CN115022964B - Indoor positioning radio map reconstruction method and system based on image signals - Google Patents

Abstract

The invention provides an indoor positioning radio map reconstruction method and system based on a map signal. By modeling each reference point as a vertex of the graph and its radio data as a graph signal, a graph signal model is first developed in which virtual reference points and their radio data can be interpolated as missing vertices into the radio map. The potential spatial structure between all real and virtual reference points is then explored to find the graph laplace operator, which is used to reconstruct the radio map by semi-supervised graph interpolation. Simulation experiments prove that the wireless map reconstruction method provided by the invention has good performance in the aspect of positioning accuracy, and shows the potential of graph-based wireless map reconstruction in indoor positioning based on deep learning.

Description

Indoor positioning radio map reconstruction method and system based on image signals

Technical Field

The invention belongs to the field of image signal processing, and particularly relates to an indoor positioning radio map reconstruction method and system based on image signals.

Background

Indoor positioning is a key technology for Location Based Services (LBS) in many other areas that are difficult to access by indoor navigation, building emergency rescue, and Global Navigation Satellite Systems (GNSS). For many indoor positioning scenarios, conventional distance-based positioning techniques, including time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), and Received Signal Strength (RSS), remain applicable. However, distance-based positioning is highly dependent on the accuracy of the signal propagation model, which means that accurate positioning typically requires line-of-sight (LOS) propagation. In contrast, indoor environments are typically more diverse and complex, so non-line-of-sight propagation (NLOS) is a more common model of channels. In the case of NLOS, the positioning by using radio fingerprint can adapt to the irregular structure of indoor environment and obtain higher positioning accuracy.

Fingerprint-based positioning is generally divided into two phases, off-line training and on-line estimation. In the off-line training phase, radio fingerprints are collected at reference points of known positioning, forming a radio map of the environment. In general, a Received Signal Strength Indicator (RSSI) and Channel State Information (CSI) may be used as the fingerprint. In this field, many machine learning algorithms, such as K-nearest neighbor (KNN), artificial Neural Networks (ANN), support Vector Machines (SVM), boltzmann machines, which are limited, have been widely used. Furthermore, since the relationship between radio fingerprints and positioning is substantially nonlinear, deep learning-based positioning is receiving increasing attention in this field. For example, deep Neural Networks (DNNs), convolutional Neural Networks (CNNs), and Recurrent Neural Networks (RNNs) have been proposed for indoor positioning of radio fingerprints. Recently, graphic Neural Networks (GNNs) have also been considered in this field. Compared with the traditional machine learning method, the indoor positioning based on the deep learning has higher positioning precision.

The quality of the radio map in the off-line stage has a great influence on the accuracy of indoor positioning. Intuitively, a radio map with higher density contains more details of the electromagnetic properties of the environment, and thus a more accurate positioning can be achieved. Furthermore, radio samples should be collected multiple times per reference point to obtain finer granularity and reliable data. However, in practice, the number of reference points is very limited due to the cost of hardware, time and labor. In some large buildings, the cost of intensive off-site surveys is even too high to be practical. Meanwhile, it is difficult to deploy as many reference points as possible to construct a dense radio map due to privacy/security issues or deployment restrictions. Second, since the indoor wireless environment is naturally time-varying, the radio map may have been in time, and the cost of real-time data calibration of a large number of reference points is not practical. In summary, repeated collection of data at the reference point is very expensive, and thus the collected data is typically not fine-grained. Furthermore, despite the above difficulties, high resolution radio maps are still not possible due to unexpected hardware failures or transmission losses, which makes the radio map spatially or temporally incomplete. In this regard, incomplete radio maps lacking radio data are one of the main challenges of deep learning based indoor positioning.

