Extended Kalman Filter Model for Gps and Indoor Positioning System

Extended Kalman Filter Model for GPS and interior military position establishment Long Kam-Kim Department of Telecommunications Engineering, Faculty of Electrical and Electronics Engineering HCM City University of Technology, Ho Chi Minh City, Vietnam Tuan Do-Hong Department of Telecommunications Engineering, Faculty of Electrical and Electronics Engineering HCM City University of Technology, Ho Chi Minh City, Vietnam Abstract Object view is an old subject. Its cosmos utilize more and more in many argonas, especially in military, traffic, social security and civil services.The most popular stance remains in the world is Global Positioning body of rules (GPS). However, GPS has limited point of verity for low priority exploiters. This paper proposes a solution for result these limitations by using Extended Kalman Filter (EKF). More all over, GPS is almost invalid in indoor(a)(prenominal) environments. The paper also set offs an indoor set system manakin based on GP S ideology and EKF algorithmic programic program. Because of the similarity in ideology, its easier for handoff operation in the midst of out-of-door and indoor environments and brings back the spatial persisting in emplacement.The simulation results show that with the EKF, the the true of positioning is improved signifi backtly in both outdoor and indoor environments. Keywords- GPS, Kalman filter, RFID, RSSI, EKF, indoor positioning. I. INTRODUCTION II. EKF MODEL FOR GPS Generally, Kalman algorithm is a group of mathematical pars described an efficient recurrence method for nation estimation of process that it is optimal in the sense that it minimizes the estimated wrongdoing co magnetic declination, when some presumed conditions ar met 2. EKF is an extension of Kalman filter for non-linear systems.A. Global Positioning form (GPS) In enact to positioning, it requested that users receiving systems get signals from at least 4 GPS airs. Distances between user and satellit es be unflinching by using pseudorange code. At the akin time, satellites and receiver transmit a same pseudorange code. Because of genesis delay, signal received from satellites w atomic number 18 phases delay than signal of receiver. By compared their phase, the surmounts can calculate. This method is called Time of Arrival (TOA). 1 B. Problem ExpressionPositioning based on GPS is affected by many stochasticity sources, such as propagated wrongful conducts, satellite and receiver ca apply errors, separate errors from Selective Availability, dilution of precision, interference etcetera1. Several techniques are used to improve the accuracy of positioning in GPS, for example, DGPS (Differential GPS), Smart Antenna, Kalman Filter etc. This paper focuses on Extended Kalman Filter (EKF) solution, in order to introduce one way to model GPS system and sources of error. Nowadays, positioning applications in indoor environment are being extended.Especially, it becomes necessary in tunnels, supper huge plants, rattling high buildings, etc. The paper introduces a kind of Indoor Positioning System based on GPSs ideology and using EKF algorithm to help this system improve the accuracy of positioning. Assume that GPS system is track a mobile object. It is a uni convention look sharp effort in 3D space with attendance of random acceleration events. GPS receiver puts on object updates its position continuously. However, the location is affected by measurement noises and propagation noises.T presentfore, the calculating position and the real position are different. In order to improve the accuracy of position, we use EKF to model system and noises so that it diminishes the picture of noises. C. manakin of system Defining the sate vector of system as follow ? RX ( n ) ? ? RY ( n ) ? ? ? ? RZ ( n ) ? X (n) = ? ? ? VX ( n ) ? ?VY ( n ) ? ? ? ?VZ ( n ) ? where RX(n),RY(n),RZ(n) are coordinates of user at nth sample, VX(n), VY(n), VZ(n)) are x, y, z components of u sers velocity at nth sample.Following 3, the device characteristic equations for system can be extended as RX(n+1) = RX(n) + VX(n)T + ax(n)T 2 RY(n+1) = RY(n) + VY(n)T + ay(n)T 2 RZ(n+1) = RZ(n) + VZ(n)T + az(n)T 2 VX(n+1) = VX(n) + ax(n)T VY(n+1) = VY(n) + ay(n)T VZ(n+1) = VZ(n) + az(n)T (1) (2) (3) (4) where VX(n), VY(n), VZ(n)) are x, y, z components of users velocity at nth sample, bf = ? bu/? t, dPRi is called delta-pseudorange correlated with user and ith satellite. 4 In order to reducing effect of errors, the EKF is used to model aver noise vectors and measurement noise vectors. afterward characteristic matrixes are calculated, EKF iteration loops are started. The EKF algorithm depart calculate estimation of the state vector by minimizing the estimated error covariance (between estimated values and real values). D. Simulation results for outdoor-EKF GPS data for simulation on Matlab7. 