A direct path resolution method based on adaptive parameter DBSCAN clustering

Abstract

The present invention proposes a direct path resolution method based on adaptive parameter DBSCAN clustering. First, the distance distribution matrix is calculated and the average nearest neighbor distance matrix is obtained by sorting and averaging operations. On this basis, the normalized distribution probability histogram obtained according to the distance matrix is filtered using a Savitzky‑Golay filter. Secondly, the peak search algorithm is used to search for the interval of the optimal neighborhood radius, and the mathematical expectation method is used to calculate the minimum number of points corresponding to the interval of the optimal neighborhood radius. Thirdly, DBSCAN clustering is performed based on the neighborhood radius and the minimum number of points and the silhouette coefficient is calculated, and the clustering result corresponding to the maximum value is selected. Finally, the maximum likelihood function is calculated based on the number of points, average value, variance and ToF characteristics of the cluster, and then the direct path is identified. The present invention performs clustering according to the characteristics of the data itself without having to determine the number of clusters, the neighborhood radius and the minimum number of points within the neighborhood radius, thereby improving the system's ability to resolve direct paths.

Description

Technical Field

[0001] The present invention belongs to the technical field of active indoor WiFi positioning, and specifically provides a direct path resolution method based on adaptive parameter DBSCAN clustering, which realizes direct path resolution by processing angle of arrival (AoA) and time of flight (ToF) data. Background Art

[0002] With the rapid development of modern technology, indoor positioning has become crucial in a variety of fields, including 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 primarily utilized the Received Signal Strength Indicator (RSSI), which measures and analyzes the physical characteristics of wireless signals to estimate the distance between the device and the signal source, thereby achieving positioning. However, in practical applications, this method is significantly affected by obstacles, multipath effects, and interference in the environment, resulting in relatively low positioning accuracy. Subsequently, researchers modified the firmware to extract Channel State Information (CSI), achieving higher-precision positioning. Thanks to Multiple-Input Multiple-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) technology, CSI provides richer channel information and stronger multipath immunity than RSSI, making it superior for wireless positioning, especially indoor positioning. In addition, CSI has the ability to distinguish different paths, allowing the positioning system to more accurately identify and process multipath signals in complex environments, thereby achieving higher-precision positioning.

[0003] In the field of wireless technology, indoor positioning systems are broadly divided into two categories: deep learning-based fingerprint positioning solutions and positioning methods based on multidimensional parameter estimation. The high deployment, maintenance, and resource consumption costs of deep learning-based fingerprint positioning solutions, as well as their sensitivity to environmental changes, limit their practical application. However, positioning methods based on multidimensional parameter estimation utilize a combination of multiple parameters to reduce the positioning system's dependence on environmental changes, resulting in lower deployment costs and, therefore, becoming increasingly mainstream. However, existing positioning methods based on multidimensional parameter estimation suffer from the effects of indoor multipath, resulting in the presence of a small number of outliers in the estimated results, in addition to the AoA and Time of Flight (ToF) parameters representing a mixture of direct and reflected paths. Therefore, simply treating AoA parameters with smaller ToF values as direct path parameters is inappropriate. To address these issues, the present invention proposes a direct path resolution method based on adaptive parameter DBSCAN clustering. First, a distance distribution matrix is calculated, sorted, and averaged to obtain an average nearest neighbor distance matrix. Based on this, the normalized distribution probability histogram derived from the distance matrix is filtered using a Savitzky-Golay filter. Secondly, the peak-finding algorithm is used to search for the interval of the optimal neighborhood radius, and the mathematical expectation method is used to calculate the minimum number of points corresponding to the interval of the optimal neighborhood radius. Again, DBSCAN clustering is performed based on the neighborhood radius and the minimum number of points, and the silhouette coefficient is calculated, and the clustering result corresponding to the maximum value is selected. Finally, the maximum likelihood function is calculated based on the number of points, mean value, variance and ToF characteristics of the cluster to identify the direct diameter. The present invention performs clustering based on the characteristics of the data itself without having to determine the number of clusters, the neighborhood radius and the minimum number of points within the neighborhood radius, thereby improving the system's ability to resolve the direct diameter. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for resolving direct paths based on adaptive parameter DBSCAN clustering in a WiFi positioning system. Without the need to determine the number of clusters, the neighborhood radius, and the minimum number of points within the neighborhood radius, clustering is performed based on the characteristics of the data itself, thereby improving the system's ability to resolve direct paths.

