An indoor positioning method and device based on RSSI fingerprint

Abstract

The embodiment of the application provides an indoor positioning method and device based on an RSSI fingerprint, and relates to the technical field of data processing.The method comprises the following steps: acquiring RSS data of a WIFI at a reference point with a known coordinate in a room and at a to-be-positioned point in different time domains, setting a coefficient K S The fingerprint dimension is expanded, an isomorphic RSSI fingerprint feature space is constructed, the RSSI fingerprint feature is reconstructed based on an attention mechanism, the weight of important features is improved, inherent hierarchical features in the fingerprint data are extracted based on a double-branch auxiliary positioning network, and the hierarchical features are fused with the reconstructed features, so that the position distinguishability of the fingerprint is improved, the network is trained by using the reference point information with a known coordinate, and the position coordinates of the to-be-positioned fingerprint features in different time domains are predicted. The scheme provided by the embodiment of the application can increase the precision and robustness of an indoor fingerprint positioning system.

Description

TECHNICAL FIELD

[0001] The embodiment of the present application relates to the technical field of data processing, in particular to an indoor positioning method and device based on RSSI fingerprint. TECHNICAL BACKGROUND

[0002] Indoor positioning is one of the key technologies of location-based services, and various different indoor positioning systems have been proposed, such as Ultra Wide Band (UWB), Wireless fidelity (WIFI), 5G, Inertial Measurement Unit (IMU), etc. Among them, fingerprint positioning has a great advantage because it does not require the position of base stations and the initial position of the target. Fingerprint positioning is usually divided into offline and online stages: in the offline stage, the signal characteristics of all access points (APs) at all reference points (RPs) are detected, such as received signal strength indicator (RSSI), channel state information (CSI), etc., to form an offline fingerprint database; in the online stage, the fingerprint of an unknown position is matched with the offline fingerprint database to realize the prediction of the user's position.

[0003] With the popularity of smart devices, fingerprint positioning based on WIFI RSSI is widely used in large shopping malls, libraries and other large multi-storey buildings because it does not require additional equipment and is easy to collect, showing great application demand and market potential. However, in the above application scenarios, due to the complex and diverse structure of buildings and the dynamic and variable indoor environment, such as the removal, addition and replacement of base station equipment within a period of time, the fingerprint positioning system based on WIFI RSSI is difficult to obtain positioning signals with high position discrimination and long-term stability, resulting in a large difference between the distribution of the RSSI fingerprint database constructed in the offline stage and the online sample, and a sharp decline in the positioning accuracy of the system. Therefore, the related technology faces the following problems: the feature spaces of the fingerprints collected from the offline stage and the online stage are heterogeneous and have low position discrimination, making it difficult to obtain accurate matching results. SUMMARY

[0004] The purpose of the embodiment of the present application is to provide an indoor positioning method and device based on RSSI fingerprint to increase the accuracy of indoor wireless fingerprint positioning systems and the robustness to changes in base station equipment.

[0005] In a first aspect, the embodiment of the present application provides an indoor positioning method based on RSSI fingerprint, which comprises:

[0006] Acquire RSS data of WIFI at indoor known coordinate reference points and at different time domains of to-be-positioned places, set coefficient KS to expand fingerprint dimension, and construct isomorphic WIFI RSSI fingerprint feature space;

[0007] Train attention network by using RSSI fingerprint at known coordinate reference points, acquire attention matrix of RSSI fingerprint at different time domains of to-be-positioned places, and reconstruct each RSSI fingerprint based on attention matrix coefficient to improve the weight of important features.

[0008] Train hierarchical feature extraction network by using reconstructed RSSI fingerprint at known coordinate reference points, extract hierarchical features of RSSI fingerprint at different time domains of to-be-positioned places, and fuse the reconstructed features to improve the position distinguishability of the fingerprint.

[0009] Train positioning network by using fused fingerprint at known coordinate reference points, and obtain position estimation of the fused fingerprint at different time domains of to-be-positioned places.

