Optimal Reduced-order Filter for Systems with Deterministic Observations and Stochastic Observations

For linear discrete time-invariant systems with deterministic observations and random observations, the optimal reduced-order filtering problem is studied. Some of the state components can be obtained directly by deterministic observation, while others can be obtained by designing a reduced-order state filter. Compared with the method of augmenting the observation, it not only reduces the calculation burden, but also avoids the problem of numerical instability caused by the singular observation noise variance matrix. The method presented in this paper can solve the estimation problem of systems with state equality constraint and singular observation noise variance matrix. A simulation example verifies the effectiveness of algorithm.