CN104936287A - Sensor network indoor fingerprint positioning method based on matrix completion - Google Patents

Abstract

The invention discloses a sensor network indoor fingerprint positioning method based on matrix completion is applicable to the robust indoor positioning method of the wireless sensor network WSN. The sensor network indoor fingerprint positioning method disclosed by the invention comprises steps of utilizing a matrix completion theory to recover a complete fingerprint database by only sampling part of signal fingerprints through utilizing the low-rank property of a fingerprint matrix, adopting a classic KNN algorithm to perform object positioning of an online phase after the fingerprint database is constructed, in the process of the fingerprint matrix complementation and for effectively eliminating the outlier noise and the Gauss noise contained by the signal fingerprint, respectively introducing an L1 norm regularized item and an F norm regularized item, modeling a fingerprint data recovery question into a norm regularized matrix complementation question and solving the question through an alternative direction mutiplier method algorithm The sensor network indoor fingerprint positioning method based on matrix completion can effectively reduce the workload of the information fingerprint database construction and can acquire positioning precision which is higher than the positioning precision obtained from the same kind method under various noise conditions.

Description

The indoor fingerprint positioning method of Sensor Network based on matrix completion

Technical field

The present invention is that one is applicable to wireless sensor network (Wireless sensor network, WSN) robust indoor orientation method, the method utilizes the low-rank characteristic of received signals fingerprint matrix, finger print data under noise jamming is recovered problem and is modeled as norm regularization matrix completion problem, introducing L1 norm and F norm are with level and smooth outlier noise and Gaussian noise on this basis, effectively solve eventually through alternating direction multiplier method.The method only need carry out a small amount of received signals fingerprint data acquisition comparatively intactly can recover fingerprint base, all can obtain the positioning precision higher than congenic method under various noise scenarios.This technology belongs to wireless sensor network field.

Background technology

In recent years, wireless sensor network (Wireless Sensor Network, WSN) technology obtains significant progress, just be widely used in the fields such as military investigation, intelligent transportation, environmental monitoring, intelligent domestic system, automatic parking distance warning, medical treatment & health monitoring, risk of forest fire monitoring etc. are the typical apply of wireless sensor network.Along with Intelligent mobile equipment universal carrying Miniature Sensor in a large number, enrich the way of realization of wireless sensor network further, extended the covering scope of wireless sensor network.

In wireless sensor network, the acquisition of sensor node own location information is vital concerning various application.Along with the development of mobile Internet and the universal of intelligent mobile terminal, indoor positioning technologies causes the extensive concern of researcher.As the continuity of outdoor positioning technology in indoor environment, indoor positioning has filled up the blank of traditional position location techniques, has a wide range of applications.As, locate the indoor occupant navigation system etc. under concrete shop and the occurred events of public safety such as intelligent shopping guide system, fire scene in shopping mall market.Under outdoor environment, be that the location technology of representative is very ripe with GPS, but in building, due to covering of the obstacle such as body of wall, glass, gps signal deep fades, the locating effect that cannot realize ideal.In addition, because indoor environment is complicated, barrier and interference source various, the multipath effect in signal communication process and noise jamming become universal phenomenon, increase the difficulty of indoor positioning further.

Existing indoor positioning technologies is mainly based on ultrasonic wave, RFID, UWB, ZigBee and WLAN etc.Compared with other technologies, the indoor positioning technologies based on WLAN signal fingerprint make use of the WLAN access point be available anywhere, and without the need to the particular device that extra installation cost is high, becomes current comparatively ripe indoor positioning technologies.But first the indoor positioning algorithms based on received signals fingerprint needs reconnoitre indoor environment and set up fingerprint base, and workload is huge; Meanwhile, due to the existence of the numerous barrier in indoor and interference source, inevitably there is error in the RSSI data collected, and then greatly reduces final positioning precision.Therefore, be badly in need of the indoor orientation method of a kind of robust of design, while reducing fingerprint base construction work amount, obtain higher positioning precision.

Summary of the invention

Technical problem: the object of the invention is to design a kind of indoor robust positioning method based on fingerprint matrices completion, be applicable to the robust indoor positioning of wireless sensor network (Wireless sensor network, WSN).The method utilizes the low-rank characteristic of received signals fingerprint matrix, finger print data under noise jamming is recovered problem and is modeled as norm regularization matrix completion problem, introducing L1 norm and F norm are with level and smooth outlier noise and Gaussian noise on this basis, effectively solve eventually through alternating direction multiplier method.The method utilizing the present invention to propose only need carry out a small amount of received signals fingerprint data acquisition comparatively intactly can recover fingerprint base, all can obtain the positioning precision higher than congenic method under various noise scenarios.