[0010] In an embodiment of the present application, the acquisition of RSS data of WIFI at indoor known coordinate reference points and at different time domains of to-be-positioned places, the setting of coefficient K S Expansion of fingerprint dimension, and construction of isomorphic WIFI RSSI fingerprint feature space, include:

[0011] Acquire RSS data of WIFI base station equipment at known coordinate reference points and at different time domains of to-be-positioned places by mobile phone, acquire RSSI data by normalizing RSS data, and then expand fingerprint dimension according to coefficient K S to obtain isomorphic WIFI RSSI fingerprint feature space.

[0012] In an embodiment of the present application, the training of attention network by using RSSI fingerprint at known coordinate reference points, the acquisition of attention matrix of RSSI fingerprint at different time domains of to-be-positioned places, the reconstruction of each RSSI fingerprint based on attention matrix coefficient, and the improvement of the weight of important features include:

[0013] Build an attention subnetwork, the subnetwork first calculates attention matrix parameters w, b. Then calculate the attention matrix A S ,A T based on RSSI fingerprint, reconstruct each RSSI fingerprint based on the attention matrix A S ,A T Finally, introduce the Dropout layer to increase the robustness of the reconstructed fingerprint to the disappearing APs.

[0014] In an embodiment of the present application, the reconstructed RSSI fingerprint training hierarchical feature extraction network at the reference point with known coordinates is used to extract hierarchical features of RSSI fingerprints at the to-be-positioned point in different time domains, and the reconstructed features are fused to improve the position distinguishability of the fingerprints, comprising:

[0015] A hierarchical feature extraction subnetwork is built, which first uses an attention subnetwork to reconstruct the RSSI fingerprint features, then uses a feedforward neural network (FNN) to extract low-dimensional hierarchical features, and finally fuses the low-dimensional hierarchical features with high-dimensional reconstructed features to obtain a fused fingerprint.

[0016] In an embodiment of the present application, the positioning network is trained by the fused fingerprint at the reference point with known coordinates to obtain the position estimate of the fused fingerprint at the to-be-positioned point in different time domains, comprising:

[0017] A positioning network is built, which first obtains the position estimate by passing the fused fingerprint obtained by splicing the attention subnetwork and the hierarchical feature subnetwork through an ascending FNN and then through a descending FNN. Joint training is performed, the fused fingerprint at the reference point with known coordinates is input into the positioning network to obtain the position estimate of the fused fingerprint at the to-be-positioned point in different time domains.

[0018] In a second aspect, an embodiment of the present application provides an indoor positioning device based on RSSI fingerprint, the device comprising:

[0019] The acquisition module is configured to acquire RSS data of WIFI at a reference point with known coordinates indoors and at a to-be-positioned point in different time domains, and set a coefficient K S The dimension of the fingerprint is expanded, and an isomorphic RSSI fingerprint feature space is constructed.

[0020] The feature reconstruction module based on the attention mechanism is configured to train an attention network by the RSSI fingerprint at the reference point with known coordinates, acquire an attention matrix of the RSSI fingerprint at the to-be-positioned point in different time domains, and reconstruct each RSSI fingerprint based on the attention matrix coefficient to improve the weight of important features.

[0021] The hierarchical feature extraction module is configured to train a hierarchical feature extraction network by the reconstructed RSSI fingerprint at the reference point with known coordinates, extract hierarchical features of the RSSI fingerprint at the to-be-positioned point in different time domains, and fuse the reconstructed features to improve the position distinguishability of the fingerprint.

[0022] The position prediction module is configured to train a positioning network by the fused fingerprint at the reference point with known coordinates to obtain the position estimate of the fused fingerprint at the to-be-positioned point in different time domains.

[0023] In an embodiment of the present application, the acquisition module is specifically configured to:

[0024] The RSS data of the WIFI base station equipment at the reference point with known coordinates and the to-be-positioned point at different time domains is acquired through a mobile phone, the RSS data is normalized to obtain RSSI data, and then the RSSI data is processed according to a coefficient K S The fingerprint dimension is expanded to obtain an isomorphic WIFI RSSI fingerprint feature space.

[0025] In an embodiment of the present application, the feature reconstruction module based on the attention mechanism is specifically used for:

[0026] The attention subnetwork is built, the subnetwork first calculates attention matrix parameters w and b, then calculates an attention matrix A according to the RSSI fingerprint S ,A T , and reconstructs each RSSI fingerprint based on the attention matrix A S ,A T Finally, the Dropout layer is introduced to increase the robustness of the reconstructed fingerprint to the disappearing APs.

