Feedback Realization of a Continuous-Time Optimal Filter

Another derivation of a continuous-time optimal linear filter is presented. Using this result as a point of departure, a feedback version of this continuous filter is postulated and shown to be optimal in the limit as the ``feedback gain' becomes infinite. It is then demonstrated that the need for this infinite feedback gain can frequently be eliminated. This feedback realization of the continuous optimal filter has application to the problem of optimally mixing two or more redundant signals, each contaminated by random noise. The feedback configuration has the advantages of simplicity and the bounding of otherwise troublesome very large errors. A simple example is given of the mixing of two (velocity) references each having exponentially correlated error.     

Comments on “A method for improving extended Kalman filterperformance for angle-only passive ranging”

Some history of this bearings-only problem at Sperry dating from 1965 is presented. The erratic estimation problems were soon recognised and labeled the “Collapse of the Covariance Matrix Problem”. A solution was soon found as a relation transformation on the covariance matrix. The angle of rotation was the difference between estimates of bearing before and after a measurement update. Based on a comparison of covariance analyses for simulated problems using the true bearings with Monte Carlo results it was concluded that no further significant improvement could be achieved. This conclusion is yet to be disproved