CN107426687B - Towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR - Google Patents
Towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
- G01C21/206—Instruments for performing navigational calculations specially adapted for indoor navigation
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0294—Trajectory determination or predictive filtering, e.g. target tracking or Kalman filtering
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/14—Determining absolute distances from a plurality of spaced points of known location
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Abstract
The invention discloses a kind of towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR, user's hand-held terminal device first is in target area, receive the RSSI from each AP, under the path loss model of logarithm normal distribution, the position of user is obtained using weighted least-squares method, user location is obtained by the appraising model in PDR algorithm simultaneously, then the location information based on propagation model is repeatedly merged with the location information of PDR using adaptive Kalman filter, obtain the optimum position of user, wherein, adaptive Kalman filter is embodied on feedback mechanism, positioning result will be merged every time, and dynamic corrections are carried out to parameters such as path loss indexes in weighted least-squares method, finally propagation model is made more to meet indoor environment.The present invention solves the problems, such as under environment indoors single WiFi positioning accuracy, and low there are accumulated errors with PDR, additionally it is possible to which the path loss index of real-time tracking propagation model enhances the stability of positioning performance.
Description
Technical field
The invention belongs to indoor positioning technologies, and in particular to a kind of towards the adaptive card for merging positioning in the room WiFi/PDR
Kalman Filtering method.
Background technique
With the rapid development of mobile communication, location based service LBS (Location Based Service) by
More and more concerns, and indoors place (such as market, airport and underground parking), existing outdoor positioning system, such as
Global position system GPS (Global Positioning System), due to the masking by facilities such as buildings, it is difficult to
Indoor realization is accurately positioned.At the same time, big due to WLAN WLAN (Wireless Local Area Network)
Scaledeployment and WLAN High-speed wireless access it is widely available, indoor user is positioned using existing WLAN infrastructure
It is increasingly valued by people, wherein be based on received signal strength RSSI (Received Signal Strength
Indication indoor WLAN location technology) is even more by extensive and in-depth research.At the same time, smart phone is also more next
More having been favored by people, they also include many advanced hardware facilities other than it can provide better software function,
Such as WiFi module, bluetooth module and various inertial sensors, researcher can directly be developed using these hardware facilities
Indoor locating system.
Positioning basic skills based on RSSI is generally divided into location fingerprint method and propagation model method.Location fingerprint method include from
Line stage and on-line stage, in on-line stage, user utilizes freshly harvested RSSI value, the location fingerprint constructed in conjunction with off-line phase
Database and matching algorithm is searched for accordingly, realize the positioning to user, but when environment once changing, fingerprint database is then answered
Work as update, and renewal process needs to consume a large amount of man power and material.For propagation model method, then building finger print data is not needed
Library is determined the distance between AP (Access Point, wireless access node) and user using rssi measurement value, then passes through structure
Hyperbolic function is made, determines the position of user.But main problem existing for propagation model method is to need an accurate channel mould
Type hardly results in the accurate parameter in Real-time Channel model due to the dynamic of environment, is also difficult to obtain between AP and user
Accurate distance so that positioning result may have severe deviations.In addition, the PDR based on mobile terminal inertial sensor
(Pedestrian Dead Reckoning, pedestrian's dead reckoning) algorithm has positioning accuracy in the short time high, but position error
When accumulating be gradually increased at any time, and WiFi being utilized to position, stand-alone position error is big but does not have the accumulation of error, above-mentioned in order to solve
The path loss index of problem and real-time tracking propagation model, the invention proposes one kind towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering.
Summary of the invention
The object of the present invention is to provide a kind of towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR,
It can effectively solve that WiFi Point-positioning Precision under environment indoors is low and PDR has accumulated error, meanwhile, this method
The path loss index of energy real-time tracking propagation model, enhances the stability of positioning performance.