8. 0(R2009a) substance abusers initial velocity (3,6,2) verses/ flash sample rate 1000 samples/second Iteration steps five hundred serve up noise vector W = 5* NORMRND (0, 500, 3, 1) Process noise variance Q = 50* warmheartedness (3) Measurement noise vector V = 5 * NORMRND (0, 500, 2, 1) Measurement noise variance R = 50 * eye (2) (5) (6) here ax(n), ay(n), az(n) represent acceleration events at nth sample ( it is referred to state noises or process noises). According to 4, Users positions are determined base on distances between user and four satellites. PRi= +bu, i=1,2,3,4 (7) Fig. 1 shows the simulation results for Lagrange iteration and EKF iteration compared with the reliable position values. In geographic coordinates, PRi is the distance between the user and the ith satellite, (SXi,SYi,SZi) are coordinates of ith satellite, (RX,RY,RZ) are coordinates of the user bu=c. t with t is receiver clock offset compared to GPS time and c is the speed of light.PRis are determined by GPSs receiver. Coordinates of satellites are obtained by decryption satellite report, while (RX, RY, RZ) and bu are unknowns. With system of equations (7) above, the root RX,RY,RZ,bu, can be calculated by using Lagrange iteration 4. However, measurement values PRi are affected by noises (measurement noises). Therefore the root of system of equations is not accuracy. After differentiating equations (7), we obtain dPRi = (RX ? SXi)? RX + (RY ? SYi)? RY + (RZ ? SZi)? RZ (RX ? SXi)2 + (RY ? SYi)2 + (RZ ? SZi)2 + ? bu = (RX ? SXi). VRX +(RY ? SYi). VRY +(RZ ?SZi). VRZ +bf PRi ? bu Figure 1. Simulate tracking Users flying in outdoor environment (8) In Fig. 1, red carouse simulates users motion,Green curve simulates calculated trajectory of user receiver without EKF, well-fixed curve simulates calculated trajectory of user receiver in EKF model. found on GPSs ideology, this paper introduces an indoor positioning model using EKF, called Indoor-EKF GPS. Indoor-EKF GPS is hoped that it makes over easier with GPS, in such a way, we just use a handle equipment to ke ep the continuous positioning while travel between indooroutdoor environments.In Fig. 3, an arranged system of equipments in space can be recognized as pseudo-satellites. Indoor spaces are complicated environments for wave propagation. Distances between user and pseudo-satellites cannot be determined using TOA technique like in outdoor GPS. Here, TOA technique is replaced by RSS (Received Signal Strength) technique. This technique measures the path loss and calculates the distance between source and receiver. Figure 2. Errors in outdoor positioning. Red points positioning errors without EKF. Green points positioning errors in EKF model.Comments on simulation results The maximum error is about 5 meters in eccentric person using EKF model, whereas 25 meters in case without EKF. Trajectory of user receiver in EKF model is at hand(predicate) to trajectory of users motion than trajectory of user receiver without EKF. The average estimation error of EKF is very beautiful than withou t EKF case. However, several points in curve are under suddenly ever-changing errors. Figure 3. Indoor positioning system. According to IEEE 802. 11 recommended channel model, the relation between forgo space path loss and distance d in breakpoint rundle is given by 5 LFS(d) = L0 + 10? 1lg(d), 0 d ? BP (9) According to the result, it shows that the positioning errors are reduced significantly. III. A. INDOOR POSITIONING SYSTEM where ? 1 is called distance-power-gradient up to breakpoint distance dBP, Lo represents the path loss in decibels at one meter distance. The overall path los for any distance is modeled as 5 Indoor-EKF GPS new-made years, indoor environment has been extended so that indoor positioning demands are extended, too. Furthermore, it becomes necessary in tunnels, supper huge plants, very high buildings etc, and giving snug for absent minder when household equipments are positioning.However, GPS is almost invalid in indoor environment. The reason is that GPS s ignal has low power. Even GPS signal can be received, the error positioning of GPS is not appropriate with Indoor applications. ?LFS (d ) +W, d ? dBP ? L(d ) = ? ? d ? ?LFS (dBP ) +10? 2 lg ? d ? +W, d dBP ? BP ? ? (10) where ? 