Technical scheme: the present invention is a kind of indoor robust positioning method based on fingerprint matrices completion.By utilizing the low-rank of fingerprint matrices, only need sampling section received signals fingerprint that matrix completion theory can be utilized to recover complete fingerprint base; After fingerprint database builds, classical k nearest neighbor (K-Nearest Neighbors, KNN) algorithm is adopted to carry out the target localization of on-line stage.In fingerprint matrices completion process, the outlier noise comprised for effective erasure signal fingerprint and Gaussian noise, introduce L1 norm regularization item and F norm regularization item respectively, problem of being recovered by finger print data is modeled as norm regularization matrix completion problem, and is solved by alternating direction multiplier method.The method effectively can reduce the workload that information fingerprint storehouse builds, and under all kinds of noise situations, obtain the positioning precision higher than congenic method.

Indoor robust positioning method based on fingerprint matrices completion is included in following concrete steps

Initial scene setting:

Step 1) set locating area as a rectangular area, by its horizontal n ₁decile, longitudinal n ₂decile, then whole region is evenly divided into n ₁× n ₂=n rectangular mesh, each grid represents a reference point, altogether n reference point;

Step 2) a random placement m WAP (wireless access point) in whole region; For any one access point APi, suppose to carry out wireless signal acquiring in all reference points, then can construct a fingerprint matrices wherein i=1,2 ..., m, matrix element is the wireless signal strength from this APi that each reference point collects;

Off-line fingerprint base builds:

Step 3) for reducing workload, only random selecting part reference point carries out wireless signal acquiring, and reference point indexed set is Ω;

Step 4) element disappearance is generated for each access point APi and the fingerprint matrices of noise may be comprised wherein i=1,2 ..., m, P _Ω() is orthogonal project operator, is defined as:

${\left[P_{\mathrm{\Ω}}\left(\mathrm{Mi}\right)\right]}_{\mathrm{jk}}=\left\{\begin{array}{cc}{\mathrm{Mi}}_{\mathrm{jk}},& \mathrm{if}(j,k)\∈\mathrm{\Ω}\\ 0,& \mathrm{otherwise}\end{array}\right.$

Represent that matrix element is the wireless signal strength value that this station acquisition arrives as subscript (j, k) ∈ Ω;

Step 5) utilize norm regularization fingerprint matrices completion algorithm by P _Ω(Mi) complete fingerprint matrices is reverted to;

Step 6) fingerprint base in whole region is constructed according to m fingerprint matrices;

Tuning on-line:

Step 7) set TP as site undetermined, at this point, wireless signal strength measurement is carried out to m access point;

Step 8) utilize classical k nearest neighbor (K-Nearest Neighbors, KNN) algorithm contrast TP and the wireless signal strength of each reference point, obtain K the reference point the most similar to TP;

Step 9) physical location of TP is the average of K reference point coordinate.

Some keys involved in above step are as follows:

Fingerprint matrices builds

As shown in Figure 1, if locating area is a rectangular area, it is evenly divided into n ₁× n ₂=n grid, then each grid represents a reference point.Sample in each reference point, then will form a n to each AP ₁× n ₂the matrix of size, the element in matrix is the wireless signal strength from this AP that the corresponding reference point in this position collects, and whole matrix can regard the received signals fingerprint distribution map of AP at locating area as, and we are referred to as fingerprint matrices.If adopt pointwise sampling method, then can obtain very high positioning precision, but huge sampling work amount often makes us bearing; Meanwhile, due to the complexity of environment, and signal measurement can be carried out in the net region of not all, usually only have a small-scale sampled point subset can be measured, therefore fingerprint matrices is incomplete, only has Partial Elements known, and absent element needs to be supplemented by matrix completion algorithm.As shown in Figure 1, grey square represents that the reference point in this position has carried out actual measurement, and the signal strength values of the corresponding reference point of white square is then obtained by matrix completion algorithm.

Fingerprint base builds

In off-line fingerprint base building process, selected part reference point carries out wireless signal strength collection, then for each reference point AP _igeneration element lacks and noisy fingerprint square by (i=1,2, L, m) the norm regularization fingerprint matrices completion algorithm utilizing the present invention to propose, we can more accurately recover original fingerprint matrix A _i, thus obtain AP _iin the signal strength signal intensity of non-sampling location.By A _iexpand into row vector then this vector representation AP _iin the wireless signal strength value of all reference point locations.We can construct the fingerprint base in whole region accordingly

$F=\left(\begin{array}{c}{a}_1\\ a_2\\ M\\ a_m\end{array}\right)=\left(\begin{array}{cccc}{P}_{\mathrm{1,1}}& P_{\mathrm{1,2}}& L& P_{1,n}\\ P_{\mathrm{2,1}}& P_{\mathrm{2,2}}& L& P_{2,n}\\ M& M& O& M\\ P_{m,1}& P_{m,2}& L& P_{m,n}\end{array}\right)$

Wherein P _i,jrepresent the wireless signal strength from i-th AP that a jth reference point locations receives.Suppose that have chosen k (k < n) individual reference point samples, then signals collecting workload is reduced to original k/n, greatly reduces the work expense that off-line fingerprint base builds the stage undoubtedly.