It is of the present invention towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR, including following step
It is rapid:
Step 1: giving the initial position X ' of user in target area0|0；
Step 2: user receives the signal strength of i-th of API=1 ..., m, m are the number of AP；
Step 3: according to the path loss model of logarithm normal distributionWherein,
A is indicated in reference distance d0The signal strength that place receives；η indicates path loss index；N0It indicates ambient noise, obeys equal
Value is 0, variances sigma2Gaussian Profile, calculate the distance between user and each AP, wherein diIndicate user and APiBetween away from
From APiIndicate i-th of AP；
Step 4: known AP1,…,APmPosition coordinates be respectively (x1,y1),…,(xm,ym), and set the position of user
Coordinate is (x, y), and the distance between the user obtained according to step 3 and each AP construct Hyperbolic Equation；
Step 5: assigning weight using weighted least-squares method to the distance between user and each AP, calculating and be based on
The estimated location of WiFi
Step 6: known users initial position X '0|0, the relative positioning to user is realized using PDR algorithm, and then calculate
User is in t outkPosition (the x at momentk,yk)；
Step 7: obtaining predicted state X ' in the forecast period of Kalman filteringk|k-1With the association side of the corresponding predicted state
Poor Pk|k-1；
Step 8: obtaining kalman gain K in the more new stage of Kalman filteringkWith the estimated state at current time
X′k|k；
Step 9: utilizing the estimated result X ' of Kalman filterk|kAs input, alignment path loss index, to obtain
The estimated state at new current time
Step 10: setting can convergent iteration thresholdWherein,WithIt is X-axis and Y-axis respectively
The variance in direction, i.e. covariance matrix Pk|kElement on diagonal line, α is adjustability coefficients, and is calculatedWherein,It indicates in the kth moment updated estimated location of iteration j,It indicates in the updated estimated location of -1 iteration of kth moment jth；
Step 11: judgementWhether threshold value T is less than；It is then to enter step 12；It is no, then
Enter step nine；
Step 12: updating rssi measurement error covariance σR；
Step 13: updating kalman gain Kk, current time estimated stateWith covariance matrix Pk|k；
Step 14: obtaining the optimum position of userAnd the initial position as subsequent time.
The step 5 the following steps are included:
5a, according to step 4, the Least Square Method based on WiFi isWherein, Between user and i-th of AP
Estimated distance, think herein the distance between user and each AP to positioning result weight having the same, but channel model
Belong to nonlinear model, therefore the path loss model based on logarithm normal distribution, user is identical in different transmission ranges
The rssi measurement error of Gaussian Profile will lead to different range measurement errors, i.e. transmission range is bigger, then range measurement error
It is bigger；So taking weighted least-squares method, formula isWherein, S isAssociation side
Poor matrix assigns lesser transmission range to biggish weight, so that the distance of estimation has higher accuracy；
5b, assume that the estimated distance between user and each AP is independent, whereinIndicate user and APiBetween estimate
Distance is counted, then covariance matrix S are as follows:
Wherein, Var indicates variance operation, that is, has
5c, the path loss model based on step 3, estimated distanceAre as follows:
Wherein,Meet logarithm normal distribution, enables μd=lndiAndThen stochastic variableK rank moment of the orign
For
5d, according to step 5c, it is available:
5e, according to step 5d, can obtain
Due to σdVariance for constant and each estimated distance contains σd, therefore about fall invariant from covariance matrix SIt will not influence based on weighted least-squares method estimated location
I.e.It is equivalent to
5f, it is based on step 5e, can obtained
5g, covariance matrix S is indicated are as follows:
5h, the therefore estimated location based on WiFi
The step 9 the following steps are included:
9a, according to step 3, it is available:
9b, using step 8 current time estimated state X 'k|k, calculateWherein,For
The position coordinates of i-th of AP, | | | |2Indicate euclideam norm；
9c, in conjunction with step 9a and step 9b, obtain:
Wherein,For currently about the updated path loss index of i-th of AP；
9d, basisIt repeats Step 4: step 5 and step 8, obtain the estimated state at new current time
The step 12 the following steps are included:
12a, calculatingWherein, ToldIndicate previous moment about all AP path loss index and, η ' is
The path loss index of i-th of AP of previous moment；
12b, calculatingWherein, TnewIndicate the updated path loss index of current time all AP
With；
12c, whenWhen update, while updating rssi measurement error covariance σR；
Wherein:Indicate updated rssi measurement error covariance,Indicate the rssi measurement error association before updating
Variance.