[0005] The method for distinguishing direct paths based on adaptive parameter DBSCAN clustering described in the present invention specifically includes the following steps:

[0006] Step 1: For the CSI data collected by a commercial WiFi device such as ASUS RT-AC86U or a host equipped with an Intel 5300 network card on the array antenna, use a subspace algorithm such as Matrix Pencil (MP) to estimate the transmitter's AoA and ToF parameters. The resulting set of raw estimation results is expressed as:

[0007] Est={(θ i ,τi )i∈{1,2,...,I}}

[0008] Among them, θ i and τ i Represent the AoA and ToF parameters of data point i (1≤i≤I), and I is the total number of data points. Due to the different scales of AoA and ToF, they need to be normalized before clustering:

[0009]

[0010] Where X is the estimated value of AoA {θ i} or ToF estimate {τ i}, X i Represents the i-th (1≤i≤I) element in the set X, and the normalized parameter set is recorded as:

[0011]

[0012] Step 2: The average nearest neighbor distance represents the distance distribution characteristics of the data points. First, calculate the distance distribution matrix:

[0013] D={Distance(u,v)u,v∈{1,2,...,I}}

[0014] Among them, Distance(u,v) represents the set Est nor The Euclidean distance from data point u to data point v in:

[0015]

[0016] Among them, (x u ,y u ) and (x v ,y v ) represent the normalized coordinates of data point u and data point v respectively.

[0017] Then, sort each row of the distance matrix D in ascending order to obtain D sort :

[0018]

[0019] Secondly, calculate the average value of the vth column (1≤v≤I) in D and get the average nearest neighbor distance of all data points

[0020]

[0021] Among them, the vth (1≤v≤I) element Represents the average distance from any data point to the nearest v-th data point.

[0022] Step 3: Determine the candidate neighborhood radius interval and the minimum number of points corresponding to the candidate neighborhood radius. Draw a distribution probability histogram:

[0023]

[0024] Among them, z represents the set of the left boundary of the histogram, b represents the interval width in the histogram, and f(z) represents the frequency. The number of elements in that fall within the interval [z,z+b).

[0025] Secondly, the histogram H(z) is smoothed using a Savitzky-Golay filter to obtain a fitting curve to reduce the number of false peaks in the histogram. Thirdly, the location of the first peak point of the fitting curve is obtained using a peak-finding algorithm, and the interval where the peak point is located is considered the optimal neighborhood radius interval.

[0026] Finally, the interval is divided by the minimum interval Δeps to obtain a set of E candidate neighborhood radii eps={eps1,eps2,...,eps E}, and then use the mathematical expectation method to find the minimum number of points corresponding to each neighborhood radius in eps:

[0027]

[0028] Among them, p(eps e ,i) represents the neighborhood radius eps e The number of neighborhood points of the i-th data point under the condition .

[0029] Step 4: Perform DBSCAN clustering based on eps and minpts and calculate the silhouette coefficient {s u}:

[0030]

[0031] Among them, u and v represent the index of the data point in the cluster, q and w represent the sequence number of the cluster, and J q and J w Represents the set of data point indices in cluster numbers q and v, n q and n w Represents the total number of data points in cluster numbers q and v respectively. u Indicates the data point u to its cluster J q The average Euclidean distance of other data points v in (u≠v), y u Indicates that the data point u is transferred to other clusters J wThe minimum value of the average Euclidean distance of the inner data point v (w≠q). In order to select the optimal neighborhood radius and the minimum number of points in the neighborhood radius, calculate the average silhouette coefficient:

[0032]

[0033] The average silhouette coefficient of the DBSCAN clustering results obtained by different neighborhood radius sets eps and different minimum point number sets minpts in the neighborhood radius is Select the clustering result corresponding to the maximum value in set s

[0034] Step 5: Calculate the maximum likelihood function l for the kth (1≤k≤K) cluster in the clustering results obtained in step 4 according to the following formula: k :

[0035] l k =exp(ω N N k -ω A σ A,k -ω T σ T,k -ω m m T,k )

[0036] Among them, N k represents the total number of data points in the kth cluster, σ A,k represents the variance of the AoA dimension of the data points in the kth cluster, σ T,k represents the variance of the ToF dimension of the data points in the kth cluster, m T,k Represents the average value of the ToF dimension of the data points in the kth cluster. N 、ω A 、ω T and ω m are all constants and represent the corresponding weights.

[0037] Finally, by calculating Get cluster number k * , that is, the kth cluster in the clustering result * The AoA and ToF parameters of each cluster represent the resolved direct path, and the centroid of the direct path data point is calculated using the following formula

[0038]

[0039] Where u represents the index of the data point in the cluster, Indicates cluster number k * The collection of data point indices in , Indicates cluster number k * The total number of data points in .

[0040] Beneficial effects

[0041] The present invention proposes a direct path resolution method based on adaptive parameter DBSCAN clustering. First, the distance distribution matrix is calculated and the average nearest neighbor distance matrix is obtained by sorting and averaging operations. On this basis, the normalized distribution probability histogram obtained according to the distance matrix is filtered using a Savitzky-Golay filter. Secondly, the peak search algorithm is used to search for the interval of the optimal neighborhood radius, and the mathematical expectation method is used to calculate the minimum number of points corresponding to the interval of the optimal neighborhood radius. Thirdly, DBSCAN clustering is performed based on the neighborhood radius and the minimum number of points, and the silhouette coefficient is calculated, and the clustering result corresponding to its maximum value is selected. Finally, the maximum likelihood function is calculated based on the number of points, average value, variance and ToF characteristics of the cluster to identify the direct path.

