Bayesian Estimation and Tracking: A Practical Guide

6.2 Linear Observation Models

If the observation equation is linear, assume that the observation equation can be written as

(6.7)

where H is an n_z × n_x deterministic matrix that is independent of x_n and of time. Therefore, we can write

(6.8)

Assuming that the observation noise w_n is a zero mean process, it follows immediately that (5.39) and (5.40) reduce to

(6.9)

and

(6.10)

where is the observation noise covariance matrix.

Finally, using (6.7) and (6.9) in (5.57) we obtain

(6.11)

This reduces to

(6.12)