Sequential State Estimation
In the developments of the previous chapters, estimation concepts are formulatedand applied to systems whose measured variables are related to the estimated parameters by algebraic equations. The present chapter extends these results to allow estimation of parameters embedded in the model of a dynamic system, where the model usually includes both algebraic and differential equations. We will find that the sequential estimation results of §1.3 and the probability concepts introduced in Chapter 2, developed for estimation of algebraic systems, remain valid for estimation of dynamic systems upon making the appropriate new interpretations of the matrices involved in the estimation algorithms. In the event that the differential equations have explicit algebraic solutions, of course, the entire model becomes algebraic equations and the methods of the previous chapters apply immediately (see example 1.8 for instance). On the other hand, we’ll find that the sequential estimation results of §1.3 must be extended to properly account for “motion” of the dynamic system between measurement and estimation epochs. We should now note that the words “sequential state estimation” and “filtering” are used synonymously throughout the remainder of the text. The concept of filtering is regularly stated when the time at which an estimate is desired coincides with the last measurement point.1 In the examples presented in this chapter and in later chapters, sequential state estimation is often used to not only reconstruct state variables but also “filter” noisy measurement processes. Thus,“sequential state estimation” and “filtering” are often interchanged in the literature.