A Wireless Localization Algorithm Based on Strong Tracking Kalman Filter

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1 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp Sensors & ransducers 204 by IFSA Publishing, S. L. A Wireless Localization Algorithm Based on Strong racking Kalman Filter Qinghui Wang, Wangyuan Huang, Li Feng Wei and Xiaomei Liu Institute of Wireless Communication echnology, Shenyang University of Chemical echnology, Shenyang 042, China el.: , fax: wangqh8008@vip.sina.com Received: 8 August 204 /Accepted: 28 November 204 /Published: 3 December 204 Abstract: Classical extended Kalman filter algorithm is often used to obtain dynamic estimation of nodes position in wireless localization. However, it is prone to generate error accumulation in the filtering process, and lead to filter divergence, which causes low accuracy. he paper explores a strong tracking extended Kalman filter with algorithm a fading factor, which can adjust the gain K in real time, so as to ensure the adaptive adjustment of the new information sequence, as well as the dynamic tracking capability in indoor wireless localization. he experimental results show that the strong tracking extended Kalman filter algorithm has a better tracking capability on dynamic targets, leading to higher tracking accuracy and, smaller absolute error. Copyright 204 IFSA Publishing, S. L. Keywords: Strong tracking filter, Extended Kalman filter (EKF), Wireless localization.. Introduction With the development of wireless communication technology [], the localization of moving nodes during the communication not only can be used as a service business, but also can be applied in security systems, military operations, detections and management tasks etc. Most of the current positioning algorithms [2] are attempting to balance the energy consumption, cost and accuracy. he research on how to improve the accuracy with a smaller node density, and smaller percentage of beacon nodes, is becoming one of the hot topics [3]. Among the localization algorithms, the extended Kalman filter (EKF) [4] is the most widely used nonlinear filtering method in indoor wireless localization. Much efforts have been made in improving its performance, and various filtering methods based on root mean square filter and the decomposition of singular value have been proposed [5, 6]. However, in practical applications, the extended Kalman filter still suffers from some disadvantages, such as poor robustness, low accuracy, and loss of the ability to track the changing status when EKF reaches a steady state. On the basis of the target motion estimation theory and in combination with the indoor environment to build wireless sensor network hardware platform, this paper analyzes the extended Kalman filter based on strong tracking filtering algorithm, and establishes a localization algorithm filtering model based on distance, which applies the strong tracking extended Kalman filtering in indoor wireless localization of mobile targets. hrough the experimental comparison of the proposed algorithm and the general extended Kalman filter, the strong tracking algorithm is proved to possess higher accuracy and better tracking capability. 55