The wireless map construction or reconstruction technology mainly comprises calibration-free data acquisition, a dynamic self-adaptive method, machine learning, deep learning and crowdsourcing. Wherein calibration-free data collection such as QR-Loc systems and the like are difficult to achieve dense scene monitoring. The kernel parameters of the improved bayesian regression method can adapt to dynamic changes, but a wireless monitor needs to be installed beside each AP, increasing the equipment cost. Based on deep learning methods, generating a countermeasure network (GAN) is mostly adopted to expand real data, and the network needs to be trained in a large amount, and such methods mainly focus on fingerprint recovery and data enhancement of time samples, and do not consider spatial enhancement. Machine-based methods, such as manifold learning techniques, gaussian process regression, etc., while possibly spatially enhanced, are largely dependent on the number and deployment of reference points and have over-smoothing problems, they are not sparse, they use complete sample information for prediction, and not all sample information contributes to the prediction. RGWR based on geographic weighting requires the logarithmic distance model to be measured in advance, which is difficult to obtain accurately throughout the environment, and the logarithmic path loss model still cannot describe the complex RSS distribution accurately. Crowd sourcing based methods require additional user intervention to fully exploit the overall perceived capabilities of the mobile device, while continuous Inertial Measurement Unit (IMU) monitoring consumes significant amounts of mobile device battery.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide an indoor positioning radio map reconstruction method and system based on image signals, so as to solve the defect that the radio map reconstruction is enhanced in space in the prior art, and improve the indoor positioning performance.

In order to achieve the purpose, the invention is realized by adopting the following technical scheme:

an indoor positioning radio map reconstruction method based on a map signal comprises the following steps:

constructing an indoor positioning frame, and obtaining an indoor initial radio map, wherein part of reference nodes are missing in the indoor initial radio map;

filling virtual reference nodes at the reference nodes of the missing part of the initial radio map to obtain a radio map to be reconstructed, regarding the reference nodes in the radio map to be reconstructed as nodes of a map topology, and regarding fingerprint information on each reference node as information on the nodes of the map topology;

recovering fingerprint information on each virtual node in the graph topology by a graph Laplace semi-supervised interpolation method; and obtaining a reconstructed radio map.

The invention further improves that:

preferably, filling a plurality of virtual nodes in other positions of the initial radio map, and obtaining a newly reconstructed radio map by a graph Laplace semi-supervised interpolation method; the other locations are locations other than the reference node in the previously reconstructed radio map.

Preferably, the reconstructed radio map is evaluated by RSS recovery accuracy analysis; the newly reconstructed radio map is evaluated by means of a DNN neural network.

Preferably, the information process of recovering each virtual node in the graph topology by the graph laplace semi-supervised interpolation method is as follows: establishing a weighted adjacency matrix reflecting K neighbors of all nodes in the graph topology, wherein the weight in the weighted adjacency matrix is based on the position relation among the nodes in the graph topology; establishing a Laplace matrix through the weighted adjacent matrix; and establishing a smoothness equation based on the Laplace matrix, converting the smoothness equation into a problem function for solving missing values in the graph topology, and completing information recovery on the virtual nodes after solving the problem function.

Preferably, the weighted adjacency matrix is W _i，j In the graph signal, the more closely the node i and node j are connected, the more W _i，j The greater the value of (2);

wherein m is _i，j Binary (0, 1) adjacency matrix for K-nearest neighbor, m if node j is the K-nearest neighbor node of node i _i，j =1, otherwise 0; g _i，j Is the euclidean distance between node pairs (i, j).

Preferably, the problem function of the missing value is:

wherein y is the signal to be recovered, x _i For the rest of the reference nodes, S _K L is the Laplace matrix, which is the set of remaining reference nodes.

Preferably, the problem function of missing values is solved by the CVX toolbox of matlab.

Preferably, the smoothness equation is:

TV(x)＝x ^T Lx＝∑ _i≠j W _ij (x _i -x _j ) ² (2)

an indoor positioning radio map reconstruction system based on map signals, comprising:

the frame construction unit is used for constructing an indoor positioning frame and obtaining an indoor initial radio map;

the map topology establishing unit is used for filling virtual nodes into the initial radio map to obtain a radio map to be reconstructed, and taking reference nodes in the radio map to be reconstructed as nodes of the map topology, and fingerprint information on each reference node is taken as information on the nodes of the map topology;

the recovery unit is used for recovering the information on each virtual node in the graph topology through a graph Laplace semi-supervised interpolation method; and obtaining a reconstructed radio map.

