Kalman filters

The file $VULCAN/src/kalman-filter.scm defines the class <kalman-filter>. Suppose a discrete system described as

3#3

where

• x(k+1) is the state vector at time k+1
• T_k is the transition matrix
• G_k is the process noise distribution matrix
• w(k) is the process noise
• z(k) is the measurement at time K
• H_k is the measurement matrix (observation matrix)
• v_k is the measurement noise

Denote the covariance matrices associated with x,w, and v are by P,Q,R respectively. The Kalman Filter works as follows:

4#4

The class <kalman-filter> implements the equations above. The methods associated with the class are:

(start (self <kalman-filter>) initial-state initial-covariance)
(project (self <kalman-filter>) reading) 
(update (self <kalman-filter>) reading) 
(new-state (self <kalman-filter>) T G Q)

The method project updates the new state of the system, given the previous state and the new reading. The method update updates the system's state given a reading. The method (new-state (self <kalman-filter>) T G Q) projects ahead the filter's state and covariance by using the dynamical part of the system. When T, G or Q are given, new-state uses them instead of the ones associated with the filter.

The state and readings of the kalman filter are represented by 1xn matrices (see 3.1.2). In the appendix we provide a complete example of how to use this class (see Appendix A.1, page ).