6.2 Linear Observation Models

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

(6.7) equation

where H is an nz × nx deterministic matrix that is independent of xn and of time. Therefore, we can write

(6.8) equation

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

(6.9) equation

and

(6.10) equation

where img is the observation noise covariance matrix.

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

(6.11) equation

This reduces to

(6.12) equation

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