[0027] In an embodiment of the present application, the hierarchical feature extraction module is specifically used for:

[0028] The hierarchical feature extraction subnetwork is built, the subnetwork first reconstructs the RSSI fingerprint feature using the attention subnetwork, then extracts low-dimensional hierarchical features using a feedforward neural network (FNN), and finally fuses the low-dimensional hierarchical features and high-dimensional reconstructed features to obtain a fusion fingerprint.

[0029] In an embodiment of the present application, the position prediction module is specifically used for:

[0030] The positioning network is built, the fusion fingerprint at the reference point with known coordinates is input, the position estimation is obtained through a dimension-increasing FNN and then through a dimension-decreasing FNN, and joint training is performed. After obtaining the training model, the fusion fingerprint at the to-be-positioned point at different time domains is input, and the position estimation of the to-be-positioned fingerprint is obtained.

[0031] The embodiment of the present application has the following beneficial effects:

[0032] The application provides an indoor positioning method and device based on RSSI fingerprint, extracts hierarchical features of the fingerprint while reconstructing a fingerprint feature space based on an attention mechanism, linearly fuses the hierarchical features, and uses the fused features as the fingerprint for indoor position estimation, thereby providing an important technical tool for indoor position service development. Compared with the related art, the indoor fingerprint positioning method and device can significantly improve the accuracy of fingerprint positioning in a complex dynamic indoor scene and the robustness to AP changes, and increase the feasibility of deploying a fingerprint positioning system in an actual indoor scene. BRIEF DESCRIPTION OF DRAWINGS

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other embodiments can also be obtained by those skilled in the art based on these drawings.

[0034] Figure 1 A flowchart of an indoor positioning method based on RSSI fingerprint provided by the embodiment of the present application;

[0035] Figure 2 A transformation diagram of heterogeneous features to homogeneous features provided by the embodiment of the present application;

[0036] Figure 3 A structure diagram of an attention subnetwork provided by the embodiment of the present application;

[0037] Figure 4 A structure diagram of a hierarchical feature extraction subnetwork provided by the embodiment of the present application;

[0038] Figure 5 A structure diagram of an indoor positioning device based on RSSI fingerprint provided by the embodiment of the present application. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art based on the present application belong to the scope of protection of the present application.

[0040] The wireless signal acquired by the indoor fingerprint positioning system is affected by the change of the base station device and fluctuates, such as the addition, removal and displacement of the base station device, which causes the composition of the fingerprint data in different time domains to be different, and aggravates the occurrence of fingerprint error matching phenomenon, and seriously affects the performance of the indoor location service. Therefore, the indoor positioning method based on the WIFI fingerprint faces the following problems: the fingerprint feature spaces extracted from the data collected in the offline stage and the online stage are heterogeneous, and therefore the robustness and discriminability are insufficient, and it is difficult to obtain accurate matching results.

[0041] To solve the above problems, the embodiments of the present application provide an indoor positioning method and device based on RSSI fingerprint, which are described below.

[0042] Firstly, an indoor positioning method based on RSSI fingerprint provided by the embodiments of the present application is described.

[0043] Referring to Figure 1 , a flowchart of an indoor fingerprint positioning method provided by the embodiments of the present application is shown, the method is applied to an electronic device with computing capability, for example, the method is applied to a computer, and the above method includes the following steps S101 to S104.

[0044] Step S101: acquiring RSS data of WIFI at a reference point with known coordinates in the room and at different time domains to be positioned, and setting a coefficient K S The fingerprint dimension is expanded, and a homogeneous WIFI RSSI fingerprint feature space is constructed.

[0045] In the process of indoor fingerprint positioning, the RSSI values of all AP signals that can be received at all RPs are acquired, and different features are constructed as WIFI RSSI fingerprints according to the differences in their Media Access Control Addresses (MAC). S The feature values of new APs in the online fingerprint are filled, the feature space is constructed in different time domains, and data normalization processing is performed.