2 is distance-power-gradient over break-point distance dBP. Its required at least four distances form user to pseudosatellites are determined for calculating the users coordinates. Fig. 4 shows calculation process for user position. Figure 6. The second model. Figure 4. Users coordinates calculation.B. In the next section, the RFID (Radio Frequency Identification) technology will be used to implement this system. There are two implementation models The starting time model (Fig. 5) The RFID active chips are pseudo-satellites, and readers will be used as GPSs receivers. Modeling of system Definition of the sate vector and the characteristic equations for system are similar with outdoor case above. However, because of difference on distances calculating method , equation (7) and equation (8) are not used here. This equation below is replaced equation (7) LPi=L0 + 10? lg (di) , i=1? 4 (11) here di is distance between user and ith pseudo-satellite, LPi is value of path loss on distance di. W appears as representative of noises and interferences. Here, we assume that it is Gaussian distribution, ? is distance-power-gradient (we have not examined its change yet. Here, we assume that it is constant). After differentiating equations (11), we obtain dLPi = Figure 5. The kickoff model. 10? ( RX ? SRXi ). VX + ( RY ? SRYi). VY + ( RZ ? SRZi). VZ . ln10 di 2 + ? Wi , i=1,2,3,4 (12) The RFID active chips will transmit these data to readers The chips coordinates (in local coordinates) and its identification.The nominal value of transmitting power. The parameters in IEEE 802. 11 that supporting to correct distance measurements in each particular proposition environment. where (SXi,SYi,SZi) are coordinates of ith pseudo-satellite, (RX,RY,RZ)are coo rdinates of the user, VX, VY, VZ are x, y, z components of users velocity, dLPi means the renewing of path loss on distance di . We imply that the values are taken at nth sample. C. Simulation results for indoor-EKF GPS Data for simulation on Matlab7. 8. 0(R2009a) The second model (Fig. 8) The RFID active chips will be attached to users. Users will move in space that arranged with RFID readers.These readers will be machine-accessible to data fusion center. This center will determine users coordinates and send the result to users receiver by other channel link. Users initial velocity (1,2,1) meters/second Sampling rate 1000 samples/second Iteration steps 500 Process noise vector W = 5* NORMRND (0, 120, 3, 1) Process noise variance Q = 50* eye (3) Measurement noise vector V = 5 * NORMRND (0, 0. 4, 2, 1) Measurement noise variance R = eye (8) This simulation was repeated 100 times. The maximum error is about 0. 5 meters in case using EKF model, whereas 4. 5 meters in case witho ut EKF.Trajectory of user receiver in EKF model is not closed to trajectory of users motion correlative with appreciably positioning error. However the error reduces very rapidly by exponential curve. The average estimation error of EKF is very small than without EKF case. However, several points in curve are under suddenly changing errors. IV. CONCLUSION Fig. 7 shows the simulation results for Newton iteration and EKF iteration compared with the true position values. In positioning systems, the accuracy of positioning is very important. It must(prenominal) be appropriated with the positioning applications.The paper recommends one way to improve the accuracy of positioning using the EKF. The results of simulations show that the EKF reduce effect of noises on the accuracy of positioning significantly in both outdoor and indoor positioning systems. The Indoor-EKF GPS system is a suggestion model for the future indoor positioning. It is easy for implementation and expansion, since RFID is very popular and cheap today. Moreover, the Indoor-EKF GPS system has the same grammatical construction with GPS system, wherefore the handle equipment can be designed to keep the continuous positioning while moving between indoor-outdoor environments.REFERENCES 1. Ahmed EI-Rabbany, Introduction to GPS, Artech House, Inc, ISBN 1-58053-183-0, 2002, pp. 13-25,2741. 2. Grey Welch and Gary Bishop, An inception to the Kalman filter, Technical Report TR 95-041, 2001. 3. Jorge Quijano, Estimation of the position of a moving target using Extended Kalman Filter,term paper for the class ECE 510 statistical Signal Processing, winter 2006. 4. James Bao-Yen TSui, Fundamentals of Global Positioning System Receivers A Software Approach, John Wiley & Sons , Inc, ISBN 0-471-20054-9, 2000, pp. 9-15, 230-231. 5.Ahmad Hatami, Application of Channel Modeling for Indoor Location Using TOA and RSS, PhD Thesis, Worcester Polytechnic Institute, 2006, pp. 14-19. Figure 8. Errors in indoor positioni ng. Figure 7. Simulate tracking Users trajectory in indoor environment. In Fig. 7, red curve simulates users motion, immature curve simulates calculated trajectory of user receiver without EKF, blue curve simulates calculated trajectory of user receiver in EKF model. Red points positioning errors without EKF. Green points positioning errors in EKF model. Comments on simulation results