Validity conditions for the linear statistical assumptions of Kalman filtering
M. Zanolin, Nicholas C. Makris · The Journal of the Acoustical Society of America · 2003
The fundamental assumption of a Kalman filter is that both the state and evolution equations are linear and that the noise in each of these equations is signal-independent, additive and Gaussian. For many practical problems in Kalman filtering and recursive estimation, however, both the state and evolution equations are actually nonlinear and may involve random variables that are neither additive nor Gaussian. Ad-hoc linearizations with little or no justification are often made to apply a Kalman filter in these cases. Validity conditions for the fundamental linear statistical assumptions of Kalman filtering are derived from the first principles of estimation theory by asymptotic analysis of the likelihood function of the general nonlinear model [E. Naftali and N. Makris, J. Acoust. Soc. Am. 110 (2001)]. An illustrative example involving remote acoustic tracking of a fluctuating target with active sonar is presented.