[0046] For example, if the total number of all detectable base station APs in an indoor positioning area is K, the total number of base stations detected in the offline stage is K O , the number of offline fingerprints collected is n O , and the number of online fingerprints collected is n T . As shown in Figure 2 , the i-th offline fingerprint is represented as:

[0047]

[0048] where j > KO Time, Let The corresponding label is The source domain D S is composed of:

[0049]

[0050] For online fingerprints, j≤K O The part of Keep unchanged and fill in the RSS value of the new AP in the fingerprint reserved dimension, that is, j>K O The part of If K>K S , delete the part of j>K S , otherwise, fill in zero after j>K. At this time, the i-th online fingerprint is represented as:

[0051]

[0052] Let The corresponding label is The target domain D U is composed of:

[0053]

[0054] We denote the RSS value of the undetected AP as 0, and the RSS value of other APs is normalized and set to a lower limit of 0.2. The RSSI value of the j-th AP of the normalized fingerprint is:

[0055]

[0056] Wherein, is the RSS value of the j-th AP of the n0 fingerprints after normalization and the average RSS value of the j-th AP, and f(·) is a mapping function.

[0057] Step S102: training the attention network using the RSSI fingerprint at the reference point with known coordinates, obtaining the attention matrix of the RSSI fingerprint at the to-be-positioned point in different time domains, and reconstructing each RSSI fingerprint based on the attention matrix (Attention, A) coefficient to improve the weight of important features.

[0058] Specifically, as Figure 3 , an attention subnetwork is built, which first generates an attention matrix through self-attention to weight the RSSI fingerprint features, and then through a Dropout layer to randomly miss some parameter values to simulate the missing of APs, and obtain the reconstructed RSSI fingerprint features, and the reconstructed feature size is the same as the input feature, that is, K S dimension.

[0059] Exemplarily, the normalized fingerprint features are passed through an attention layer, and the matrices Q, K, V are actually: Q = w q *X + b q K = w k *X + b k V = w v *X + b v , where trainable parameters w q , w k , w v , b q , b k , b v are constants. For Q and K similarity, the dot product method is used herein to calculate the A matrix, which is specifically represented as:

[0060]

[0061] Then pass through the Dropout layer, the new ith source domain fingerprint and the target domain fingerprint can be represented as:

[0062]

[0063] where are the corresponding attention matrices of the ith source domain fingerprint and the ith target domain fingerprint , and Drop(·) is processed through the Dropout layer.

[0064] Step S103: training the hierarchical feature extraction network using the reconstructed RSSI fingerprint at the reference point with known coordinates, extracting the hierarchical features of the RSSI fingerprint at the to-be-positioned point in different time domains, and fusing the reconstructed features to improve the position distinguishability of the fingerprint.

[0065] Specifically, a hierarchical feature extraction subnetwork is built, which extracts low-dimensional hierarchical features of the reconstructed RSSI fingerprint through a dimension-reduced FNN, and linearly fuses the extracted hierarchical features with the reconstructed features to obtain fused features with high position distinguishability.

[0066] Exemplarily, the reconstructed feature is passed through a dimension-reduced FNN to obtain the output hierarchical feature, such as Figure 4 , the size of which is related to the extracted hierarchical information, such as a positioning area being a m-layer building, and the hierarchical feature dimension being m. Then the extracted hierarchical feature is dimensionally spliced with the Ks-dimensional reconstructed feature to obtain K S +m-dimensional fused features.

[0067] Step S104: training the positioning network with the fusion fingerprints at the reference points with known coordinates to obtain the position estimation of the fusion fingerprints at the to-be-positioned points in different time domains.

[0068] Specifically, the RSSI data obtained at the reference points and the reference point coordinates are jointly input into an indoor fingerprint positioning model, and a pre-trained model updates and adjusts model parameters; after obtaining the above pre-trained model, RSSI data obtained at unknown coordinates in the same indoor scene is input to obtain position information of the to-be-positioned fingerprint features output by the fingerprint positioning model.

[0069] For example, in the offline stage, the K S +dimensional fusion fingerprint input positioning network, such as Figure 4 , first embeds the fingerprint features into an n>2K S +2m+2-dimensional space through a dimension-increasing FNN1, and then obtains the position estimation of the fingerprint through a dimension-decreasing FNN2 to train the network to obtain the mapping from the fingerprint to the position. The overall loss is:

[0070] l=CE(Y f ,F)+MSE(Y c ,C),

[0071] where CE is the cross-entropy loss, MSE is the mean square error loss, F and C represent the floor and the position coordinates respectively.