Preferably, the method further comprises:

an RSS recovery precision evaluation unit for evaluating the reconstructed radio map by means of RSS recovery precision analysis;

and the DNN neural network evaluation unit is used for evaluating the newly reconstructed radio map through the DNN neural network.

Compared with the prior art, the invention has the following beneficial effects:

the invention provides a map-based radio map reconstruction method, which is used for indoor positioning based on deep learning. By modeling each reference point as a vertex of the graph and its radio data as a graph signal, a graph signal model is first developed in which virtual reference points and their radio data can be interpolated as missing vertices into the radio map. The potential spatial structure between all real and virtual reference points is then explored to find the graph laplace operator, which is used to reconstruct the radio map by semi-supervised graph interpolation. Under the established graph signal processing model, the invention takes the reconstruction of the radio map as the sampling and recovering problem of the graph signal, and carries out semi-supervised interpolation on the existing radio map by adopting a proper graph signal algorithm by means of the prior space smoothing knowledge of the graph signal, thereby finally completing the reconstruction of the radio map and realizing the improvement of the spatial resolution. And then evaluating whether the RSS recovery precision is good or not by the reconstructed radio map, or training the radio map by using the RSS recovery precision in a deep neural network, and verifying whether the accuracy of indoor positioning is improved is helpful.

Simulation experiments prove that the wireless map reconstruction method provided by the invention has good performance in the aspect of positioning accuracy, and shows the potential of graph-based wireless map reconstruction in indoor positioning based on deep learning. Compared with the prior method, the method utilizes the spatial smoothness of the graphic signal, does not need early training, and can be directly used for reconstructing the signal of the unknown region. This approach can take advantage of the potential spatial correlation between the data rather than just the relationship of the data surfaces. Thus, the method has the advantage of recovering the fingerprint information corresponding to most of APs.

Furthermore, the indoor positioning scene is blocked by a wide NLOS, so that some area spaces are not smooth, the positioning performance of the reconstructed radio map based on the image signal method can be influenced, and therefore, the invention also designs and discusses a method for avoiding NLOS, the reconstructed radio map is designed carefully by maximally utilizing the potential smoothness of the space, a plurality of virtual nodes are filled in the initial indoor positioning radio map carefully, the newly reconstructed indoor positioning radio map is obtained, the performance of the newly reconstructed indoor positioning radio map in the positioning aspect is better, the error is lower, the number of nodes can be effectively saved in the early reference node deployment stage by the filling method, and the cost of offline map construction is reduced, so that the image signal recovery method has obvious advantages in the positioning performance test compared with the traditional method. .

Drawings

Fig. 1 is a schematic collection of radio fingerprints for indoor positioning.

Fig. 2 is an indoor radio map reconstruction positioning system architecture based on the graph signal method.

Fig. 3 is a uci and oor radio map.

Fig. 4 is a radio map of a fourth floor of the first building selected by uci-and-oor.

Fig. 5 is an RSS recovery accuracy error diagram of the AP 41.

Fig. 6 is an RSS recovery accuracy error diagram of the AP 253.

Fig. 7 is a radio map schematic diagram after 40 reference nodes are lost.

Fig. 8 is a schematic diagram of a well-designed interpolation of a virtual node between two neighboring nodes.

Fig. 9 is a graph of the cumulative error distribution function CDF for different algorithms.

Fig. 10 is a schematic diagram after removing the interference point.

Fig. 11 is a graph of average positioning errors after various algorithms remove the interference points.

Fig. 12 is a diagram of a change in positioning error of a UWB ranging 3D map after 50 reference nodes are lost, which is filled three times.

Fig. 13 is a diagram of a change in positioning error of the UWB ranging 3D map after the 20 reference nodes are lost, which is filled three times.

Detailed Description

The invention is described in further detail below with reference to the attached drawing figures:

for the original radio map, the existing reference nodes may be damaged or lost due to certain factors, resulting in incomplete radio maps. Either some reference nodes are discarded to adjust the layout of the existing reference nodes and the radio map is reconstructed or it is filled directly from the existing reference points. The present invention refers to these cases in general as radio map reconstruction problems. The aim is to obtain better positioning performance. These incomplete radio maps, or radio maps after manually discarding nodes, are called initial radio maps.