[0042] The present invention performs clustering based on the characteristics of the data itself without determining the number of clusters, the neighborhood radius and the minimum number of points within the neighborhood radius, thereby improving the system's ability to resolve direct paths. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a block diagram of the direct path resolution method based on adaptive parameter DBSCAN clustering of the present invention. Specific implementation plan

[0044] The purpose of the present invention is to provide a method for resolving direct paths based on adaptive parameter DBSCAN clustering in a WiFi positioning system. Without the need to determine the number of clusters, the neighborhood radius, and the minimum number of points within the neighborhood radius, clustering is performed based on the characteristics of the data itself, thereby improving the system's ability to resolve direct paths.

[0045] The present invention provides a method for resolving direct path based on adaptive parameter DBSCAN clustering, and the specific implementation scheme includes the following steps:

[0046] Step 1: For the CSI data collected by a commercial WiFi device such as ASUS RT-AC86U or a host equipped with an Intel 5300 network card on the array antenna, use a subspace algorithm such as Matrix Pencil (MP) to estimate the transmitter's AoA and ToF parameters. The resulting set of raw estimation results is expressed as:

[0047] Est={(θ i ,τ i )i∈{1,2,...,I}}

[0048] Among them, θ i and τ iRepresent the AoA and ToF parameters of data point i (1≤i≤I), and I is the total number of data points. Due to the different scales of AoA and ToF, they need to be normalized before clustering:

[0049]

[0050] Where X is the estimated value of AoA {θ i} or ToF estimate {τ i}, X i Represents the i-th (1≤i≤I) element in the set X, and the normalized parameter set is recorded as:

[0051]

[0052] Step 2: The average nearest neighbor distance represents the distance distribution characteristics of the data points. First, calculate the distance distribution matrix:

[0053] D={Distance(u,v)u,v∈{1,2,...,I}}

[0054] Among them, Distance(u,v) represents the set Est nor The Euclidean distance from data point u to data point v in:

[0055]

[0056] Among them, (x u ,y u ) and (x v ,y v ) represent the normalized coordinates of data point u and data point v respectively.

[0057] Then, sort each row of the distance matrix D in ascending order to obtain D sort :

[0058]

[0059] Secondly, calculate the average value of the vth column (1≤v≤I) in D and get the average nearest neighbor distance of all data points

[0060]

[0061] Among them, the vth (1≤v≤I) element Represents the average distance from any data point to the nearest v-th data point.

[0062] Step 3: Determine the candidate neighborhood radius interval and the minimum number of points corresponding to the candidate neighborhood radius. Draw a distribution probability histogram:

[0063]

[0064] Among them, z represents the set of the left boundary of the histogram, b represents the interval width in the histogram, and f(z) represents the frequency. The number of elements in that fall within the interval [z,z+b).

[0065] Secondly, the histogram H(z) is smoothed using a Savitzky-Golay filter to obtain a fitting curve to reduce the number of false peaks in the histogram. Thirdly, the location of the first peak point of the fitting curve is obtained using a peak-finding algorithm, and the interval where the peak point is located is considered the optimal neighborhood radius interval.

[0066] Finally, the interval is divided by the minimum interval Δeps to obtain a set of E candidate neighborhood radii eps={eps1,eps2,...,eps E}, and then use the mathematical expectation method to find the minimum number of points corresponding to each neighborhood radius in eps:

[0067]

[0068] Among them, p(eps e ,i) represents the neighborhood radius eps e The number of neighborhood points of the i-th data point under the condition .

[0069] Step 4: Perform DBSCAN clustering based on eps and minpts and calculate the silhouette coefficient {s u}:

[0070]

[0071] Among them, u and v represent the index of the data point in the cluster, q and w represent the sequence number of the cluster, and J q and J w Represents the set of data point indices in cluster numbers q and v, n q and n w Represents the total number of data points in cluster numbers q and v respectively. u Indicates the data point u to its cluster J q The average Euclidean distance of other data points v in (u≠v), y u Indicates that the data point u is transferred to other clusters J w The minimum value of the average Euclidean distance of the inner data point v (w≠q). In order to select the optimal neighborhood radius and the minimum number of points in the neighborhood radius, calculate the average silhouette coefficient:

[0072]

[0073] The average silhouette coefficient of the DBSCAN clustering results obtained by different neighborhood radius sets eps and different minimum point number sets minpts in the neighborhood radius is Select the clustering result corresponding to the maximum value in set s

[0074] Step 5: Calculate the maximum likelihood function l for the kth (1≤k≤K) cluster in the clustering results obtained in step 4 according to the following formula: k :

[0075] l k =exp(ω N N k -ω A σ A,k -ω T σ T,k -ω m m T,k )

[0076] Among them, N k represents the total number of data points in the kth cluster, σ A,k represents the variance of the AoA dimension of the data points in the kth cluster, σ T,k represents the variance of the ToF dimension of the data points in the kth cluster, m T,k Represents the average value of the ToF dimension of the data points in the kth cluster. N 、ω A 、ω T and ω m are all constants and represent the corresponding weights.

