Online Stochastic Convergence Analysis of the Kalman Filter

Matthew B. Rhudy, Yu Gu
2013 International Journal of Stochastic Analysis  
This paper presents modifications to the stochastic stability lemma which is then used to estimate the convergence rate and persistent error of the linear Kalman filter online without using knowledge of the true state. Unlike previous uses of the stochastic stability lemma for stability proof, this new convergence analysis technique considers time-varying parameters, which can be calculated online in real-time to monitor the performance of the filter. Through simulation of an example problem,
more » ... example problem, the new method was shown to be effective in determining a bound on the estimation error that closely follows the actual estimation error. Different cases of assumed process and measurement noise covariance matrices were considered in order to study their effects on the convergence and persistent error of the Kalman filter.
doi:10.1155/2013/240295 fatcat:n27k45smzjdp7hl7luajc4iyre