected from the reflection paths with power greater than the direct path. If there is only one such path, it is selected. The average delay difference between the reflection path and the direct path is calculated using power weighting, and this delay difference is used to compensate for the FTM receiving timestamp to obtain the corrected ranging distance. This invention does not require a preset number of paths, is highly adaptive, and significantly improves the accuracy of FTM ranging in non-line-of-sight environments.

Description

Technical Field

[0001] This invention belongs to the technical field of active indoor WiFi positioning, specifically relating to a method for estimating multipath parameters using Wi-Fi Channel State Information (CSI) and compensating for non-line-of-sight (NLOS) errors in Fine Timing Measurement (FTM) ranging results. Background Technology

[0002] With the rapid development of modern technology, indoor positioning plays a vital role in various fields such as precise navigation, security management, and device tracking. In the development of indoor positioning technology, WiFi positioning has become a research focus due to its wide coverage and readily available infrastructure. Early traditional indoor positioning technologies mainly utilized Received Signal Strength Indicator (RSSI) to estimate the distance between the device and the signal source by measuring and analyzing the physical characteristics of the wireless signal. However, this method is significantly affected by environmental obstacles, multipath effects, and interference in practical applications, resulting in relatively low positioning accuracy. With a deeper understanding of physical layer signal characteristics, CSI has become the focus of Wi-Fi sensing and positioning research. CSI provides fine-grained frequency domain channel characteristics, including amplitude and phase information on multiple subcarriers and spatial links, enabling the estimation of multipath propagation delay parameters using super-resolution algorithms. However, in practical systems, imperfect clock synchronization between the transmitter and receiver introduces sampling frequency offset (SFO), carrier frequency offset (CFO), and packet detection delay (PDD), leading to nonlinear phase distortion and significantly reducing ranging accuracy. Meanwhile, as the next-generation Wi-Fi positioning standard, IEEE 802.11az introduced the FTM mechanism, enabling distance estimation based on round-trip time (RTT) measurements. FTM calculates the signal round-trip time by recording four timestamps (t1, t2, t3, t4) from both the initiator and responder to obtain the distance. Theoretically, FTM can achieve sub-meter ranging accuracy, thus becoming an important technology for high-precision Wi-Fi positioning.

[0003] However, FTM ranging is also severely affected by multipath and NLOS environments: when the direct path is blocked, the first path detected by the receiver is actually the reflected path, causing the measured reception timestamp to be greater than the actual arrival time of the direct path, resulting in a positive distance deviation. To address these issues, this invention proposes an FTM non-line-of-sight ranging error compensation method based on CSI multipath parameter estimation using a matrix beam algorithm. This method first adaptively estimates the number of multipaths using the Minimum Description Length (MDL) criterion, avoiding manual pre-setting of the path number while providing an accurate propagation path number for subsequent delay estimation, thereby improving the accuracy of path parameter estimation. Secondly, the delay estimate for each path is obtained based on the matrix beam algorithm; then, a Vandermonde matrix is ​​constructed, and the received power of each path is calculated using the least squares method. Finally, the proportion of the direct path power to the total power is defined as a reliability factor; when this factor is below a predetermined threshold, it is determined to be an NLOS state, requiring compensation. Finally, the second strongest path is selected from the reflection paths with power greater than the direct path. If only one path exists, that path is chosen. The power and delay of this path are compared with the power and delay of the direct path to estimate the average delay difference between the reflection path and the direct path detected by FTM using a weighted method. This average delay difference is then used to compensate for the FTM receiving timestamp, thereby correcting the ranging distance. The entire method requires no modification to the FTM protocol, has a moderate computational load, and can significantly improve the ranging accuracy of FTM in non-line-of-sight environments. Summary of the Invention

[0004] The purpose of this invention is to provide an FTM correction non-line-of-sight ranging method based on matrix bundle CSI multipath parameter estimation in WiFi positioning systems. This method adaptively estimates multipath parameters based on the characteristics of CSI data itself without the need for preset path numbers or manual intervention, and improves the FTM ranging accuracy in NLOS environments through reliability factors and weighted excessive delay compensation.