The invention has the following advantages that user's hand-held terminal device in target area, receives the RSSI from each AP,
Under the path loss model of logarithm normal distribution, the position of user is obtained using weighted least-squares method, while calculating by PDR
Appraising model in method obtains user location, then using adaptive Kalman filter by based on propagation model location information with
The location information of PDR is repeatedly merged, and the optimum position of user is obtained, wherein adaptive Kalman filter is embodied in feedback
In mechanism, i.e., each fusion positioning result is subjected to dynamic to parameters such as path loss indexes in weighted least-squares method and repaired
Just, finally propagation model is made more to meet indoor environment.Compared to traditional Kalman's fusion and positioning method, the present invention can be real-time
The path loss index for tracking propagation model, enhances the stability of positioning performance.The present invention can apply to radio communication
Network environment, solving the problems, such as under environment indoors single WiFi positioning accuracy, low there are accumulated errors with PDR.
Detailed description of the invention
Fig. 1 be the present invention in step 1 to step 11 flow chart；
Fig. 2 be the present invention in step 11 to step 14 flow chart；
Fig. 3 is simulated environment schematic diagram；
Fig. 4 is the collecting sample of RSSI；
Fig. 5 is the position error cumulative distribution function comparison diagram of the distinct methods under the first paths；
Fig. 6 is the track comparison diagram of the distinct methods under the first paths；
Fig. 7 is the average localization error comparison diagram of the distinct methods under the first paths；
Fig. 8 is the position error cumulative distribution function comparison diagram that the RSSI before and after η is updated under the first paths；
Fig. 9 is the position error cumulative distribution function comparison diagram under the second paths；
Figure 10 is the track comparison diagram of the distinct methods under the second paths；
Figure 11 is the average localization error comparison diagram of the distinct methods under the second paths；
Figure 12 is the position error cumulative distribution function comparison diagram that the RSSI before and after η is updated under the second paths；
Figure 13 is the position error cumulative distribution function comparison diagram under third path；
Figure 14 is the track comparison diagram of the distinct methods under third path；
Figure 15 is the average localization error comparison diagram of the distinct methods under third path；
Figure 16 is the position error cumulative distribution function comparison diagram that the RSSI before and after η is updated under third path；
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
It is as shown in Figure 1 to Figure 2 towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR, including with
Lower step:
Step 1: giving the initial position X ' of user in target area0|0。
Step 2: user receives the signal strength of i-th of AP(number that i=1 ..., m, m are AP).
Step 3: according to the path loss model of logarithm normal distributionWherein,
A is indicated in reference distance d0The signal strength that place receives；η indicates path loss index；N0It indicates ambient noise, obeys equal
Value is 0, variances sigma2Gaussian Profile, calculate the distance between user and each AP, wherein diIndicate user and i-th of AP (i.e.
APiThe distance between).
Step 4: known AP1,…,APmPosition coordinates be respectively (x1,y1),…,(xm,ym), and set the position of user
Coordinate is (x, y), and the distance between the user obtained according to step 3 and each AP construct Hyperbolic Equation；Specifically include with
Lower step:
4a, Hyperbolic Equation are as follows:
4b, the Hyperbolic Equation of step 4a is unfolded and can be obtained after eliminating quadratic term:
4c, since there are measurement errors, so we can only obtain estimated distance valueFormula is expressed in the matrix form
Are as follows:
Wherein,
Step 5: assigning weight using weighted least-squares method to the distance between user and each AP, calculating and be based on
The estimated location of WiFiSpecifically includes the following steps:
5a, according to step 4, the Least Square Method based on WiFi isWherein, Between user and i-th of AP
Estimated distance, think herein the distance between user and each AP to positioning result weight having the same, but channel model
Belong to nonlinear model, therefore the path loss model based on logarithm normal distribution, user is identical in different transmission ranges
The rssi measurement error of Gaussian Profile will lead to different range measurement errors, i.e. transmission range is bigger, then range measurement error
It is bigger.So taking weighted least-squares method, formula isWherein, S isAssociation side
Poor matrix assigns lesser transmission range to biggish weight, so that the distance of estimation has higher accuracy.