Based on the above problems, an embodiment of the present invention discloses a method for reconstructing an indoor positioning radio map based on a map signal, which includes the steps of:

step 1, establishing a system model: the invention firstly selects information given in the data set in the indoor positioning data set so as to conveniently construct a reference node area (such as a certain building, a certain layer or all spaces) of the space map topology, thereby selecting and constructing an original radio map based on the invention. The invention considers most of the reference nodes of the original radio map to be lost, and obtains an initial radio map containing only a small number of partial reference nodes, and uses the initial radio map as the initial radio map before reconstruction.

Based on the selected reference node area, an indoor positioning frame based on fingerprints is established, the reference nodes are regarded as nodes in the graph topology, fingerprint data are regarded as graph data, and the whole system is abstracted into a graph signal processing (Graph Signal Processing) model, namely a graph topology structure.

Fig. 1 shows the collection of radio fingerprints for indoor positioning. Assuming four AP nodes in the room, the initial radio map has N _r Reference points. Taking the first reference point as an example. A reference point receives a plurality of wireless fingerprint information from different AP nodes, wherein

Fingerprint information indicating that the nth AP transmits to the reference point. And a total of N is acquired at different times _s Samples. Thus, the size of the fingerprint dataset is N _r ×N _s ×N _AP ，N _s Is the number of samples at a reference point, N _AP Is the number of AP nodes, i.e. the size of the feature dimension of the fingerprint data.

Assuming that the number of reference points after the reconstruction of the wireless map is N, the final fingerprint data set size is N×N _s ×N _AP . The radio map reconstruction problem can be described as using the original N _r ×N _s ×N _AP Data set, expansion or adjustment N _r To obtain reconstructed NN _s ×N _AP Data.

The method provided by the invention aims to reduce the cost of manually reconstructing the offline radio map by utilizing fingerprint information and space topology information of a coverage reference point area. Fingerprints of non-covered reference point areas are generated to achieve more accurate indoor positioning. The overall positioning system architecture is shown in fig. 2. The system structure mainly comprises radio map reconstruction, node data recovery by using a graphic signal and a DNN positioning model.

Step 2: and (5) reconstructing a radio map. The radio map reconstruction of the present invention is based on the initial radio map, followed by filling in virtual nodes (which may be randomly filled or may be filled in a selected specific location) and performing the reconstruction, regarding all reference nodes (actual and virtual) as map topology nodes, fingerprint information as map signals. And then generating fingerprint information on the virtual nodes by using a graph signal method (graph Laplace semi-supervised interpolation) of the formula (3), so as to obtain different indoor positioning fingerprint training sets.

The filled radio map has N reference nodes and information of the existing K actual reference nodes. Data loss from other (N-K) nodes is considered. In addition to filling virtual nodes in original lost positions to verify RSS recovery accuracy, the invention also carefully designs a new reconstruction mode, and inserts a virtual node between each pair of actual nodes which are already very close along a certain direction (longitude, latitude or x, y or z direction) to an initial radio map. This construction of the invention can overcome most NLOS situations.

The invention uses a graph signal processing means to restore or generate fingerprint data on a reconstructed virtual reference node, and the specific graph Laplace semi-supervised interpolation process is as follows:

(1) Consider those signals associated with undirected, weighted, connected graphs, denoted as

And a weighted undirected graph corresponding to the signal is denoted +.>

Where v= {1, …, N } is a set of N vertices, +.>

Is a collection of edges between nodes. Can use x _i To represent the signal value size at node i e v. The adjacency matrix W is a weighted symmetric matrix reflecting the connection strength relationship between edges, and if edges (i, j) ∈ε are present, W _i，j Not less than 0, otherwise W _i，j =0. The closer the association (correlation) of node i and node j, then W _i，j The greater the value of (2). A laplace matrix l=d-W is introduced, where D is the degree matrix.