[0077] Finally, by calculating Get cluster number k * , that is, the kth cluster in the clustering result * The AoA and ToF parameters of each cluster represent the resolved direct path, and the centroid of the direct path data point is calculated using the following formula

[0078]

[0079] Where u represents the index of the data point in the cluster, Indicates cluster number k * The collection of data point indices in , Indicates cluster number k * The total number of data points in .

Claims

1. A method for distinguishing direct paths based on adaptive parameter DBSCAN clustering, comprising the following steps: Step 1: For the CSI data collected by the host using commercial WiFi equipment on the array antenna, the transmitter's AoA and ToF parameters are estimated using the subspace algorithm. The set of raw estimation results is expressed as: Is={(θ i ,τ i )|i∈{1,2,...,I}} Among them, θ i and τ i They represent the AoA and ToF parameters of data point i, respectively, where 1≤i≤I and I is the total number of data points. Due to the different scales of AoA and ToF, they need to be normalized before clustering: Where X is the estimated value of AoA {θ i } or ToF estimate {τ i }, X i represents the i-th element in the set X, where 1≤i≤I, and the normalized parameter set is recorded as: Step 2: The average nearest neighbor distance represents the distance distribution characteristics of the data points; first, calculate the distance distribution matrix: D={Distance(u,v)|u,v∈{1,2,...,I}} Then, sort each row of the distance matrix D in ascending order to obtain D sort ; Secondly, calculate the average value of the vth column in D and get the average nearest neighbor distance of all data points Among them, 1≤v≤I; Step 3: Determine the candidate neighborhood radius interval and the minimum number of points corresponding to the candidate neighborhood radius; first, Draw a distribution probability histogram; secondly, smooth the histogram through the Savitzky-Golay filter to obtain a fitting curve to reduce the number of false peaks in the histogram; thirdly, obtain the position of the first peak point of the fitting curve through the peak-finding algorithm, and the interval where it is located is regarded as the optimal neighborhood radius interval; finally, divide the interval by the minimum interval Δeps to obtain a set of E candidate neighborhood radii eps = {eps1,eps2,...,eps E }, and then use the mathematical expectation method to find the minimum number of points corresponding to each neighborhood radius in eps: Among them, p(eps e ,i) represents the neighborhood radius eps e The number of neighborhood points of the i-th data point under the condition of ; Step 4: Perform DBSCAN clustering based on eps and minpts and calculate the silhouette coefficient {s u }: Among them, u and v represent the index of the data point in the cluster, q and w represent the sequence number of the cluster, and J q and J w Represents the set of data point indices in cluster numbers q and v, n q and n w Respectively represent the total number of data points in cluster numbers q and v; x u Indicates the data point u to its cluster J q The average Euclidean distance of other data points v in , where u≠v, y u Indicates that the data point u is transferred to other clusters J w The minimum value of the average Euclidean distance of the inner data point v, where w≠q; in order to select the optimal neighborhood radius and the minimum number of points in the neighborhood radius, calculate the average silhouette coefficient: The average silhouette coefficient of the DBSCAN clustering results obtained by different neighborhood radius sets eps and different minimum point number sets minpts in the neighborhood radius is Select the clustering result corresponding to the maximum value in set s Step 5: Calculate the maximum likelihood function l for the kth cluster in the clustering result obtained in step 4 according to the following formula: k , where 1≤k≤K: l k =exp(ω N N k -oh A s A,k -oh T s T,k -oh m m T,k ) Among them, N k represents the total number of data points in the kth cluster, σ A,k represents the variance of the AoA dimension of the data points in the kth cluster, σ T,k represents the variance of the ToF dimension of the data points in the kth cluster, m T,k represents the average value of the ToF dimension of the data points in the kth cluster; ω N 、ω A 、ω T and ω m are all constants and represent the corresponding weights; Finally, by calculating Get cluster number k * , that is, the kth cluster in the clustering result * The AoA and ToF parameters of each cluster represent the resolved direct path, and the centroid of the direct path data point is calculated using the following formula Where u represents the index of the data point in the cluster, Indicates cluster number k * The collection of data point indices in , Indicates cluster number k * The total number of data points in .

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