On initialization of the Kalman filter

As a recursive algorithm, the Kalman filter (KF) assumes the initial state distribution is known a priori, while the initial distributions used in practice are commonly treated as design parameters. In this paper, the influences of initial states are analyzed under the KF framework. That is, we address the questions about how the initial mean and variance affect the subsequent estimates and how much performance is sacrificed if incorrect values are used. Based upon this, two initialization methods are developed for the cases with large initial uncertainties. A drafting stochastic resonator model is employed to verify the theoretical analysis result as well as the proposed initialization approach.