This chapter begins with a disussion of several important assumptions that have been made to simplify analysis. Next, the Kalman filter equations anh the equations of sensitivity analysis are given | Chapter 5 Analysis Details Introduction This chapter ties together the material of the previous chapters bringing the theories established in Chapter 2 to bear on the Kalman filter presented in this chapter. This chapter begins with a discussion of several important assumptions that have been made to simplify analysis. Next the Kalman filter equations and the equations of sensitivity analysis are given. Most of these equations were already presented in Chapter 3 as sensor error models. However in this chapter the equations are grouped more conveniently for readers interested in the details of the Kalman filter and the sensitivity analysis mechanization. Readers who are not interested in these details may skip Sections and without loss of continuity. Simplifications A general analysis of an automobile navigation system bears certain complications that must be simplified in order to obtain meaningful results efficiently. In this section four important simplifications that are made in the analysis in this research are introduced and justified. 89 CHAPTER 5. ANALYSIS DETAILS 90 Dealing with Trajectory Dependencies The first such issue arises in connection with the effect that the vehicle s trajectory has on the performance of a navigation system. Simply stated the vehicle s motion . how often the vehicle turns how fast the vehicle moves how often the vehicle changes lanes etc. will have an impact on the positioning accuracy of its navigation system. This fact is readily seen when one realizes that certain sensor errors will change as the vehicle moves. For example a rate gyro scale factor error contributes more to heading error when the vehicle turns and the magnitude of the errors caused by the odometer depends on the vehicle s speed. Because the magnitude of some sensor errors vary with the vehicle s motion analysis results are trajectory-dependent and therefore specific to the chosen trajectory. This makes it more difficult to perform a .
