Design and implementation of non-linear minimum variance filters

Abstract

The non-linear minimum variance (NMV) filtering problem for a non-linear multi-input and multi-output (MIMO) discrete-time system is considered. The NMV filter is designed to minimise a minimum variance criterion. The system model includes channel non-linearities that may be treated as a black box. The NMV filter can avoid the need for a linearisation stage that is required in the extended Kalman filter (EKF). The MIMO NMV filter algorithm is easy to implement, in comparison to the EKF. The main contribution of this paper lies in the design and evaluation of the NMV algorithm for the non-linear MIMO filtering problem. A case study is used to demonstrate performance that is based upon a problem in the medical signal processing area. The design and the real time implementation of the NMV estimator is also considered, for a laboratory based ball and beam experiment. The performance is compared with that of an EKF and real time implementation of both estimators is discussed

Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

“…The NMV filter involves matrix calculations so its on-line computational might be large but this is not true because the major matrix calculations are offline to be conducted during the design phase and these have no impact in the implementation phase. The computational complexity and implementation issues of the NMV filter are discussed in some detail in [25].…”

“…The most practical way to implement the estimator is in discrete form but there is a much greater level of mathematical abstraction involved [24]. Extended Kalman filter: A comparison is described in [21] and [25] that includes detailed discussions about the performance of NMV filter with the extended Kalman filter implemented on the ball and beam system in real time. The comparison results are shown in Fig.…”