The goal in this section is to explain the fundamentals of Kalman filter theory by a few illustrative examples. The Kalman filter requires a state space model for describing the signal dynamics. To describe its role, we need a concrete example, so let us return to the target tracking example from Chapter 1. Assume that we want a model with the states z1 = X , x2 = Y, x3 = X och x4 = Y . This is the simplest possible case of state vector used in practice. Before we derive a model in the next section, a few remarks will be given on what role. | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic Part IV State estimation Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic 8 Kalman filtering . . State space . Sampling . Physical . Using known transfer . Modeling . The Kalman . Basic . Numerical . Optimality . Time-invariant signal . Error . Observer .288 . Frequency . Spectral factorization .289 . Smoothing .290 . Fixed-lag . Fixed-interval smoothing .292 . Computational . . Cross correlated . Bias . Sequential . Square root . Time and measurement updates .301 . Kalman . Kalman . Sensor . The information . Centralized . The general fusion . Decentralized . The extended Kalman 264 Kalman filtering . Measurement . Time . Linearization . Discretization of state . Whiteness based change detection using the Kalman . Estimation of covariances in state space models . 326 . Applications .327 . DC . Target . . Basics The goal in this section is to explain the fundamentals of Kalman filter theory by a few illustrative examples. The Kalman filter requires a state space model for describing the signal dynamics. To describe its role we need a concrete example so let us return to the target tracking example from