(2) And then constructing a space diagram topology by using a K-nearest neighbor method. Specifically, the distance g between all node pairs (i, j) is calculated from the geographical locations of all nodes _i，j A distance matrix G is formed. It is then necessary to eliminate some connections between nodes that are less physically distance dependent. Thus, an all zero matrix M is created, then the first k elements with the smallest distance need to be found for the ith row of the matrix G, recorded as

Then let M's corresponding element be 1, record as +.>

The weight of each edge is inversely proportional to the square of the distance between two nodes. Finally, the following weighted adjacency matrix W is constructed:

when W is constructed, the corresponding degree matrix D and laplace matrix l=d-W may also be constructed. In the scene of the invention, nodes are taken as vertexes of the graph, the distance relation among the nodes is taken as the weight of the edge, and fingerprint data is taken as information on the nodes of the graph.

(3) Many recovery methods are based solely on the surface relationships of the data, without extracting the underlying relationships of the data. In this embodiment, a potential spatial feature exists between the reconstructed actual reference node and the virtual reference node. Wireless fingerprint information between nodes closer in distance should be similar, while data between nodes farther in distance should be more different, a characteristic known as spatial smoothness. Spatial smoothness is an important feature of the graphics signal. On a connected graph, assuming that graph information is continuously spread, the signal values of different nodes will gradually become similar over time. In the limit, the signal values of all nodes on the graph will become uniform. In order to measure the smoothness or signal correlation of the signal y, the relationship is described using the lower graph laplace quadratic form. The smaller the value of the equation, the smoother the signal on the graph.

TV(y)＝y ^T Ly＝∑ _i≠j W _ij (y _i -y _j ) ² (2)

The present invention solves this problem by a graph semi-supervised learning framework when data for one or more nodes is lost. The framework assumes that the data is located in the graph nodes. The more spatially adjacent the data between nodes should be smoother, i.e. the graph signal is smooth, the smaller the value of the smoothness equation as shown in equation (2) should be. The invention considers that the value of the missing position has the smooth relation with the value of the adjacent known node to obtain the space smoothness expression y ^T Ly. Then, the smoothness equation is converted into a solutionThe problem function of the missing values in the graph topology is as shown in formula (3), the global quantity of the space smoothness representation is optimized through formula (3) to find the missing values, namely the information on the virtual nodes is recovered, and the radio map can be reconstructed through solving of formula (3). The constraint in this process limits that the value generated at the known location should be equal to the known value.

Specifically, if y is the signal to be recovered, then the signals on K nodes are known to be x. The purpose of the semi-supervised interpolation of the graph is to estimate y and ensure that x is at a known node _i ＝y _i ，i∈S _K . Similar to low rank matrix recovery, this approach is semi-supervised. These unobserved values are calculated at each time step of a given observation. The method does not require a training phase when node S is observed _K The missing N-K node data may be reconstructed directly, or when a virtual sensor containing an unknown value is desired. This problem can be expressed as:

solving the above problem through a CVX toolbox of matlab, obtaining a signal y to be recovered, namely obtaining fingerprint information in a reconstructed radio map, and correspondingly obtaining the reconstructed radio map, wherein the radio map is provided with N reference nodes, each reference node has respective longitude and latitude, and each reference node has corresponding fingerprint information.

Further, although nodes have potential graph structural features, there is a common NLOS problem in indoor environments due to the specificity of indoor positioning scenarios. Leading to the fact that: the distance between the generated virtual node and its neighboring nodes may be relatively large, so their fingerprint data may be not smooth due to signal occlusion and interruption. This problem may limit the application of graph smoothness to some extent. In the radio map reconstruction problem of the present invention, it is desirable to maximize the potential smoothness of the map, although NLOS can obscure the map. Therefore, the embodiment also provides a well-designed radio map filling mode, and the positioning precision of the test set is used as an indirect evaluation index. Filling a plurality of virtual nodes in other positions of the reconstructed radio map, repeating the steps (1) to (3), recovering fingerprint information on newly added reference nodes, and obtaining a newly reconstructed radio map by a graph Laplace semi-supervised interpolation method;

further, given that there are areas within the building that are walls or other non-free spaces where no targets are likely to occur, the present invention will also eliminate these extra interfering position reference nodes that are added in a carefully designed filling pattern. The indoor positioning accuracy of the radio map newly reconstructed by the method is better than the positioning accuracy of the initial radio map and is also better than the positioning accuracy of the new reconstructed base line method.