Norm regularization fingerprint matrices completion algorithm

For reducing the workload building fingerprint base, the algorithm that the present invention proposes only gathers a small amount of wireless signal fingerprint, and utilizes the low-rank characteristic of fingerprint matrices, is recovered complete fingerprint base by matrix completion theory.Under indoor positioning scene, often there is error in the wireless signal strength value collected.Except common Gaussian noise, outlier noise (i.e. the data of those super normal range (NR)s far away) is also very important noise contribution.

For effectively processing the noise jamming in wireless signal acquiring, herein Regularization Technique being incorporated in matrix completion problem, respectively by L0 norm and F norm, outlier noise and Gaussian noise being portrayed.If A is fingerprint matrices, Z is sparse outlier matrix, P _Ω(M) be sampling matrix, then the received signals fingerprint matrix completion under outlier noise conditions can be modeled as following problem:

Because rank of matrix and L0 norm are non-convex function, problem (1) is a NP-hard problem.Rank of matrix functional relaxation is matrix nuclear norm by we, the L0 norm of matrix is relaxed as L1 norm, and therefore the problems referred to above can relax as following convex optimization problem:

We adopt alternating direction multiplier method (ADMM) to solve this problem.First the constraint of this problem is rewritten as linear forms:

The Augmented Lagrangian Functions of problem (3) correspondence is:

$\begin{array}{c}{L}_{\mathrm{\&rho;}}(A,Z,G,E,Y)={\left|\right|A\left|\right|}_{*}+\mathrm{\&lambda;}{\left|\right|Z\left|\right|}_1+\mathrm{\&mu;}{\left|\right|G\left|\right|}_F^2\\ +\&lang;Y,A+Z+G+E-M\&rang;+\frac{\mathrm{\&rho;}}{2}{\left|\right|A+Z+G+E-M\left|\right|}_F^2\end{array}---\left(4\right)$

To (4) application alternating direction multiplier method, and initial value Z is set ₀=G ₀=E ₀=Y ₀=0, we can try to achieve the solution of problem (3) by following sequence of iterations.

After several times iteration, matrix A finally converges to its optimal value, namely recovers complete comparatively accurate fingerprint matrices.

Beneficial effect: use the indoor fingerprinting localization algorithm based on matrix completion that the present invention proposes, corresponding scheme has the following advantages:

1. effectively reduce the workload that off-line fingerprint base builds the stage

Indoor positioning algorithms based on received signals fingerprint comprises off-line sample phase and tuning on-line stage, and off-line phase needs reconnoitre indoor environment and set up fingerprint base.Traditional algorithm adopts pointwise sampling method to build fingerprint base, and workload is very huge; And this programme is in off-line fingerprint base building process, only chooses a small amount of reference point and carry out wireless signal strength collection, the signal strength values of all the other reference points is then recovered by norm regularization matrix completion algorithm, effectively can reduce the workload of off-line phase.

2. effectively process the noise jamming in wireless signal acquiring process

In wireless signal acquiring process, due to the existence of the numerous barrier in indoor and interference source, inevitably there is error in the RSSI data collected.Except common Gaussian noise, the abnormal RSSI value (we are referred to as outlier noise, Outlier) being moved far super normal range (NR) such as the part caused with environmental change etc. by equipment fault, personnel is also very important noise contribution.The existence of these noises has had a strong impact on the authenticity of fingerprint base, and then greatly reduces final positioning precision.Regularization Technique is incorporated in matrix completion problem by this programme, respectively by L0 norm and F norm to outlier noise and Gaussian noise smoothing, effectively can process the noise jamming in wireless signal acquiring process, under Gaussian noise condition, under outlier noise conditions and under Gauss's outlier mixed noise condition, all can obtain the positioning precision higher than analogous algorithms.

3. stronger adaptability

This programme can be applied to all kinds of scene by the adjustment of relevant parameter.When positioning accuracy request is higher, the reference point quantity of carrying out signals collecting suitably can be improved; When positioning accuracy request is not high, then can reduce the reference point quantity of carrying out signals collecting, thus reduce the workload that off-line fingerprint base builds the stage further.Meanwhile, by the adjustment to L0 norm and F norm penalty factor, this programme all can obtain higher positioning precision under noise free conditions, under Gaussian noise condition, under outlier noise conditions and under Gauss's outlier mixed noise condition.

Accompanying drawing explanation

Fig. 1 based on the locating area schematic diagram of stress and strain model and fractional-sample,

Fig. 2 is protocol procedures figure.

