LOCATION-CONSTRAINED PARTICLE FILTER FOR RSSI-BASED INDOOR HUMAN POSITIONING AND TRACKING SYSTEM Chih-Hao Chao, Chun-Yuan Chu, and An-Yeu Wu Graduate Institute of Electronics Engineering and Department of Electrical Engineering National Taiwan University Taipei, Taiwan, 10617, R.O.C. Contact information:
[email protected];
[email protected] discrete implementation of recursive Bayesian filtering, is emerging to solve the nonlinearity problem. Fig. 1 shows the system block diagram and the combination of radio fingerprint and particle filter. The estimation result of radio fingerprint is further processed by PF to generate smooth trajectories, which improves accuracy with the aid of human walking model. This paper aims at constraining walking model and PF to improve accuracy by geolocations of map.
ABSTRACT This paper proposes a Location-Constrained Particle Filter (LC-PF) for Radio Signal Strength Indication (RSSI) based indoor localization system. Based on proposed LC-PF, the RSSI fluctuation problem can be restrained. The proposed methods include locationconstrained importance weight updating (LC-WU) and location-constrained propagation model (LC-model). LC-WU eliminates particles in prohibited regions based on the geolocation of the map. The LC-model propagates particles based on different turning probabilities in different regions. These two methods can be applied separately or jointly. The proposed LC-PF has 2.48m average accuracy improvement over basic PF with 68% error reduction, and results in 2.07m accuracy with 90% confidence.
Location Constrained Propagation Model
RF
Index Terms— Particle filter, RSSI indoor localization
Network Process
RSSI Database
Walking Model
Map
Radio Fingerprint
Particle Filter
Display system
Location Constrained Weight Updating
1. INTRODUCTION
Figure 1: Add Location Constraints to Particle Filter in RSSI-based Positioning/Tracking System for Better Accuracy.
Context-aware computing [1] recently becomes engrossing and is viewed as important technology for services of the future ubiquitous computing [2]. Many applications emphasize the importance of indoor positioning [3], and improving the accuracy of location estimation is the key to enable services. For indoor locating and tracking, existing outdoor solutions such as GPS/AGPS are not suitable because of the NLOS propagation. Currently Radio Signal Strength Indication (RSSI) based location system is now combined with fingerprint technique as the method [4]. However, the accuracy varies with RSSI fluctuation over time, which usually results in discontinuous trajectory and even loss of position of tracking targets. To minimize the effect of RSS fluctuation, filters on the radio fingerprint output are required. Many researchers have shown linear filters, such as Kalman filter and Extended Kalman filter [5], can improve the accuracy but still hard to handle the nonlinearity in the location system and the environment [6]. The Particle Filter (PF) [7], a
Particle filters model the hidden state (location) as a spatial posterior Probability Density Function (PDF), and predict and correct the PDF recursively. Prediction needs diversity to cover the uncertain parts of motion model. Correction has to update the prior PDF (prediction state) based on the measurement of hidden state. With articulate human walking model and map aid, the achievable accuracy can be further improved. Existing approaches include voronoi tracking [9], map-aided positioning [10], and mapfiltering [11]. These methods limit the particle movements by graph representations of corridors or geolocation of walls, and they have been proved majorly contribute to high level positioning: locate on which corridor or in which room. Voronoi tracking-based PFs [9][10] project the two dimensional free space onto one dimensional voronoi graph and strongly constrains the propagation model. Hence the particles never propagate through the wall. However, the strong constraints reduce the flexibility of propagation
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SiPS 2008
model which we need to compensate the unawareness of target's behavior of motion. Map filtering based PF [11] does not constrain propagation of particle. Instead, a crossing wall test is applied to eliminate violated particles. In complex constrained maps, the less of ruling propagation causes large number of particles being eliminated in each iteration. Based on these observations, the left problems are how to enhance flexibility of motion model with less loss of efficiency on applying ruled propagation. This paper proposes a Location-Constrained Particle Filter (LC-PF) for RSS-based indoor human positioning and tracking. The key idea of our approach is to combine location constraints with updating operation and propagation operation in the particle filter. The main contributions of this paper are proposing: z z
Iteration at ti (Ӱ,V) Prior ti
(X,Y) Prior ti
Radio Fingerprint Estimation ti Hidden True State ti
Iteration at ti+1 (Ӱ,V) Posterior ti
(X,Y) Posterior ti
(Ӱ,V) Prior ti+1
(X,Y) Prior ti+1
State Correction Location-Constrained Weight Updating Location-Constrained Particle Propagation
Figure 2: Space State Model for RSSI-based Indoor Human Localization.
Location-Constrained Weight Updating (LC-WU) Location-Constrained Propagation Model (LC-model)
3. PROPOSED LOCATION-CONSTRAINED PARTICLE FILTER
The function correctness and estimation accuracy is checked with experiments based on modeling of a real RSSbased positioning system. With LC-WU and LC-model, the accuracy can be improved separately by 0.79m and 0.52m. Their combination, LC-PF, can greatly reduce estimation error by 2.48m with 2.07m accuracy in 90% confidence.
