ABSTRACT
Linear dynamic systems are used by communications and control engineers to monitor and control the state of a system as it evolves through time. Finding the state of the system from noisy measurements is called estimation and estimation is essential to monitoring the system as it evolves through time. This chapter explains linear dynamic model and reviews Kalman filter, and then develops the Bayesian analysis for control, adaptive estimation, and nonlinear filtering. The Kalman filter is a recursive algorithm to estimate the current states of the system at each time point. Smoothing is a way to improve one's estimate of previous states beyond that given by Kalman filter and is a post-mortem operation. Prediction in the context of linear dynamic systems means something other than the way prediction is used with time series analysis. In time series, to predict means to forecast future observations, while with linear dynamic systems, to predict means to forecast the future states of the system.
