TABLE OF CONTENTS Many of the optimization methods to be presented rely on finding an estimate based on minimizing the error between the estimate and the actual value of the PF. Therefore, this section presents the general development of the optimal LSE estimator. Here, the recursive form of LSE estimation is assumed such that measurements are made sequentially at time instants 0, 1, ..., k, ..., M - 1. That is, measurements are available at time instants k and before. LSE estimation can be applied to any appropriate set of data points [2], however, to include the case when the estimate is not obtained until all the data points are available.
Let the linear estimation model for the kth time instant be given by
| (2.3) |  |
where x k is the vector of measurements up to time k, and H k is the observation matrix such that measurement x k at time instant k is related to the vector ? k by
| (2.4) |  |
where h k is the kth row vector in H k and ? k is the unknown parameter vector up to k. Noise term n k is the measurement noise vector for sample time k.
The estimation model for x k is given by
| (2.5) |  |
The goal is to find the optimum estimate for ?, denoted by 
, such that some cost function is minimized. For LSE estimation,...