5b, assume that the estimated distance between user and each AP is independent, whereinIndicate user and APiBetween
Estimated distance, then covariance matrix S are as follows:
Wherein, Var indicates variance operation, that is, has
5c, the path loss model based on step 3, estimated distanceAre as follows:
Wherein,Meet logarithm normal distribution, enables μd=ln diAndThen stochastic variableK rank origin
Square is
5d, according to step 5c, it is available:
5e, according to step 5d, can obtain
Due to σdVariance for constant and each estimated distance contains σd, therefore about fall invariant from covariance matrix SIt will not influence based on weighted least-squares method estimated location
I.e.It is equivalent to
5f, it is based on step 5e, can obtained
5g, covariance matrix S is indicated are as follows:
5h, the therefore estimated location based on WiFi
Step 6: known users initial position X '0|0, the relative positioning to user is realized using PDR algorithm, and then calculate
User is in t outkPosition (the x at momentk,yk)；Specifically includes the following steps:
6a, user are in t1Position (the x at moment1,y1) are as follows:
6b, user are in t2Position (the x at moment2,y2) are as follows:
6c, go down in prediction on such basis, then user is in tkPosition (the x at momentk,yk) are as follows:
Wherein, (xk-1,yk-1) it is tk-1The user location at moment, SLiIt is walking step-length or ti-1To tiThe displacement of time interval
Amount, θiIt is the direction of motion vector.Therefore the estimated location X ' of the user at current time can be speculated according to last momentk|k-1。
Step 7: obtaining predicted state X ' in the forecast period of Kalman filteringk|k-1With the association side of the corresponding predicted state
Poor Pk|k-1；Specifically includes the following steps:
7a, predicted state X ' is calculatedk|k-1, its calculation formula is:
Wherein: parameter k indicates the kth moment,Indicate velocity vector, Δ T indicates the update cycle of Kalman filter.
7b, the covariance P for calculating the corresponding predicted statek|k-1, its calculation formula is:
Pk|k-1=Pk-1|k-1+Qk；
Wherein Pk-1|k-1It is estimated state Xk-1|k-1Covariance matrix, QkIt is the covariance matrix of active procedure noise.
7c、QkCalculation formula are as follows:
Wherein: I indicates unit matrix, σaAnd σvRespectively indicate the standard deviation of acceleration transducer and velocity sensor.
Step 8: obtaining kalman gain K in the more new stage of Kalman filteringkWith the estimated state at current time
X′k|k；Specifically includes the following steps:
8a, kalman gain K is calculatedk:
Kk=Pk|k-1CT(CPk|k-1CT+Rk)-1；
Wherein, C is observing matrix,RkIt is the covariance matrix of observation noise.
8b、RkIt is embodied as:
Wherein, Qk/INSWith QkIt is identical, Rk/RSSIIt is the covariance matrix of the positioning result based on WiFi, initial value R0/RSSIExpression
Formula are as follows:
Wherein,It is the standard deviation of the positioning result based on WiFi, which can be determined by experiment.
8c, the estimated state X ' at current timek|kIts calculation formula is:
X′k|k=X 'k|k-1+Kk(Zk-CX′k|k-1)
Wherein, ZkIt is the observed result from WiFi and PDR,
Step 9: utilizing the estimated result X ' of Kalman filterk|kAs input, alignment path loss index, to obtain
The estimated state at new current timeSpecifically includes the following steps:
9a, according to step 3, it is available:
9b, using step 8 current time estimated state X 'k|k, calculateWherein,For
The position coordinates of i-th (i=1 ..., m) a AP, | | | |2Indicate euclideam norm.
9c, in conjunction with step 9a and step 9b, obtain:
Wherein,For currently about the updated path loss index of i-th of AP.
9d, basisIt repeats Step 4: step 5 and step 8, obtain the estimated state at new current timeStep 10: setting can convergent iteration thresholdWherein,WithIt is X-axis and Y-axis side respectively
To variance, i.e. covariance matrix Pk|kElement on diagonal line, Pk|k=(I-KkC)Pk|k-1, α is adjustability coefficients, and is calculatedWherein,It indicates in the kth moment updated estimated location of iteration j,It indicates in the updated estimated location of -1 iteration of kth moment jth.
Step 11: judgementWhether threshold value T is less than；It is then to enter step 12；It is no,
Then enter step nine.
Step 12: updating rssi measurement error covariance σR；Specifically includes the following steps:
12a, calculatingWherein, ToldIndicate previous moment about all AP path loss index and, η ' is
The path loss index of i-th of AP of previous moment；
12b, calculatingWherein, TnewIndicate the updated path loss index of current time all AP
With；
12c, whenWhen update, while updating rssi measurement error covariance σR；
Wherein:Indicate updated rssi measurement error covariance,Indicate the rssi measurement error association before updating
Variance.