[0005] The present invention discloses an FTM non-line-of-sight ranging error compensation method based on CSI multipath parameter estimation using a matrix beam algorithm, which specifically includes the following steps:

[0006] Step 1: In FTM, the initiator and responder obtain four timestamps through frame exchange: the initiator's sending time. Response time Response time Initiator's Receiving Time Meanwhile, the signal is transmitted by the OFDM system, OFDM has The system uses several subcarriers to acquire CSI information of the WiFi signals in two transmission directions when the initiator and responder are respectively acting as receivers. The signal propagation in the wireless channel exhibits multipath effects. There are several paths leading to a uniform linear array, among which The signal's flight time is The center frequency is The subcarrier spacing is The receiver has a single antenna. On each subcarrier, among which, The CSI data of a single received data packet is represented as follows:

[0007]

[0008] in, Indicates the first CSI data for each subcarrier;

[0009] Step 2: Smooth the CSI data blocks to remove interference between coherent signals, thus obtaining the Hankle matrix. ,in, Represented as a complex field, , L is the sliding window size for smoothing CSI data within a CSI data block; to increase the inherent number of snapshots, an augmented matrix is ​​defined in a forward and backward manner. , is represented as: ,in, for The complex conjugate matrix, and Let be the permutation matrix. Given the real number field, perform singular value decomposition on the augmented matrix to obtain the left singular matrix and singular values;

[0010] Step 3: Calculate the average power of the CSI data for each received individual data packet and convert it to logarithmic power. :

[0011]

[0012] The search range is set to the maximum range based on the estimated number of propagation paths according to the power magnitude. :

[0013]

[0014] For the singular value vector obtained in step two ,according to Separate the singular value subsets corresponding to the noise subspace Based on the flatness of the noise subspace, a likelihood function is established by calculating the ratio of the arithmetic mean to the geometric mean of the subset:

[0015]

[0016] in, This represents the estimated number of candidate propagation paths. Establish MDL criterion functions:

[0017]

[0018] Select to make smallest Number of valid paths ;

[0019] Step 4: For the left singular matrix obtained in Step 2 and the matrix obtained in Step 3... The signal subspace and noise subspace are solved, and then a shift-invariant matrix is ​​constructed from the signal subspace using the matrix bundle algorithm. The path delay is then estimated using generalized eigenvalue decomposition. ,in, It is a direct-path TOF. ;

[0020] Step 5: Use the time delay estimated in Step 4 The construction dimension is Vandermonde matrix :

[0021]

[0022] in, This matrix is ​​used to subsequently solve for the complex gain of each path and establish linear equations:

[0023]

[0024] in, The received CSI matrix is ​​processed using least squares left division to obtain the complex gain vector. for: Seeking ,in and Elements correspond one-to-one by index in the complex gain vector The element With the time delay vector The first in element Represents the complex gain and propagation delay along the same path;

[0025] according to Calculate the received power for each path, the first path... The received power of each path is: The power vector received is: , No. The received power and delay of each path are .

[0026] Step Six: Calculate the total power of all paths based on the received power obtained in Step Five: Calculate the ratio of direct beam power to total power: ,in, Set a threshold for the received power of the direct path. ,if Greater than No FTM error compensation is needed; otherwise, the arrival time of the reflected path corresponding to the timestamp of FTM recognition and the arrival time of the direct path need to be calculated for FTM error compensation.

[0027] Step Seven: When Less than Then, based on the received power and delay of all paths obtained in step five, find all paths with received power greater than [a certain value]. The reflection paths are then arranged in descending order of power as follows: The corresponding delay is ,in, For power greater than The number of reflection paths is used to select the power and propagation delay of the second strongest path among these reflection paths as the reflection path for FTM identification: , ,Will and Used for calculation If greater than Number of reflection paths Then the power and propagation delay of this unique path are used as the reflection path for FTM identification: , The expression for calculating the average propagation delay difference between the reflected path and the direct path identified by FTM is:

[0028]

[0029] Step 8: Using the average time delay difference between the reflection path and the direct path identified by FTM in the two transmission processes of initiator → responder and responder → initiator obtained in steps 2 to 7. and For the receiver timing of the responder in FTM ranging and the time of receipt by the initiator The corrections are performed separately, and the expression for correcting FTM non-line-of-sight ranging is as follows:

[0030]

[0031] in, It's the speed of light.

