**3.3. Observer design**

The submersible vehicle's system equations were verified observable by calculation of a fullranked observability matrix in Section 2.3. A full sate observer was designed first to permit vehicle control with "full state feedback", yet without directly measuring velocity. Observer gains may be tuned using classical methods in the general spirit of duality between controller and observers. Their dual nature also permits the matrix Riccati equation to produce optimal gains for a linear-quadratic cost function that exclusively emphasizes state estimation error, unlike the controller optimization where the cost function balanced control effort with state error. State observers permit the vehicle operator to have smooth calculated estimates of all states at all times, which proves useful in the event of sensor interruptions or failures, and reduced-ordered observers may be used in instances where computations on-board the vehicle must be limited, for example to minimize computer size, weight, and/or power.

Especially in light of naturally occurring (roughly) sinusoidal variations in ocean current, the system equations were augmented to include the presumed-unknown disturbance as a state.