Step 13: updating kalman gain Kk, current time estimated stateWith covariance matrix Pk|k；Specifically
The following steps are included:
13a, kalman gain K is updatedk, i.e., repeatedly step 8a.
13b, the estimated state for updating current timeRepeat step 8c.
13c, covariance matrix P is updatedk|k, its calculation formula is:
Pk|k=(I-KkC)Pk|k-1。
Step 14: obtaining the optimum position of userAnd the initial position as subsequent time.
As shown in figure 3, the area of simulated environment is 57m × 25m, it is distributed 6 AP, model DLINK DAP altogether
2310, coordinate be respectively (0m, 3m), (11.6m, 7.44m), (24.8m, 11.04m), (15.6m, 0m), (56.5m, 0m),
(51m, 16.8m), in this experiment, in order to verify the validity of the method for the present invention, devising path, 1. straight line is walked, and path is 2.
It turns back walking, 3. broken line is walked in path.
It is illustrated in figure 4 the collecting sample of RSSI, MAC Address and timestamp comprising signal strength indication, AP.
As shown in figure 5, path is given 1. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, the error accumulation probability distribution comparison of Kalman's fusion method.As it can be seen that in reality
It tests in result, using towards the method for adaptive kalman filtering positioning accurate with higher for merging positioning in the room WiFi/PDR
Degree.
As shown in fig. 6, path is given 1. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, the run trace comparison of Kalman's fusion method.As it can be seen that in run trace
In, using the track walked towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR closer to true rail
Mark.
As shown in fig. 7, path is given 1. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, the average localization error comparison of Kalman's fusion method.As it can be seen that being tied in experiment
It is minimum using the average localization error towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR in fruit.
As shown in figure 8, giving path 1. under experimental situation, the position error cumulative distribution of the RSSI before and after η is updated
Function comparison diagram.As it can be seen that the positioning accuracy for updating the RSSI after η significantly improves in experimental result.
As shown in figure 9, path is given 2. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, the error accumulation probability distribution comparison of Kalman's fusion method.As it can be seen that in reality
It tests in result, using towards the method for adaptive kalman filtering positioning accurate with higher for merging positioning in the room WiFi/PDR
Degree.
As shown in Figure 10, path is given 2. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, Kalman's fusion method run trace comparison.As it can be seen that in run trace
In, using the track walked towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR closer to true rail
Mark.
As shown in figure 11, path is given 2. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, Kalman's fusion method average localization error comparison.As it can be seen that testing
As a result minimum using the average localization error towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR in.
As shown in figure 12, path is given 2. under experimental situation, updates the position error cumulative distribution of the RSSI before and after η
Function comparison diagram.As it can be seen that the positioning accuracy for updating the RSSI after η significantly improves in experimental result.
As shown in figure 13, path is given 3. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, Kalman's fusion method error accumulation probability distribution comparison.As it can be seen that
In experimental result, using towards the method for adaptive kalman filtering positioning accurate with higher for merging positioning in the room WiFi/PDR
Degree.
As shown in figure 14, path is given 3. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, Kalman's fusion method run trace comparison.As it can be seen that in run trace
In, using the track walked towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR closer to true rail
Mark.
As shown in figure 15, path is given 3. under experimental situation, it is of the invention towards fusion positioning in the room WiFi/PDR
Method for adaptive kalman filtering and PDR, RSSI, Kalman's fusion method average localization error comparison.As it can be seen that testing
As a result minimum using the average localization error towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR in.
As shown in figure 16, path is given 3. under experimental situation, updates the position error cumulative distribution of the RSSI before and after η
Function comparison diagram.As it can be seen that the positioning accuracy for updating the RSSI after η significantly improves in experimental result.