Step 4: training set training phase. Inputting the fingerprint information in the reconstructed radio map generated in the step 2 into the neural network for training, obtaining the target longitude and latitude corresponding to each fingerprint data through the neural network, comparing the calculated longitude and latitude with the actual longitude and latitude of the fingerprint data, obtaining a loss function, and when the loss function meets the set requirement, ending the neural network training, and finally saving the obtained network model parameters. The indoor positioning model used in the invention is a three-layer DNN model. The input size of the network is (n×n _s )×N _AP I.e. there is NxNxN _s A plurality of samples, each sample having a feature dimension of N _AP . The number of neurons in layers 1, 2 and 3 is different for different data sets. The robbery can be determined by the actual situation. The neural network positioning test set selects the area selected by the method to carry out positioning performance test corresponding to the original test set.

Using the MSE function as a loss function for DNN, the network will directly output the coordinates of the target. Using Adam optimizer, the initial learning rate of the network is 0.01. Using L ₂ Loss as weight decay and set the value to 5 x 10 ^-4 Furthermore, to avoid death of network neurons to some extent, the activation function of each FC layer uses a LeakyThe relu function.

Step 5: and a performance verification stage. Inputting the test set data into the network model stored in the step 3, and verifying the positioning performance of the method.

To facilitate analysis of RSS recovery accuracy. Assuming that the original radio map has N reference nodes, N remains after the node is randomly lost _r If the reference nodes are reconstructed into the radio map identical to the previous reference nodes, since the lost points are randomly distributed, the method can be equivalent to a random reconstruction mode, and the fingerprint information in the reconstructed radio map and the information of the known original N reference nodes are subjected to RSS recovery accuracy analysis.

Evaluating the gap between a radio map reconstructed at the original lost node position by using the graph signal method and a baseline method through RSS recovery precision analysis; furthermore, for the new layout mode of the careful design of the invention, the DNN neural network in the step 4 is used for evaluating the positioning accuracy performance gap used as indoor positioning between the radio map newly reconstructed at the carefully designed position and the baseline method by using the map signal method as an indirect evaluation standard of the radio map reconstruction because the positions of the original N reference points are not known. The existing conventional method for restoring the graph signal is set as a baseline method. As a result, it was found that the RSS information recovery accuracy of the radio map reconstructed using the graph signal method at the lost node position is better than the RSS recovery accuracy of the baseline method.

The invention also discloses an indoor positioning radio map reconstruction system based on the map signals, which comprises:

the frame construction unit is used for constructing an indoor positioning frame and obtaining an indoor initial radio map;

the map topology establishing unit is used for filling virtual nodes into the initial radio map to obtain a radio map to be reconstructed, and taking reference nodes in the radio map to be reconstructed as nodes of the map topology, and fingerprint information on each reference node is taken as information on the nodes of the map topology;

the recovery unit is used for recovering the information on each virtual node in the graph topology through a graph Laplace semi-supervised interpolation method; and obtaining a reconstructed radio map.

Further, the method further comprises the following steps:

an RSS recovery precision evaluation unit for evaluating the reconstructed radio map by means of RSS recovery precision analysis;

and the DNN neural network evaluation unit is used for evaluating the newly reconstructed radio map through the DNN neural network.

Example 1

The invention will now be described in further detail with reference to the drawings and to specific examples.

In the experiment, the numerical result display is carried out on the algorithm performance under the 2D scene of the fourth layer of the first building under the UCIIndor data set and the UWB ranging 3D scene data set respectively. Meanwhile, gaussian Process Regression (GPR) and Linear interpolation (Linear) are selected as comparison methods of the invention.