Particle filter is a discrete typed Bayesian filter that estimates posterior distribution over the hidden state xi of a dynamic system. The inference is conditioned on all sensor information collected so far for positioning, which can be described by: ሺݔ ȁݖଵǣ ሻ ןሺݖ ȁݔ ሻ න ሺݔ ȁݔିଵ ሻ ሺݔିଵ ȁݖଵǣିଵ ሻ݀ݔିଵ
2. SPACE STATE MODEL FOR RSSI-BASED INDOOR HUMAN LOCALIZATION
(1)
Here ݖଵǣ is the history of all sensor measurements from iteration 1 to i at time ti. In the space state model described in section 2, xi includes (X,Y, ߠ ,V)-space. The term ሺݔ ȁݔିଵ ሻ is a probabilistic model of the target dynamics, and ሺݖ ȁݔ ሻ describes the likelihood over space of making observation given true state xi. The probability density function of (1) is assimilated for implementation by
Indoor location and tracking is a stochastic estimation problem which typically modeled by Hidden Markov Model (HMM) [7]. Fig. 2 shows the state model for RSS based location system using the proposed methods. The proposed method is applied on the arrows of LC-WU and LC-model. The radio fingerprint generates a measurement state (X,Y), coordinates of physical position, for particle filter to correct the (X,Y) prior predicted by (ߠ,V) prior, prediction of direction and speed, on previous (X,Y) posterior. The corrected (X,Y) posterior is further used to correct current (ߠ,V) prior and generate (ߠ,V) posterior. The (X,Y) and (ߠ,V) prior are both corrected by the normal measurement likelihood function, and then the constraints of geolocations are applied to the corrected states. The constraints update the weight of particles in the impossible region to zero. The proposed location-constrained propagation models is applied on (ߠ,V) posterior to generate (ߠ,V) prior for next iteration. The prediction of Ʌ is made by οߠ , which is a zero-mean conditioned normal distribution function. The variance of the normal distribution alters with different locations. For regions with higher probability to turn, the variance is larger. On thin corridors, the variance is smaller. The prediction of speed is based on another condition normal distribution, which mean is based on [12].
ሾݔ ȁݖଵǣ ሿ ൌ σே௦ ୀଵ ݓ ȉ ߜሺݔ െ ݔ ሻ,
(2) th
Where Ns stands for particle number, and n for n particle. ݔ is the position of nth particle and ݓ is its importance weighting. A complete particle filter pipeline of iteration includes four steps, and the operation is shown by Fig. 3. 3.1. Correction: Location-Constrained Weight Updating The estimation of radio fingerprint, a measurement location, is applied to update importance weight of each particle through observation likelihood, which is defined by (3). ܺ௭ is position estimated by radio fingerprint, and ܺ௫ is position of nth particle. The inverse measurement confidence, ߪ , is a parameter related to variations of the RSS and radio fingerprint estimation. For precise measurements, ߪ is small, which means more confident. In our experimental environment, ߪ ൌ ͷ is optimum. The importance weight of particle is updated as (4). The location is set to zero in impossible region, constraint term ܷܥିଵ where human cannot stay. If the location constraints are . time invariant, ܷܥ ൌ ܷܥିଵ
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ሾݖ ȁݔ ሿ ൌ
ͳ
݁ ݔቈെ
ሺܺ௭ െܺ െ ௫ ሻଶ ʹ ȉ ߪଶ
ߨߪ ξʹߨ ݓ ൌ ݓି ܷିଵ ଵ ȉ ሾݖ ȁݔ ሿ ȉ ܷܥ
(3) (4)
3.2. Weight Normalizatio N n and Outpu ut Estimation For output estimation and rresampling, thhe weight of particle p mation here com mputes has to be norrmalized. The output estim the expectatioon of locationn from all partticles by multtiplying each particle’s weight to itss location andd accumulatingg.
esstimation error of radio finngerprint is modeled m as [13], a Wi-Fi based RSSI W R indoor location systtem setup inn our deepartment buiilding in NT TU. The amplitude of error is sim mplified as N(4m,1m) N w with uniform random direcction. Thhe update ratte for RSSI observation is 1Hz. The true poosition on paath and meassurement sequuence for parrticle fillter is synthesiized and show wn by Fig. 4(bb). For clarity, only the first 100 staates are drawn.
3.3. Resamplling / Redraw w Resampling is critical in paarticle filter to o prevent degeeneracy problem [7],, and is appplied in everry iteration as the Sequential Im mportance Saampling and Resampling (SISR) particle filterr [6]. Besidess, if sample impoverishmeent [7] occurs, the filter will fail tto localize thee target and reesult in loss of trackiing. To decide which one should be executed, the sum of total t weight aaccumulated for f normalizaation is used. If the suum is less thann the predefinned threshold (10 ( -6 in our system), a uniform redraw r of paarticle in estiimating region will bee executed. 3.4. Predictioon: Location Constrained Propagation n Model In the predicction stage, particles p are moved m with motion model ሾݔାଵ ȁݔ ሿ . The proposed loocation consstrained propagation model m is definned as followinng: ܲܥ௧శభ ൌ ࣹ൫ܺ௧ ǡ ܻ௧ ൯ ܥ ࣨ ԭሺܲܥ௧శభ ሻሻ ሻ (in rad) ቐ ߠ௧శభ ൌ ߠ௧ ࣨሺͲǡ ܸ௧శభ ൌ ࣨሺͶǡ ࣺ ࣺሺܲܥ௧శభ ሻሻ (in m/s) ܺ ܺ௧శభ ൌ ܺ௧ ܸ௧శభ ȉ ሺݐାଵ െ ݐ ሻ ȉ ܿݏሺߠ௧శభ ሻ ቊ ܻ ܻ௧శభ ൌ ܻ௧ ܸ௧శభ ȉ ሺݐାଵ െ ݐ ሻ ȉ ݊݅ݏሺߠ௧శభ ሻ
(5) (6)
Figure 3: Pippeline of Locatiion-Constrained d Particle Filterr.