[0072]

[0073]

[0074] where, y i and are the true label and the prediction result of the to-be-positioned feature respectively, x i is the network input, f(·) represents the positioning network mapping, and the optimization of l is performed to improve the floor classification accuracy and the positioning accuracy in the case of AP change. In the application stage, the collected RSSI data is input into the above positioning model, and the model outputs the position prediction of the to-be-positioned fingerprint feature.

[0075] Corresponding to the foregoing indoor fingerprint positioning method, the embodiment of the application further provides an indoor fingerprint positioning device.

[0076] Referring to Figure 5 , a structural schematic diagram of an indoor positioning device based on RSSI fingerprint provided by the embodiment of the application, the device is applied to an electronic device with computing capability, and the device comprises:

[0077] The acquisition module 501 is used for acquiring RSS data of WIFI at a known coordinate reference point and at a to-be-positioned place in different time domains, and setting a coefficient K S The fingerprint dimension is expanded, and an isomorphic WIFI RSSI fingerprint feature space is constructed.

[0078] The feature reconstruction module 502 based on an attention mechanism is used for training an attention network by using the RSSI fingerprint at the known coordinate reference point, acquiring an attention matrix of the RSSI fingerprint at the to-be-positioned place in different time domains, reconstructing each RSSI fingerprint based on an attention matrix coefficient, and improving the weight of important features.

[0079] The hierarchical feature extraction module 503 is used for training a hierarchical feature extraction network by using the reconstructed RSSI fingerprint at the known coordinate reference point, extracting hierarchical features of the RSSI fingerprint at the to-be-positioned place in different time domains, and fusing the hierarchical features with the reconstructed features to improve the position distinguishability of the fingerprint.

[0080] The position prediction module 504 is used for training a positioning network by using the fused fingerprint at the known coordinate reference point, and obtaining a position estimation of the fused fingerprint at the to-be-positioned place in different time domains.

[0081] In one embodiment of the present application, the acquisition module 501 is specifically used for:

[0082] The RSS data of WIFI base station equipment at the known coordinate reference point and at the to-be-positioned place in different time domains are acquired by a mobile phone, the RSS data is normalized to obtain RSSI data, and then the RSSI data is reconstructed according to the coefficient K S The fingerprint dimension is expanded, and an isomorphic WIFI RSSI fingerprint feature space is obtained.

[0083] In one embodiment of the present application, the feature reconstruction module 502 based on the attention mechanism is specifically used for:

[0084] An attention subnetwork is built, the subnetwork first calculates attention matrix parameters w and b, then calculates an attention matrix A S ,A T based on the RSSI fingerprint, and reconstructs each RSSI fingerprint. S ,A T Finally, a Dropout layer is introduced to increase the robustness of the reconstructed fingerprint to disappearing APs.

[0085] In one embodiment of the present application, the hierarchical feature extraction module 503 is specifically used for:

[0086] A hierarchical feature extraction subnetwork is built, the subnetwork first uses an attention subnetwork to reconstruct the RSSI fingerprint feature, then uses an FNN to extract a low-dimensional hierarchical feature, and finally fuses the low-dimensional hierarchical feature with the high-dimensional reconstructed feature to obtain a fused fingerprint.

[0087] In one embodiment of the present application, the position prediction module 504 is specifically used for:

[0088] A positioning network is built, the fused fingerprint obtained by splicing the attention subnetwork and the hierarchical feature subnetwork is first passed through an FNN for dimension increasing and then passed through an FNN for dimension decreasing to obtain a position estimate. Joint training is performed, the fused fingerprint at the reference point with a known coordinate is input to train the positioning network, and the position estimate of the fused fingerprint at the to-be-positioned point in different time domains is obtained.

