Extended Kalman Filter Model for GPS and Indoor Positioning System 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 positioning is an old subject. It’s being used more and more in many areas, especially in military, traffic, social security and civil services. The most popular positioning system in the world is Global Positioning System (GPS). However, GPS has limited degree of accuracy for low priority users. This paper proposes a solution for solving these limitations by using Extended Kalman Filter (EKF). Moreover, GPS is almost invalid in indoor environments. The paper also introduces an indoor positioning system model based on GPS ideology and EKF algorithm. Because of the similarity in ideology, it’s easier for handoff procedure between outdoor and indoor environments and brings back the spatial continuous in positioning. The simulation results show that with the EKF, the accuracy of positioning is improved significantly in both outdoor and indoor environments. Keywords- GPS, Kalman filter, RFID, RSSI, EKF, indoor positioning. I. INTRODUCTION
EKF MODEL FOR GPS
Generally, Kalman algorithm is a group of mathematical equations described an efficient recurrence method for state estimation of process that it is optimal in the sense that it minimizes the estimated error covariance, when some presumed conditions are met . EKF is an extension of Kalman filter for non-linear systems. A. Global Positioning System (GPS)
In order to positioning, it requested that user’s receivers get signals from at least 4 GPS satellites. Distances between user and satellites are determined by using pseudorange code. At the same time, satellites and receiver transmit a same pseudorange code. Because of propagation delay, signal received from satellites have phases delay than signal of receiver. By compared their phase, the distances can calculate. This method is called Time of Arrival (TOA).  B. Problem Expression
Positioning based on GPS is affected by many noise sources, such as propagated errors, satellite and receiver caused errors, other errors from Selective Availability, dilution of precision, interference etc . 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, very high buildings, etc. The paper introduces a kind of Indoor Positioning System based on GPS’s ideology and using EKF algorithm to help this system improve the accuracy of positioning.
Assume that GPS system is tracking a mobile object. It is a uniform speed motion 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. Therefore, 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 effect of noises. C. Modeling 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 user’s velocity at nth sample. Following , the characteristic equations for system can be extended as RX(n+1) = RX(n) + VX(n)T + ax(n)T 2...
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