A study of the Kalman filter as a state estimator of deterministic and stochastic systems
M.W.A. Smith, A. P. Roberts · International Journal of Systems Science · 1979
It is shown that the optimality of the Kalman filter prevents its application to estimate the state of deterministic; systems but that if the gain is slightly modified a deterministic filter is possible. Such a filter is subsequently used to explain some of the difficulties encountered in Kalman filter computations, from which it transpires that much Kalman filtering is essentially an application of a deterministic filter to stochastic problems. To reduce the order of the algorithm the concept of observer robustness is incorporated into the subsequent development of the deterministic filter. Exactly equivalent discrete- and continuous-time algorithms are derived and used for a new treatment of the problem of obtaining estimates of the state variables of a stochastic system when the measurements are free of noise.