Introduction

In this chapter we will show how extended Kalman filtering can be used to locate a receiver based on range measurements from a number of satellites to the receiver. Although many simplifications are made, some aspects of problems of this type are similar to those encountered by a receiver processing measurements from the global positioning system (GPS). ^[1] We will first investigate the case in which filtering is not used at all, but we solve simply the noisy algebraic equations for the receiver location. Next, we will attempt to improve the accuracy in locating the receiver by filtering the range measurements. We will then show that even more accuracy can be achieved by using extended Kalman filtering. Once the filter is built, we will see what happens to accuracy and to the filter when the receiver is moving. All of the experiments will be conducted in two dimensions with either one or two satellites.