Enhanced Kalman Filter Method for Estimating Statistical Fields of Transport Dynamics-1. Mathematical Basis.
Michio NONAKA, Neale H. Thomas · Shigen-to-Sozai · 1996
We report the mathematical basis of a recent enhancement incorporated within an algorithm entitled “Switching mode Enhanced Extended Kalman” (SEEK) filter algorithm. The SEEK filter algorithm was inspired by the motive of enhancing the convergence rate of the estimation error covariance matrix by optimally selecting the observation matrix. As a measure of the convergence rate we focus attention on the trace of the Jacobian matrix for the Riccati-type matrix differential equation consisting of the current state transition matrix, the driving matrix, the observation matrix and the observation noise covariance matrix. In the SEEK filter algorithm the observation matrix is switched so as to ensure the objective function is maximised. As a demonstration here, we offer the dual-states Lorenz system with superimposed Gaussian white noise, and the discrete vortex models characterising three vortices behaviour are also identified. We confirm a singular improvement achieved by the SEEK algorithm over the conventional extended Kalman filter.