Claims

1. A RSSI fingerprint based indoor positioning method, characterized in that, The method comprises: applying RSS data at a reference point with known coordinates indoors and at a to-be-positioned place in different time domains to construct an isomorphic WIFI RSSI fingerprint feature space, comprising: The attention network is trained by acquiring RSSI fingerprints of reference points with known coordinates through a mobile phone, and a coefficient K is set S The fingerprint dimension is expanded to obtain an isomorphic WIFI RSSI fingerprint feature space; obtaining an attention matrix of the RSSI fingerprint at the to-be-positioned place in different time domains, reconstructing each RSSI fingerprint based on the attention matrix coefficients, and improving the weight of important features; training a hierarchical feature extraction network by using the reconstructed RSSI fingerprint at the reference point with known coordinates, extracting hierarchical features of the RSSI fingerprint at the to-be-positioned place in different time domains, and fusing the hierarchical features with the reconstructed features to improve the position distinguishability of the fingerprint; training a positioning network by using the fused fingerprint at the reference point with known coordinates to obtain a position estimate of the fused fingerprint at the to-be-positioned place in different time domains, comprising: building a positioning network, inputting the fused fingerprint obtained by splicing the attention sub-network and the hierarchical feature sub-network, and obtaining the position estimate through a dimension-increasing FNN and then a dimension-decreasing FNN, and performing joint training, inputting the fused fingerprint at the reference point with known coordinates into the positioning network to obtain the position estimate of the fused fingerprint at the to-be-positioned place in different time domains.

2. The method of claim 1, wherein, The method comprises: An attention subnetwork is constructed, wherein the subnetwork first calculates the attention matrix parameters w and b; then it calculates the attention matrix A based on the RSSI fingerprint. S A T Based on attention matrix A S A T Reconstruct each RSSI fingerprint; finally, introduce a Dropout layer to increase the robustness of the reconstructed fingerprint to missing access points.

3. The method of claim 1, wherein, The method comprises: The method comprises:

4. An RSSI fingerprint-based indoor positioning apparatus, characterized by The device comprises: The acquisition module is used for acquiring RSS data of WIFI at a reference point with known indoor coordinates and at a to-be-positioned position in different time domains, and setting a coefficient K S The fingerprint dimension is expanded, and an isomorphic WIFI RSSI fingerprint feature space is constructed, specifically by acquiring RSS data of WIFI base station equipment at a reference point with known coordinates and at a to-be-positioned position in different time domains through a mobile phone, performing normalization processing on the RSS data to acquire RSSI data, and then according to the coefficient K S The fingerprint dimension is expanded, and an isomorphic WIFI RSSI fingerprint feature space is constructed. a feature reconstruction module based on an attention mechanism: training an attention network by using the RSSI fingerprint at the reference point with known coordinates, obtaining an attention matrix of the RSSI fingerprint at the to-be-positioned place in different time domains, reconstructing each RSSI fingerprint based on the attention matrix coefficients, and improving the weight of important features; a hierarchical feature extraction module: training a hierarchical feature extraction network by using the reconstructed RSSI fingerprint at the reference point with known coordinates, extracting hierarchical features of the RSSI fingerprint at the to-be-positioned place in different time domains, and fusing the hierarchical features with the reconstructed features to improve the position distinguishability of the fingerprint; a position prediction module: training a positioning network by using the fused fingerprint at the reference point with known coordinates to obtain a position estimate of the fused fingerprint at the to-be-positioned place in different time domains, specifically for: building a positioning network, inputting the fused fingerprint at the reference point with known coordinates, obtaining the position estimate through a dimension-increasing FNN and then a dimension-decreasing FNN, and performing joint training; after obtaining the training model, inputting the fused fingerprint at the to-be-positioned place in different time domains to obtain the position estimate of the to-be-positioned fingerprint.

5. The apparatus of claim 4, wherein, The feature reconstruction module based on the attention mechanism is specifically used for: Build an attention subnetwork, which first calculates attention matrix parameters w, b; then calculates attention matrix A according to the RSSI fingerprint S , A T , reconstructs each RSSI fingerprint based on the attention matrix A S , A T Finally, introduce a Dropout layer to increase the robustness of the reconstructed fingerprint to the disappearing APs.

6. The apparatus of claim 4, wherein, The hierarchical feature extraction module is specifically used for: A hierarchical feature extraction subnetwork is built, which first uses an attention subnetwork to reconstruct the RSSI fingerprint features, then uses an FNN to extract low-dimensional hierarchical features, and finally fuses the low-dimensional hierarchical features with the high-dimensional reconstructed features to obtain a fused fingerprint.

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