Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Toni Karvonen (Aalto University, Finland)
This talk discusses stability of a class of Kalman-Bucy filters (including the classical extended Kalman-Bucy filter) for continuous-time systems with non-linear dynamics and linear measurements. The presented results, similar to those appearing in recent work by Del Moral, Kurtzmann, and Tugaut, are in the form of exponential concentration inequalities for the filtering error. The results are based on the strong assumptions of contractivity of the filtering error process and boundedness of the error covariance matrix. In most cases, verifying these assumptions requires that the model is fully observed. Three scenarios in which this verification is possible are reviewed: fully observed models with (i) contractive dynamics or (ii) the filter making use of covariance inflation and (iii) certain simple integrated velocity models where the part that is not directly observed is exponentially stable. This is a joint work with Silvère Bonnabel (Mines ParisTech), Eric Moulines (École Polytechnique), and Simo Särkkä (Aalto University).