Fig. 3 is a uciindor original radio map, X-axis is longitude, Y-axis is latitude, and Z-axis is floor, and it is difficult to establish one connectivity map at all reference points because the three buildings are far apart from each other. Moreover, the raw data set does not give rise to floor height and is therefore unsuitable for forming a distance-based three-dimensional graphical topology. For this purpose, fig. 4 is a radio map of the fourth floor of the first building selected, with 68 reference nodes in total. Table 1 and fig. 5, fig. 6 shows the RSS recovery accuracy of the original lost node (random reconstruction mode) recovered by using the remaining 28 reference nodes after the 40 reference nodes are lost randomly, and since there are 520 APs in total, a part of the representative results are not shown in detail, the abscissa indicates the 40 lost nodes, and the ordinate indicates the RSS deviation. The fingerprint data recovery precision of the method of the image signal can be found to be highest and is superior to that of the traditional method of comparison.

Fig. 7 is a schematic diagram of a radio map after 40 reference nodes are lost, and fig. 8 is a schematic diagram of a carefully designed interpolation of one virtual node between two neighboring nodes. Table 2 shows that 40 nodes are randomly lost twice in the original data set, which are called Case1 and Case2 respectively, and according to the average positioning errors of the test set of the semi-supervised interpolation of the graph laplace, the regression of the gaussian process and the linear interpolation in the reconstruction of the radio map in the present embodiment, it can be found that the positioning errors of the method of the graph signal are obviously superior to those of the regression of the gaussian process and the linear interpolation in the scene of the present embodiment. Fig. 9 is a cumulative error distribution function of different algorithms, and it can be found that the method of this embodiment is superior to the comparative scheme, especially for controlling larger errors.

TABLE 1

RSS estimation error performance comparison (DBM) for different algorithms for reconstructing raw position data

Method	AP7	AP15	AP23	AP69	AP184	AP185	AP220	……	Average
										Graph	0.1438	0	2.1633	0	1.0890	1.0858	0	……	0.4864
GPR	0.2045	0	2.2292	0	1.2045	1.3392	0	……	0.5192
										Linear	0.4561	0	5.5733	0	1.4225	1.3939	0	……	0.8981

TABLE 2

Different algorithmic performance comparisons to reconstruct well-designed new position data

Scenario	Nolost	Lostbutnotrecovery	Graph	GPR	Linearinterp
						case1	10.3687m	12.1040m	11.1908m	11.6164m	13.2037m
case2	10.3687m	10.6638m	10.4294m	10.9735m	12.4048m

Furthermore, because the building is "X" shaped, it is possible to find that the middle portion of the "X" may be a wall or other portion that cannot be free space. These new nodes in the middle part are therefore not possible in practice, so they already become sources of interference data for the interference location results and should be eliminated. Fig. 10 is a schematic diagram after removing the interference point. The invention uses the suffix 'r' to represent the deleted condition. Fig. 11 is an average positioning error after various algorithms remove the interference points. It can be found that after the interference point is removed, the positioning accuracy of either method is further improved, and the method of the image signal is still the optimal method among them.

Also, the above method may be applied to a 3D scene. Fig. 12, 13 shows that after the UWB ranging 3D data set (with 324 reference nodes) is randomly lost by 50 and 20 reference nodes, respectively, it is first padded into the symmetrical 324 nodes as before. More virtual nodes are then populated in a well-designed manner, first according to the x-direction and then the y-direction. Finally, the radio maps containing 324, 612 and 1156 points, respectively, are built up with an average positioning error trend graph. The method for mapping signals provided by the invention can be found to not only obtain performance improvement in a 2D scene, but also obviously improve the positioning performance of the system in a 3D scene.

The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.

