2019/01/02 by Reddy, Anugu Sumith, Amit Apte, Apte, Amit +2
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #60G35 #93E11 #FOS: Mathematics #Optimization and Control (math.OC) #Scientific Research and Discoveries #Stochastic processes and financial applications #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1901.00307
openalex publication_date 2019/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that Kalman-Bucy filter is stable with respect to initial conditions under the conditions of uniform complete controllability and uniform complete observability (Bishop et. al 2017, Ocone et. al 1996). In this paper, we prove the stability of Kalman-Bucy filter for the case of noise free dynamical system. The earlier stability results cannot be applied for this case, as the system is not controllable at all. We further show that the optimal linear filter for certain class of non-Gaussian initial conditions is asymptotically proximal to Kalman-Bucy filter. It is also shown that the filter corresponding to non-zero system noise in the limit of small system noise approaches the filter corresponding to zero system noise in the case of Gaussian initial conditions.