(7) (8) (9)
The constrainned parameterr ܲܥ௧శభ is a function f of poosterior only, which determines d thhe probability to turn. Function ࣹ defines the prrobability, whhich has to be setup or updaated by parameter leaarning algoritthm. The ߂ߠ ߠ and ܸ௧శభ arre both conditioned normal n distribuution, and theeir variance is related to the locattion constrainned model ܲܥ ܥ௧శభ . For ߠ௧శభ , ͲǤͲͷߨ ԭ ͲǤͷߨ, and foor ܸ௧శభ , Ͳ ࣺ Ͷ. The position p prediction is based on speed and directiion predictionn. With the proposed location consstrained propaagation modell, fewer e by through-wall test in thin coorridors particles are eliminated and still preserve the flexiibility to let particle p free-m move in large space such s as room m or in high turning probbability region.
(a)
First 100 seconds (along the corridor, about 5 circles around the centtral room)
4. EXP PERIMENTS S ment Environm ment 4.1. Experim The setup of experiment ennvironment is shown by Figg. 4(a). A 40m x 40m m square regiion with four 3m wide corrridors, and the widthh of door is 1m. 1 The synthhesis of humaan walk follows [12]. The walkinng target traaverse the coorridors around the ceentral room wiith speed profi file N(4m,1m)). The
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(b) Figure 4: (a) Floorplan oof Experiment Environment; E ( True Positioon and Measureement Sequencee for Particle Fiilter (b) ( (Estimation of R Radio Fingerpriint).
Figure 5: 5 Reachable Accuracy A with Proposed P Metho ods.
F Figure 6: Cumu ulative Distributtion Function of o Estimation Errror.
4.2. Result Analysis A
5. CONC CLUSIONS
The estimatio on performancce with differeent particle nu umbers is shown by Fig. 5. For ju ustified comp parison, the sttandard m. The deviation of weight updatiing function is setup to 5m gation model and weight up pdating location consttrained propag are separately y applied to baasic SISR parrticle filter, an nd their combination, location-connstrained partticle filter (L LC-PF). he estimation error can be reduced r All particle fiilters shows th with more paarticles. Howeever, basic PF F saturates earrly and cannot reducee the estimatiion error even n with large number n of particles. With W the prop posed method ds, the accuraacy can be further imp proved with laarge number of o particle. For real application in our enviro onment, the particle p number is sett to 1600, whhich means 1 particle/m2 in n initial state and red draw state fo or sample im mpoverishmen nt. The cumulative distribution d ffunction of estimation errror is shown is shown in Fig. 6. With the pro oposed metho ods, the probability off estimation error e larger th han 2.3m is less than 1%. Table 1 summarizes the performan nce of the prroposed methods. Thee proposed loocation-constrrained particle filter has 90% con nfidence of 22.07m accuraacy for N(4m m, 1m) amplitude with w random direction of radio fing gerprint estimation ressult. The averrage performaance improvem ment in comparison with w basic PF is 2.48m, and d the error red duction over basic PF F is 68%. The accu uracy improveement of the combination of LCmodel and LC C-WU is superior to the sum s of improv vement by applied LC-model L and LC-WU in ndividually. This T is because of the t informatiion of map geolocation can c be further utilizeed in the pipeeline of PF: th he location predicted by LC-model is corrected by LC-WU.
Baase on our ex xperiment, thee proposed location-constraained paarticle filter caan improve esstimation accu uracy by 68% % and haas 2.07m accu uracy in a typical case. Thee result showss that the proposed LC-WU L and L LC-model are effective and d can eaasily adapt to o the map ggeolocation. Their T cooperration grreatly improvees accuracy. Therefore, ev ven only with h few paarticles, the errror is still lesss than 2.5m. ACKNOWL LEDGEMEN NT Thhis work was supported by National Scieence Council under u grrant NSC 96-2 2220-E-002-0224. REFE ERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [100]
Table 1: Experimental E ressult
90% confidencee accuracy Avg. accuuracy improvement oveer basic PF Error Redu uction over basicc PF
[111]
Basic PF
w/ LC model
w/ LC updating
L LC-PF
4.665m
4.09m
3.77m
2.07m
N N/A
0.52m
0.79m
2.48m
0 0%
12%
20%
68%
[122] [133]
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