[0032] Beneficial effects

[0033] This invention proposes an FTM-corrected non-line-of-sight ranging method based on matrix-bundled CSI multipath parameter estimation. First, the method adaptively estimates the number of multipaths using the Minimum Description Length (MDL) criterion. This avoids manually pre-setting the number of paths and provides an accurate propagation path count for subsequent delay estimation, thereby improving the accuracy of path parameter estimation. Second, the delay estimates for each path are obtained based on the matrix-bundled algorithm. Then, a Vandermonde matrix is ​​constructed, and the received power of each path is calculated using the least squares method. Next, the proportion of direct path power to total power is defined as a reliability factor. When this factor is below a predetermined threshold, it is determined to be in an NLOS state, requiring compensation. Finally, the second strongest path is selected from the reflection paths with power greater than the direct path. If only one path exists, it is selected. Using the power and delay of this path and the power and delay of the direct path, the average delay difference between the reflection path and the direct path detected by FTM is estimated using a weighted method. This average delay difference is then used to compensate for the FTM receiving timestamp, thereby correcting the ranging distance.

[0034] The method of this invention does not require modification of the FTM protocol, has a moderate computational load, and can significantly improve the FTM ranging accuracy in non-line-of-sight environments. Attached Figure Description

[0035] Figure 1 This is a block diagram of an FTM-corrected non-line-of-sight ranging method based on matrix bundle CSI multipath parameter estimation according to the present invention. Detailed Implementation Plan

[0036] The purpose of this invention is to provide an FTM correction non-line-of-sight ranging method based on matrix bundle CSI multipath parameter estimation in Wi-Fi FTM ranging systems. Without the need for preset path number or manual intervention, the multipath parameters are adaptively estimated based on the characteristics of the CSI data itself. Furthermore, the accuracy of FTM ranging in NLOS environments is improved through reliability factors and weighted excessive delay compensation.

[0037] The present invention discloses an FTM-corrected non-line-of-sight ranging method based on matrix bundle CSI multipath parameter estimation, which specifically includes the following steps:

[0038] Step 1: In FTM, the initiator and responder obtain four timestamps through frame exchange: the initiator's sending time. Response time Response time Initiator's Receiving Time Meanwhile, the signal is transmitted by the OFDM system, OFDM has The system uses several subcarriers to acquire CSI information of the WiFi signals in two transmission directions when the initiator and responder are respectively acting as receivers. The signal propagation in the wireless channel exhibits multipath effects. There are several paths leading to a uniform linear array, among which The signal's flight time is The center frequency is The subcarrier spacing is The receiver has a single antenna. On each subcarrier, among which, The CSI data of a single received data packet is represented as follows:

[0039]

[0040] in, Indicates the first CSI data for each subcarrier;

[0041] Step 2: Smooth the CSI data blocks to remove interference between coherent signals, thus obtaining the Hankle matrix. ,in, Represented as a complex field, , L is the sliding window size for smoothing CSI data within a CSI data block; to increase the inherent number of snapshots, an augmented matrix is ​​defined in a forward and backward manner. , is represented as: ,in, for The complex conjugate matrix, and Let be the permutation matrix. Given the real number field, perform singular value decomposition on the augmented matrix to obtain the left singular matrix and singular values;

[0042] Step 3: Calculate the average power of the CSI data for each received individual data packet and convert it to logarithmic power. :

[0043]

[0044] The search range is set to the maximum range based on the estimated number of propagation paths according to the power magnitude. :

[0045]

[0046] For the singular value vector obtained in step two ,according to Separate the singular value subsets corresponding to the noise subspace Based on the flatness of the noise subspace, a likelihood function is established by calculating the ratio of the arithmetic mean to the geometric mean of the subset:

[0047]

[0048] in, This represents the estimated number of candidate propagation paths. Establish MDL criterion functions:

