Efficiency of the Extended Kalman Filter for Nonlinear Systems with Small Noise
Jean Paul Picard · SIAM Journal on Applied Mathematics · 1991
The problem of nonlinear filtering is studied asymptotically as the noise tends to zero. Detectability conditions ensuring that the filtering error tends to zero are derived, and under these conditions, it is proved that the extended Kalman filter provides a good suboptimal filter; the smoothing problem is also studied. The proofs use some estimates for the linearization of stochastic systems, some changes of probability, and stochastic differentiation techniques.