Embodiment

The core design thought of the indoor fingerprint positioning method implementation of the Sensor Network based on matrix completion is: matrix completion theory is applied to the indoor positioning based on wireless signal fingerprint, by utilizing the low-rank of fingerprint matrices, only need sampling section received signals fingerprint that matrix completion theory can be utilized to recover complete fingerprint base; After fingerprint database builds, classical KNN algorithm is adopted to carry out the target localization of on-line stage.In fingerprint matrices completion process, the outlier noise comprised for effective erasure signal fingerprint and Gaussian noise, introduce L1 norm regularization item and F norm regularization item respectively, problem of being recovered by finger print data is modeled as norm regularization matrix completion problem, and is solved by alternating direction multiplier method.The method effectively can reduce the workload that information fingerprint storehouse builds, and under all kinds of noise situations, obtain the positioning precision higher than congenic method.

Concrete steps comprise:

Initial scene setting:

Step 1) set locating area as the rectangular area of 50m × 100m, be that horizontal and vertical decile will be carried out in interval with 2m, then whole region is evenly divided into 25 × 50=1250 rectangular mesh, and each grid represents a reference point, totally 1250 reference points;

Step 2) random placement 30 WAP (wireless access point) in whole region; For any one access point APi, suppose to carry out wireless signal acquiring in all reference points, then can construct a fingerprint matrices wherein i=1,2 ..., 30, matrix element is the wireless signal strength from this APi that each reference point collects;

Off-line fingerprint base builds:

Step 3) for reducing workload, only random selecting part reference point carries out wireless signal acquiring, and reference point indexed set is Ω;

Step 4) element disappearance is generated for each access point APi and the fingerprint matrices of noise may be comprised wherein i=1,2 ..., m, P _Ω() is orthogonal project operator, is defined as:

${\left[P_{\mathrm{\&Omega;}}\left(\mathrm{Mi}\right)\right]}_{\mathrm{jk}}=\left\{\begin{array}{cc}{\mathrm{Mi}}_{\mathrm{jk}},& \mathrm{if}(j,k)\&Element;\mathrm{\&Omega;}\\ 0,& \mathrm{otherwise}\end{array}\right.$

Represent that matrix element is the wireless signal strength value that this station acquisition arrives as subscript (j, k) ∈ Ω;

Step 5) utilize norm regularization fingerprint matrices completion algorithm by P _Ω(Mi) complete fingerprint matrices is reverted to;

Step 6) fingerprint base in whole region is constructed according to 30 fingerprint matrices;

Tuning on-line:

Step 7) set TP as site undetermined, in this o'clock, wireless signal strength measurement is carried out to 30 access points;

Step 8) utilize classical KNN algorithm contrast TP and the wireless signal strength of each reference point, get K=20 in experiment, namely obtain 20 reference points the most similar to TP;

Step 9) physical location of TP is the average of 20 reference point coordinates.

Claims (1)

1., based on the indoor fingerprint positioning method of Sensor Network of matrix completion, it is characterized in that the method comprises following concrete steps:

Initial scene setting:

Step 1) set locating area as a rectangular area, by its horizontal n ₁decile, longitudinal n ₂decile, then whole region is evenly divided into n ₁× n ₂=n rectangular mesh, each grid represents a reference point, altogether n reference point;

Step 2) a random placement m WAP (wireless access point) in whole region; For any one access point APi, suppose to carry out wireless signal acquiring in all reference points, then can construct a fingerprint matrices wherein i=1,2 ..., m, matrix element is the wireless signal strength from this APi that each reference point collects;

Off-line fingerprint base builds:

Step 3) for reducing workload, only random selecting part reference point carries out wireless signal acquiring, and reference point indexed set is Ω;

Step 4) element disappearance is generated for each access point APi and the fingerprint matrices of noise may be comprised wherein i=1,2 ..., m, P _Ω() is orthogonal project operator, is defined as:

${\left[P_{\mathrm{\&Omega;}}\left(\mathrm{Mi}\right)\right]}_{\mathrm{jk}}=\left\{\begin{array}{cc}{\mathrm{Mi}}_{\mathrm{jk}},& \mathrm{if}(j,k)\&Element;\mathrm{\&Omega;}\\ 0,& \mathrm{otherwise}\end{array}\right.$

Represent that matrix element is the wireless signal strength value that this station acquisition arrives as subscript (j, k) ∈ Ω;

Step 5) utilize norm regularization fingerprint matrices completion algorithm by P _Ω(Mi) complete fingerprint matrices is reverted to;

Step 6) fingerprint base in whole region is constructed according to m fingerprint matrices;

Tuning on-line:

Step 7) set TP as site undetermined, at this point, wireless signal strength measurement is carried out to m access point;

Step 8) utilize classical k nearest neighbor algorithm KNN to contrast the wireless signal strength of TP and each reference point, obtain K the reference point the most similar to TP;

Step 9) physical location of TP is the average of K reference point coordinate.