Toshiaki Tabuchi

A method on parameter estimation of nonlinear systems

It is developed that the state estimation of nonlinear system model based on maximum a posteriori (MAP) estimation. This is equivalent to the minimization problem of the object function derived from a posteriori probability density function.It is shown that the minimizer based on Newton-method becomes to iterated extended Kalman filter (IEKF). A method on the gain adjustment of the MAP estimator is given so as to improve the performance of it. Then a method of the parameter setting for the gain adjustment is given.

Dynamically-variable adaptive algorithms

Variations of the statistical properties of system inputs may cause a fall of adaptation abilities of the adaptive algorithms. To overcome this problem, we propose a dynamically-changing method of the form of the adaptive algorithms among Kalman filter based, normalized least mean square and recursive least squares methods. The validity of our method was confirmed in the numerical experiments.

An executable and asymptotically optimal adaptive RLS algorithm

A setting method for the forgetting factor in recursive least squares (RLS) algorithms is presented. In a general adaptive setting method, to obtain the optimal value of the forgetting factor, the cost function constructed with the mean squared prediction errors is differentiated and the derivative that is set to zero is solved numerically. The problem of this method is that just one of local minimums is obtained unless the cost function is confirmed as unimodal. The main object of this contribution is to show the unimodality of the cost function of the RLS algorithm.