[0049]

[0050] Select to make smallest Number of valid paths ;

[0051] Step 4: For the left singular matrix obtained in Step 2 and the matrix obtained in Step 3... The signal subspace and noise subspace are solved, and then the path delay is estimated by constructing a shift-invariant matrix in the signal subspace using the matrix bundle algorithm and generalized eigenvalue decomposition. ,in, It is a direct-path TOF. ;

[0052] Step 5: Use the time delay estimated in Step 4 The construction dimension is Vandermonde matrix :

[0053]

[0054] in, This matrix is ​​used to subsequently solve for the complex gain of each path and establish linear equations:

[0055]

[0056] in, The received CSI matrix is ​​processed using least squares left division to obtain the complex gain vector. for: Seeking ,in and Elements correspond one-to-one by index in the complex gain vector The element With the time delay vector The first in element Represents the complex gain and propagation delay along the same path;

[0057] according to Calculate the received power for each path, the first path... The received power of each path is: The power vector received is: , No. The received power and delay of each path are .

[0058] Step Six: Calculate the total power of all paths based on the received power obtained in Step Five: Calculate the ratio of direct beam power to total power: ,in, Set a threshold for the received power of the direct path. ,if Greater than No FTM error compensation is needed; otherwise, the arrival time of the reflected path corresponding to the timestamp of FTM recognition and the arrival time of the direct path need to be calculated for FTM error compensation.

[0059] Step Seven: When Less than Then, based on the received power and delay of all paths obtained in step five, find all paths with received power greater than [a certain value]. The reflection paths are then arranged in descending order of power as follows: The corresponding delay is ,in, For power greater than The number of reflection paths is used to select the power and propagation delay of the second strongest path among these reflection paths as the reflection path for FTM identification: , ,Will and Used for calculation If greater than Number of reflection paths Then the power and propagation delay of this unique path are used as the reflection path for FTM identification: , The expression for calculating the average propagation delay difference between the reflected path and the direct path identified by FTM is:

[0060]

[0061] Step 8: Using the average time delay difference between the reflection path and the direct path identified by FTM in the two transmission processes of initiator → responder and responder → initiator obtained in steps 2 to 7. and For the receiver timing of the responder in FTM ranging and the time of receipt by the initiator The corrections are performed separately, and the expression for correcting FTM non-line-of-sight ranging is as follows:

[0062]

[0063] in, It's the speed of light.

