New insights into minimum-variance reduced-order filters
Roy Setterlund · Journal of Guidance Control and Dynamics · 1988
The minimum-variance reduced-order (MVRO) filter is an algorithm that has become popular in the guidance and navigation community as a tool for designing and evaluating the performance of candidate reduced-order filters. Its utility rests on the assumption that the MVRO algorithm yields the optimum (in a minimum-varian ce sense) performance possible with a given reduced-order filter. The analysis and examples in this paper show that this is not the case and that the MVRO algorithm merely yields an optimal estimate immediately after the first measurement update. It is shown how a new MVRO gain matrix may be derived that will yield optimum results at some specified time in the future. The main point of the analysis is to prove that, in general, it is not possible to specify a discrete reduced-order filter that is always minimum-variance. The minimum-variance condition can only be achieved at a specific time-before and after that time, other filter gain histories could provide better performance.