Claims (5)

1. An indoor positioning radio map reconstruction method based on a map signal is characterized by comprising the following steps:

constructing an indoor positioning frame, and obtaining an indoor initial radio map, wherein part of reference nodes are missing in the indoor initial radio map;

filling virtual reference nodes at the reference nodes of the missing part of the initial radio map to obtain a radio map to be reconstructed, regarding the reference nodes in the radio map to be reconstructed as nodes of a map topology, and regarding fingerprint information on each reference node as information on the nodes of the map topology;

recovering fingerprint information on each virtual node in the graph topology by a graph Laplace semi-supervised interpolation method; obtaining a reconstructed radio map;

step 1, signals related to undirected, weighted and connected graphs are recorded as

Weighted undirected corresponding to the signalThe drawing is marked as->

Wherein->

Is a set of N vertices, < >>

Is a collection of edges between nodes; by x _i Is indicated at node->

Signal value magnitude at; the adjacency matrix W is a weighted symmetric matrix reflecting the connection strength relationship between edges, and if edges (i, j) ∈ε are present, W _i,j Not less than 0, otherwise W _i,j =0; introducing a laplace matrix l=d-W, wherein D is a degree matrix;

step 2, constructing a space diagram topology by using a K-nearest neighbor method; calculating the distance g between all node pairs (i, j) according to the geographic positions of all nodes _i,j Forming a distance matrix G; creating an all-zero matrix M, then finding the first k elements with the smallest distance for the ith row of the matrix G, and recording as

Then let M's corresponding element be 1, record as +.>

The weight of each edge is inversely proportional to the square of the distance between two nodes; finally, the following weighted adjacency matrix W is constructed:

when W is constructed, the corresponding degree matrix D and laplace matrix l=d-W are also constructed; taking nodes as vertexes of the graph, taking distance relations among the nodes as weights of edges, and taking fingerprint data as information on the nodes of the graph;

in step 3, on the connected graph, in order to measure the smoothness or signal correlation of the signal y, TV (y) is solved using the following laplace quadratic form, where TV (y) is:

TV(y)＝y ^T Ly＝Σ _i≠j W _ij (y _i -y _j ) ² (2)

when data of one or more nodes is lost, the data is solved by a graph semi-supervised learning framework, and the value of the missing position is considered to have a smooth relation with the value of the adjacent known nodes on the premise that the framework data is positioned in the graph nodes, so that the spatial smoothness is expressed as y ^T Ly; then, converting the smoothness equation into a problem function for solving missing values in the graph topology, optimizing the global quantity expressed by the space smoothness through the formula (3), and finding the missing values so that the information on the virtual nodes is recovered, wherein the problem function is shown in the formula (3);

solving a formula (3) to obtain a signal y to be recovered, obtaining fingerprint information in a reconstructed radio map, and correspondingly obtaining the reconstructed radio map, wherein the radio map is provided with N reference nodes, each reference node has respective longitude and latitude, and each reference node has corresponding fingerprint information;

filling a plurality of virtual nodes in other positions of the reconstructed radio map, repeating the steps 1-3, recovering fingerprint information on newly added reference nodes, and obtaining the newly reconstructed radio map through a graph Laplace semi-supervised interpolation method.

2. The indoor positioning radio map reconstruction method based on the map signal according to claim 1, wherein the reconstructed radio map is evaluated by RSS restoration accuracy analysis; the newly reconstructed radio map is evaluated by means of a DNN neural network.

3. The indoor positioning radio map reconstruction method based on the map signal according to claim 1, wherein the problem function of the missing value is solved by a CVX toolbox of matlab.

4. A map reconstruction system for indoor positioning radio based on map signals for implementing the method of claim 1, comprising:

the frame construction unit is used for constructing an indoor positioning frame and obtaining an indoor initial radio map;

the map topology establishing unit is used for filling virtual nodes into the initial radio map to obtain a radio map to be reconstructed, and taking reference nodes in the radio map to be reconstructed as nodes of the map topology, and fingerprint information on each reference node is taken as information on the nodes of the map topology;

the recovery unit is used for recovering the information on each virtual node in the graph topology through a graph Laplace semi-supervised interpolation method; and obtaining a reconstructed radio map.

5. An indoor positioning radio map reconstruction system based on a map signal as recited in claim 4, further comprising:

an RSS recovery precision evaluation unit for evaluating the reconstructed radio map by means of RSS recovery precision analysis;

and the DNN neural network evaluation unit is used for evaluating the newly reconstructed radio map through the DNN neural network.

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