Claims

1. A non-line-of-sight ranging method based on matrix bundle CSI multipath parameter estimation using FTM correction, comprising the following steps: Step 1: In FTM, the initiator and responder obtain four timestamps through frame exchange: the initiator's sending time. Response time Response time Initiator's Receiving Time Meanwhile, the signal is transmitted by the OFDM system, OFDM has The system uses several subcarriers to acquire CSI information of the WiFi signals in two transmission directions when the initiator and responder are respectively acting as receivers. The signal propagation in the wireless channel exhibits multipath effects. There are several paths leading to a uniform linear array, among which The signal's flight time is The center frequency is The subcarrier spacing is The receiver has a single antenna. On each subcarrier, among which, The CSI data of a single received data packet is represented as follows: ； in, Indicates the first CSI data for each subcarrier; Step 2: Smooth the CSI data blocks to remove interference between coherent signals, thus obtaining the Hankle matrix. ,in, Represented as a complex field, , L is the sliding window size for smoothing CSI data within a CSI data block. To increase the inherent number of snapshots, an augmentation matrix is ​​defined in a forward and backward manner. , is represented as: ,in, for The complex conjugate matrix, and Let be the permutation matrix. Given the real number field, perform singular value decomposition on the augmented matrix to obtain the left singular matrix and singular values; Step 3: First, calculate the average power of CSI and convert it to a logarithmic power value. Different maximum candidate propagation path numbers are set for different power ranges, based on... Determine the maximum number of candidate propagation paths ,pass Solve for the singular value vectors in the noise subspace from the singular value vectors obtained in step two, and calculate the noise energy ratio by dividing the arithmetic mean of the vectors by the geometric mean of the vectors. And calculate the MDL cost function in combination with the number of subcarriers. ,in, For the estimated number of propagation paths, Select the value corresponding to the minimum cost function As an effective transmission path number ; Step 4: For the left singular matrix obtained in Step 2 and the matrix obtained in Step 3... The signal subspace and noise subspace are solved, and then a shift-invariant matrix is ​​constructed from the signal subspace using the matrix bundle algorithm. The path delay is then estimated using generalized eigenvalue decomposition. ,in, The propagation delay along the direct path, ; Step 5: Construct the Vandermonde matrix using the time delay obtained in Step 4, estimate the complex gain of each path using the least squares method and calculate the received power of different paths, and synchronously sort them in ascending order of estimated time delay to realize the correspondence between time delay and received power. Step Six: Calculate the total power of all paths based on the received power obtained in Step Five: Calculate the ratio of direct beam power to total power: ,in, Set a threshold for the received power of the direct path. ,if Greater than No FTM error correction is needed. Conversely, if the FTM recognition timestamp is corrected, the arrival time difference between the reflected path and the direct path corresponding to the timestamp needs to be calculated for FTM error correction. The average time delay difference between the reflected path and the direct path recognized by FTM is also required. ; Step 7: Find all receivers with a power greater than [a certain value]. The reflection path, and their received power arranged in descending order as follows: The corresponding latency is ,in, For power greater than The number of reflection paths is used to select the receiving power of the second strongest path. and latency Used for calculation If greater than Number of reflection paths Then the received power of this unique path and latency Used for calculation If the received power without a reflection path is greater than ,but Calculate the average time delay difference between the reflected path and the direct path identified by FTM. The expression is: ; Step 8: Utilize the average time delay difference between the reflected path and the direct path identified by the FTM receiver in the two transmission processes obtained in Steps 2-7 (Initiator → Response and Response → Initiator). and For the receiver timing of the responder in FTM ranging and the time of receipt by the initiator The corrections are performed separately, and the expression for correcting FTM non-line-of-sight ranging is as follows: ； in, It's the speed of light.

2. The FTM-corrected non-line-of-sight ranging method based on matrix bundle CSI multipath parameter estimation according to claim 1, wherein step three, adaptive estimation of the number of propagation paths, comprises the following steps: Calculate the average power of the CSI data for each received individual data packet and convert it to logarithmic power. : ； The search range is set to the maximum range based on the estimated number of propagation paths according to the power magnitude. : ； For the singular value vector obtained in step two ,according to Separate the singular value subsets corresponding to the noise subspace Based on the flatness of the noise subspace, a likelihood function is established by calculating the ratio of the arithmetic mean to the geometric mean of the subset: ； in, This represents the estimated number of candidate propagation paths. Establish MDL criterion functions: ； in, The number of subcarriers; select the one that makes smallest Number of valid paths .

3. The FTM-corrected non-line-of-sight ranging method based on matrix beam CSI multipath parameter estimation according to claim 1, wherein steps six and seven, specifically for estimating the arrival time difference between the reflected path identified by the FTM and the direct path to compensate for the FTM ranging error, are as follows: Calculate the total power of all paths based on the received power of different paths obtained in step five: ； Calculate the ratio of received power to total power along the direct path: ； Set threshold ,if Greater than This indicates that the FTM identifies the arrival timestamp of the direct path, and no FTM error compensation is needed. Conversely, if the FTM identifies the arrival timestamp of the reflected path, the average time delay difference between that path and the direct path needs to be estimated. Perform FTM error compensation; when Less than Then, based on the received power and delay of all paths obtained in step five, find all paths with received power greater than [a certain value]. The reflection paths are then arranged in descending order of power as follows: The corresponding delay is ,in, For power greater than The number of reflection paths is used to select the power and propagation delay of the second strongest path among these reflection paths as the reflection path for FTM identification: , ,Will and Used for calculation If greater than Number of reflection paths Then the power and propagation delay of this unique path are used as the reflection path for FTM identification: , The expression for calculating the average propagation delay difference between the reflected path and the direct path identified by FTM is: ； Will Used for receiving timestamp correction.

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