2 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp Design of Strong racking EKF In wireless sensor network localization, typically the extended Kalman filter algorithm will be employed due to the general nonlinearity of the measurement equation. Compared with the extended Kalman filter, the strong tracking extended Kalman filter gains the following advantages [7]: the stronger robustness to model mismatch, the lower sensitivity to the noise and initial value on the statistical properties, stronger tracking ability on the changing status, and acceptable computational complexity. he design of the filter introduces a fading factor, P adjusts the r (k+ k) K (k+), which reduces the influence of the past data on the current filter value through on-site adjustment of the covariance matrix of state prediction error P(k+ k), and the corresponding gain matrix K(k+). Because of the fading factor, the strong tracking extended Kalman filter maintains error of different time to be orthogonal everywhere. Its physical meaning is: when model uncertainty exists, on-site adjustment of gain matrix can always keep the property of Gauss white noise. he state equation and the observation equation are assumed as: [ ] X ( k + ) = f k, X( k) +Γ ( k) v( k), () zk ( + ) = hkxk [, ( )] + wk ( ), (2) where X ( k ) is the motion state vector of the object in time k; zk ( ) is the observation vector of the object in time k; vk ( ), wk ( ) are the Gaussian noise with zero mean value, Γ ( k) is the noise control matrix. Assume the covariance matrixes of process noise vk ( ) and observation noise wk ( ) are Qk ( ) and R( k ), and the status transform matrix and observation matrix are expressed by A( k ) and H ( k ). If f and h are both nonlinear, linearization is done by fkuk (,(), Xk ()) Ak () = X ( k ) = X ( kk ), (3) X hk ( +, Xk ( + )) Hk () = Xk ( += ) Xk ( + k ), (4) X General extended Kalman filter can be obtained by X (k+ k) =A(k) X (k k), (5) Pk ( + k) = AkPk ( ) ( k) A( k), (6) +Γ( kqk ) ( ) Γ ( k) Kk ( + ) = Pk ( + kh ) ( k)[ HkPk ( ) ( + k) H () k + Rk ()], (7) Xk ( + k+ ) = Xk ( + k) + Kk ( + ) γ( k+ ), (8) Pk ( + k+ ) = [ I Kk ( + ) Hk ( )] Pk ( + k), (9) where γ ( k + ) in (8) is the output error, and can be obtained by (0) γ ( k+ ) = z( k) H( k) X( k+ k), (0) When the system becomes stable, i.e. EKF also is in stable status, its prediction error covariance Pk ( + k) tends to its minimum, which renders the gain Kk+ ( ) minimized, and incapable of adjustment. When state X( k+ ) changes, output error γ ( k + ) is increased. However, the gain Kk+ ( ) does not increase with the increase in output error, stays its minimum. herefore, in this manner, EKF essentially loses the tracking capability of changing statues [4]. o improve the tracking capability of changing statues, a fading factor λ ( k + ) is introduced to adjust covariance Pk ( + k) and gain matrix Kk+ ( ). herefore, (4) is converted to: P( k+ k) = λ( k+ ) Ak () P( k k) A () k +Γ() k Q() k Γ () k () From Principle of orthogonality, the fading factor ( k ) λ + can be obtained by where λ0 λ0 λ( k + ) =, (2) λ0 < tr[ N( k + )] λ0 =, (3) tr[ M ( k + )] γ() γ () k = 0 Vk 0( + ) = [ ρvk 0( ) + γ( k+ ) γ ( k+ )] + ρ, (4) k N(k+)=V 0 (k+)-h(k) Γ(k)Q(k) Γ (k)h (k)- β Rk ( ) (5) 56

3 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp M ( k + ) = A( k) P( k k) A ( k) H ( k) H ( k) (6) where 0< ρ is forgetting factor ρ = 0.95, β is a selected weaken factor. Weaken factor is used to make the state estimation more smooth. his value can be set empirically, or by computer simulation according to the formula below: [8] he sampling frequency [2] in this system is 200 ms, because we believe the step length L, and distance r keep unchanged unless their appearance number x is larger than threshold N( x N ). L n β = min xi( k) xi( k k) β, (7) k= 0 i= his paper uses empirically obtained value, which is 2. ill now, the strong tracking filter has been constructed. When the model has enough accuracy, and initial values X(0 0) and P(0 0) are properly selected, the accurate state estimation can be obtained by the above method. Fig.. Schematic diagram of localization. 3. Experiments and Result Analysis 3.. Inhibition of Non-line of Sight In wireless sensor networks, especially in the indoor environment, the LOS (line of sight) path between the sensor nodes may be missing, while only the reflection and diffraction path exist. Since it is unable to detect the direct path signal at the receiving end, the SDS-WR distance measurement inevitably contains NLOS error [9]. Because NLOS propagation path is longer than LOS propagation path, the measurements of SDS-WR [0] have some delay, i.e. NLOS error is random error with a positive mean. herefore, in the environment of NLOS, the measured distance between nodes is usually larger than the actual distance. NLOS error can be defined as the additional propagation distance larger than direct path, NLOS error is always positive. In the practical environment, NLOS propagation is ubiquitous. Inhibition of NLOS error has become the key to improve the localization accuracy Data Rejection In the wireless data transmission process, packet loss inevitably occurs []. here may be some very unreliable data of four measured distances, such as zero or negative, which make the localization have big error. How to eliminate these error caused by the hardware is one target in the project. Fig. is a schematic diagram of localization, where tag is the mobile node, and carried by a walking person, four anchors are the fixed base stations. ) When a measured distance is zero, it is rejected, and the last measurement is used as Fig. 2. Fig. 2. Measured data. 2) When the measured distance is negative, same processing will be done. hat is: it is discarded and the last normal measurement will be used. 3) Following the characteristic of human walking, we assume that the distance between the tag and a node (Anchor for example) r, and the next measurement of the upper distance is recorded as r. We assume that there is a threshold f. When r r f, we believe that r is acceptable in environment with NLOS. Otherwise, we use r to replace r. In the meantime, we also consider the number of sampling, that is, if r appears for 8 times, we believe r is correct. 4) After the rejection of rough data, a second rejection is required. he idea behind this is that the distance between the first measurement and the third measurement cannot be larger than a threshold. An example can be found in Fig. 3, which shows that there is an obvious error in Although the accuracy of distance measurement between two individual nodes is relatively high, the accuracy of many nodes localization in networks is much lower due to the negative effect of hardware, 57