Claims (2)
1. towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR, which comprises the following steps:
Step 1: giving the initial position X ' of user in target area0|0；
Step 2: user receives the signal strength of i-th of APM is the number of AP；
Step 3: according to the path loss model of logarithm normal distributionWherein, A table
Show in reference distance d0The signal strength that place receives；η indicates path loss index；N0Indicate ambient noise, obeying mean value is
0, variances sigma2Gaussian Profile, calculate the distance between user and each AP, wherein diIndicate user and APiThe distance between,
APiIndicate i-th of AP；
Step 4: known AP1,…,APmPosition coordinates be respectively (x1,y1),…,(xm,ym), and set the position coordinates of user
For (x, y), the distance between the user obtained according to step 3 and each AP construct Hyperbolic Equation；
Step 5: assigning weight using weighted least-squares method to the distance between user and each AP, calculating based on WiFi
Estimated location
Step 6: known users initial position X '0|0, the relative positioning to user is realized using PDR algorithm, and then extrapolate use
Family is in tkPosition (the x at momentk,yk)；
Step 7: obtaining predicted state X ' in the forecast period of Kalman filteringk|k-1With the covariance of the corresponding predicted state
Pk|k-1；
Step 8: obtaining kalman gain K in the more new stage of Kalman filteringkWith the estimated state X ' at current timek|k；
Step 9: utilizing the estimated result X ' of Kalman filterk|kAs input, alignment path loss index, to obtain newly
The estimated state at current timeSpecifically includes the following steps:
9a, according to step 3, it is available:
9b, using step 8 current time estimated state X 'k|k, calculateWherein,It is i-th
The position coordinates of AP, | | | |2Indicate euclideam norm；
9c, in conjunction with step 9a and step 9b, obtain:
Wherein,For currently about the updated path loss index of i-th of AP；
9d, basisIt repeats Step 4: step 5 and step 8, obtain the estimated state at new current time
Step 10: setting can convergent iteration thresholdWherein,WithIt is X-axis and Y direction respectively
Variance, i.e. covariance matrix Pk|kElement on diagonal line, α is adjustability coefficients, and is calculated
Wherein,It indicates in the kth moment updated estimated location of iteration j,It indicates at the kth moment the
The updated estimated location of j-1 iteration；
Step 11: judgementWhether threshold value T is less than；It is then to enter step 12；It is no, then enter
Step 9；
Step 12: updating rssi measurement error covariance σR；Specifically includes the following steps:
12a, calculatingWherein, ToldIndicate previous moment about all AP path loss index and, η ' be it is previous
The path loss index of i-th of AP of moment；
12b, calculatingWherein, TnewIndicate the updated path loss index of current time all AP and；
12c, whenWhen update, while updating rssi measurement error covariance σR；
Wherein:Indicate updated rssi measurement error covariance,Indicate the rssi measurement error association side before updating
Difference；
Step 13: updating kalman gain Kk, current time estimated stateWith covariance matrix Pk|k；
Step 14: obtaining the optimum position of userAnd the initial position as subsequent time.
2. it is according to claim 1 towards the method for adaptive kalman filtering for merging positioning in the room WiFi/PDR, it is special
Sign is: the step 5 the following steps are included:
5a, according to step 4, the Least Square Method based on WiFi isWherein, Between user and i-th of AP
Estimated distance, think herein the distance between user and each AP to positioning result weight having the same, but channel model
Belong to nonlinear model, therefore the path loss model based on logarithm normal distribution, user is identical in different transmission ranges
The rssi measurement error of Gaussian Profile will lead to different range measurement errors, i.e. transmission range is bigger, then range measurement error
It is bigger；So taking weighted least-squares method, formula isWherein, S isAssociation side
Poor matrix assigns lesser transmission range to biggish weight, so that the distance of estimation has higher accuracy；
5b, assume that the estimated distance between user and each AP is independent, whereinIndicate user and APiBetween estimation away from
From then covariance matrix S are as follows:
Wherein, Var indicates variance operation, that is, has
5c, the path loss model based on step 3, estimated distanceAre as follows:
Wherein,Meet logarithm normal distribution, enables μd=ln diAndThen stochastic variableK rank moment of the orign be
5d, according to step 5c, it is available:
5e, according to step 5d, can obtainBy
In σdVariance for constant and each estimated distance contains σd, therefore about fall invariant from covariance matrix SIt will not influence based on weighted least-squares method estimated location
I.e.It is equivalent to
5f, it is based on step 5e, can obtained
5g, covariance matrix S is indicated are as follows:
5h, the therefore estimated location based on WiFi
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