CHAPTER 2

SYSTEM DYNAMICS AND MODELS

The performance of estimation algorithms is highly dependent on the accuracy of models. Model development is generally the most difficult task in designing an estimator. The equations for least squares and Kalman filtering are well documented, but proper selection of system models and parameters requires a good understanding of the system and of various trade-offs in selecting model structure and states. We start by discussing dynamic and measurement models. This provides the reader with a better understanding of the problem when estimation algorithms are presented in later chapters.

Chapter 1 was deliberately vague about the structure of models because
the intent was to present concepts. The dynamic (time evolution) model of the true
system used in Figure 1.1 was a generic form. The system state vector x(t) was an n-element linear or nonlinear function of various constant parameters
p, known time-varying inputs u(τ) defined over the time interval t_{0} ≤ τ ≤ t, random process noise q(τ) also defined over the time interval t_{0} ≤ τ ≤ t, and possibly time, t:

Function f_{t} was defined as a time integral of the independent
variables. The m-element measurement vector y(t) was assumed to be a
function of x(t) with additive
random noise:

(2.0-2)

However, these models are too general to be useful for estimation. We now consider the ...