4 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp movement, and multiple nodes in NLOS. hat is, any one in ri= i(,2,3,4) has an error, which may be as large as 3 meter. herefore, this condition will introduce big error to localization of moving nodes. How to eliminate the error in NLOS is the issue we must figure out. between the node in (4,2) and the nodes in coordinate (0,0), (3,0), (3,20), (0,20). Besides, we still need to find out the true value of the distance vector y. his vector can be obtained from computing the distances of the coordinates by MALAB. hat is, the true distances between node (4,2) and other nodes in (0,0), (3,0), (3,20), (0,20) are y = [ ]. able. Measured data of vector x. Fig. 3. Measured data. Assume the correlation coefficient between the measured values of the distances from the moving node to other four nodes and their true values P, vector x is used to represent the measured values: x = [ rrrr], (8) Vector y represents the true values: hen we have: y = [ a a a a ], (9) y = xp, (20) Multiply both sides of formula (4-3) by we obtain x y x, and = x xp, (2) Sampling time r r2 r 3 r 4 2:2: :23: :25: :28: :30: :32: :35: :37: :39: :4: :43: :46: In this manner, we can collect data in other coordinates and obtain thousands of measurements. he correlation coefficient P can be obtained as below. his paper hereinafter will compare the localization accuracy between the condition with trained P and that with untrained P P = he walking route is shown as Fig. 4 when the data is collected. Multiple both sides of formula (4-4) by we have: hat is: [ ] [ ] xx x y xx x xp [ ] xx, =, (22) [ P xx ] x y =, (23) where P is the 4 4 matrix. We can train P using plenty measurement of x and y. he result becomes more accurate when the measurements are richer. able I is a set of data measured in coordinate (4,2). ri= i(,2,3,4) is the measured distance vector Fig. 4. he diagram of the route of the moving node. 58

5 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp We have collected a large quantity of data, which can be divided into 4 2=294 groups, and saved as.txt format. Each group contains a number of measurements, and there are 92 measurements in total. Next the simulation is done using Matlab on the collected data. Firstly, t localization accuracy between the condition with trained P and that with untrained P is compared as Fig. 5 and Fig. 6. he measurement equation is: ( xk ( ) ax, )( yk ( ) a,) y r r2 ( xk ( ) ax,2 )( yk ( ) ay,2) =, (25) r3 ( xk ( ) ax,3 )( yk ( ) ay,3) r4 ( xk ( ) ax,4 )( yk ( ) ay,4) where is the observation period. vx( k+ ), vy ( k+ ) are speed in axis X and Y, respectively. w ( ) x k, wy ( k ) are both Gaussian white noise with zero mean value. ( a x, i, a yi, ) ( i =,2,3,4) are coordinates of the four anchors. Observation parameters ri= i(,2,3,4) are the measured distance between the moving node and the four anchors. In the experiment, the initial values are: Sampling period: =0.2 s; Estimated value of state variable: Fig. 5. Localization result without P. x (0 0) = [ ], which are the speeds in axis X, Y. Initial prediction of state vector covariance matrix is P(0 0) = diag[ ] he noise matrix of the system is Q= diag[ ] he noise matrix in measurement is R= diag[ ] Fig. 6. Localization result with P. he result indicates that the localization of the moving node possesses higher accuracy when P is used. his demonstrates that the coefficient P obviously improves the localization accuracy. he experiment is done in a room with a 6 m 2 m space in Fig. 7. he four anchors are fixed while one wireless moving node needs localization. he Kalman state equation is as below: xk ( + ) 0 0xk ( ) 0 yk ( ) 0 0 yk ( ) 0 + = + vx( k+ ) 0 0 0vx( k) wx( k) vy( k+ ) vy( k) wy( k) (24) Fig. 7. Wireless sensor network in the experiment. Fig. 8 shows the actual route by the black bold line, which means the moving node starts from (4.5,2) and ends in (6,2). he route is three 59

