Indoor Location Estimation in NLoS Environment
Based on ToA Method with Particle Filter
Atsushi Yoshida∗, Takenori Sakumura†, Toshinari Kamakura†
Abstract — We study the location estimation in the indoor environment. We use ToA (Time-of-Arrival) information obtainedfrom AN (an anchor node) and TN (a target node). The ToA method measures the distance between AN and TN. However,since the distance by the method often includes a positive error due to the NLoS (Non-Line-of-Sight) environment, it isdiﬃcult to estimate the position of TN from ToA information directly. Therefore, we propose a method to localize TN basedon particle filter with the correction of the error.

Keyword: Indoor Location Estimation; Time-of-Arrival (ToA); Non-Line-of-Sight (NLoS); Auxiliary Particle
Filter.
1 Introduction
We aim at the improvement of the accuracy on indoor position estimation through the statisticalapproach. Since there is the prospect of utilizations in the fields of such as marketing science andlocation-based service, the study on indoor localization is important. As the applications, in case of theformer, it is considered as the use to get an interesting product shelf information for a customer andto analysis the behavior in the store. In the latter case, we may become able to receive the navigation
service anywhere in a shopping mall or a museum (Chong, Watanabe, and Inamura, 2006; Sahinoglu,Gezici and Guvenc, 2008).
Global Positioning System (GPS) is well known as a typical localization method. However its
accuracy is within about 1 to 5 meter even if it is outside, it will not be anticipated the further accuracy
in urban area and the indoor environment. Hence, a method in Wireless Sensor Network (WSN) iswidely used for indoor localization. The localization method in WSN is mainly classified as either therange-free method or the range-based method. The range-free method estimates a position from a networklike view with many devices, and provides a much lower accurate position than the range-based methodthat uses ranges between each device. Therefore, we use the latter in this study.
Using the range-based method, we need to prepare for several devices as anchor node (AN) andtarget node (TN) and handle the distances between them. In addition, there are some kinds of radio
signal information to measure a distance, such as Received Signal Strength (RSS) (Okusa and Kamakura,2015), Time-of-Arrival (ToA) (Kamakura and Okusa, 2013; Venkatraman, Caﬀery and You, 2004; Watabeand Kamakura, 2010), and Angle-of-Arrival (AoA). We have to select or combine the information toestimate the position of TN. In thsis study, we propose the position estimation method based on ToA.
ToA is the information to estimate the distance between AN and TN based on time. When we calla measurement method using the ToA information as ToA method, this method measures the radio
signal’s travel time between AN and TN that are completely synchronized, and estimates the distance.
For instance, when a radio signal is transmitted from TN at time t0 and it is received by AN at time t1 ,the distance R is calculated as follows:
R = C(t1 − t0 ),(1.1)

where C is the speed of light. Thus, if the distance was measured correctly, we could estimate theposition of TN using trilateration.
However, since the distance often includes not also random error but positive systematic error in
the actual environment, it is diﬃcult to estimate the accurate position of TN. It is said that the cause of∗ Graduate School of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan, Email: jundoll33@gmail.com† Faculty of Science and Engineering, Chuo University, 112-8551, Japan

the systematic error has Non-Line-of-Sight (NLoS) conditions, multipath and clock oﬀ (Go and Chong,2015; Sahinoglu, et al., 2008). Especially, the error in NLoS environment, where a radio signal pathbetween devices is partially obstructed, seriously aﬀects the accuracy (Go and Chong, 2015). Therefore,
we focus on the error which we call NLoS error.
Yoshida, Sakumura and Kamakura (2016) proposed the equation to correct with Gamma regression
model. However, the method is not practical because several measurements are regarded as one
measurement at same time. Therefore, we propose a more practical method to sequentially estimate
the position of TN by modeling the state space model with the new correction equation in this paper.
2The proposed method

The following model is typically assumed in ToA-based location estimation (Sahinoglu, et al., 2008).
{R+ε(if LoS)
(2.1)ℓ=
R+b+ε(if NLoS),(2.2)
where ℓ is a measured distance, R is an actual distance, b is a NLoS error, and ε is a random error which
follows a normal distribution N(0, σ2 ). We show the equation to correct NLoS error.
log b = β0 + β1 R.

(2.3)

Eq. (2.3) is devised using the characteristic of the correction equation by Yoshida et al. (2016). We
formulated Eq. (2.3) based on the conditions as follows:• NLoS error is a positive value.
• The larger actual distance is, the larger NLoS error is.
• The smaller actual distance is, the smaller NLoS error is.
We combine Eq.(2.2) and Eq.(2.3) and construct the following state space model. Our method performs
sequential estimation using Auxiliary Particle Filter (Pitt and Shephard, 1999) based on the model.
 
 xt   1 ∆T 0 0   xt−1   vx,t   0 1 0 0   vx,t−1 
 =  
 + wt , wt ∼ N(0, Σ1,t ), yt   0 0 1 ∆T   yt−1 
 

v y,t
0 0 0 1v y,t−1

 
 
 ℓ1   d(xt , yt , a1 )   exp(β0,t + β1,t d(xt , yt , a1 ))  .  


..
..
 .  =  +  + v , v ∼ N(0, Σ ),tt2,t .  
 

.
.

  
ℓKd(xt , yt , aK )exp(β0,t + β1,t d(xt , yt , aK ))

(2.4)

(2.5)

where xt , yt are the coordinate of the position of TN, vx,t , v y,t are the velocity of TN, ∆T is a time interval,√d(xt , yt , ak ) = (xt − ax,k )2 + (yt − a y,k )2 , ak = (ax,k , a y,k )T , and β0,k , β1,k , Σ1,t , Σ2,t are unknown parameters.
These parameters are estimated by the simultaneous estimation method of the unknown parameter by
Liu and West (2001).
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