6 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp quarters of a rectangle. he outer trace is the result of EKF, the middle one is the result of the proposed algorithm. algorithm to refinement of localization, and compares the new algorithm with general EKF. Fig. 8. Comparison between the result of EKF and that of strong tracking EKF. Fig. 9 and Fig. 0 show the comparison of absolute values of the errors in axis X and Y between the proposed algorithm and the EKF. During the experiment, as seen from Fig., EKF has big sharp error when state changes, such as walking starts. he maximum error is about 3 meters. On the other hand, the tracking has good performance when the moving reaches a stable state. From the comparison, the proposed algorithm can reduce the error under meter. It improves the localization accuracy, and outperforms EKF which is with more uncertainty and bigger error. Fig. 0. he comparison of error in axis Y between the two algorithms. he experimental results show that, the strong tracking Kalman filter outperforms the classical Kalman filter on the target model and the adaptability of noise signal. Furthermore, the smaller minimum mean square error criterion can be obtained. herefore, it has stronger capability in tracking objects with changing moving statues. his paper also demonstrates the validity of the proposed algorithm in indoor wireless sensor network localization. he algorithm can greatly improve the localization accuracy without additional hardware, and realize the wireless localization with low energy and high accuracy. It will be of significant value in further investigating localization in stable and complex environment. References Fig. 9. he comparison of error in axis X between the two algorithms. 4. Conclusions hrough establishing model of moving object in indoor wireless sensor network, this paper applies fading adaptive strong tracking Kalman filter []. L. R. Wan, Y. Liu, L. Wang, Application of the ZigBee wireless communication technology on the endless rope continuous tractor derailment monitoring system, in Proceedings of the International Conference of Communication, Electronics and Automation Engineering, Xian, P. R. China, August 202, pp [2]. S. eng, S. Huang, Y. Huo, A new positioning algorithm in mobile network, in Proceedings of the International Conference of Pervasive Computing and the Networked World, Istanbul, urkey, November 202, pp [3]. Jiangwen Wan, Jialing Wu and Renjian Feng, he application of Kalman filter in wireless sensor network, High echnology Letters, Vol. 9, Issue 2, 2009, pp [4]. J. Liu, G. Ji, S. Zhou, Applying and Implementation of the Extended Kalman Filter (EKF) with Sensitive Equation: A PEMFC Case Study, in Proceedings of the International MultiConference of Engineers and Computer Scientists, Hong Kong, 4-6 March 202, pp

7 Sensors & ransducers, Vol. 83, Issue 2, December 204, pp [5]. C. S. Ahn and S. Y. Oh, Robust vocabulary recognition clustering model using an average estimator least mean square filter in noisy environments, Personal and Ubiquitous Computing, Vol. 8, Issue 6, 203, pp [6]. Shu Xu, Yihui Jin and Ruijuan Yang, Multiple objects tracking based on strong tracking filter, Sensor echnology, Vol. 2, Issue 5, 2002, pp [7]. D. H. Zhou and Q. L. Wang, Strong tracking filtering of nonlinear systems with colored noise, Journal of Beijing Institute of echnology, Vol. 7, Issue 3, 997, pp [8]. Donghua Zhou, Yinzhong Ye, Modern fault diagnosis and fault tolerant control, singhua University Press, Beijing, [9]. C. Gentile, N. Alsindi and R. Raulefs, Geolocation echniques, Springer, New York, 203. [0]. L. Wei, Z. Jian and W. Chunzhi, Kalman Filter localization algorithm based on SDS-WR ranging, ELKOMNIKA Indonesian Journal of Electrical Engineering, Vol., Issue 3, 203, pp []. C. Lumezanu, K. Guo, N. Spring, he effect of packet loss on redundancy elimination in cellular wireless networks, in Proceedings of the 0 th ACM SIGCOMM Conference on Internet Measurement, New Delhi, India, 3-9 September 200, pp [2]. O. M. Bouzid, G. Y. ian and J. Neasham, Investigation of sampling frequency requirements for acoustic source localization using wireless sensor networks, Applied Acoustics, Vol. 74, Issue 2, 203, pp Copyright, International Frequency Sensor Association (IFSA) Publishing, S. L. All rights reserved. ( 6