We present a Forward-Backward Kalman smoother derivation that functions for small observation noise. Whilst this smoother can be found by judicious transformation of the standard Forward-Backward equations, we introduce an auxiliary variable trick which greatly simplifies the derivation, based on the probabilistic interpretation of the Kalman Filter, allowing one to work directly with moments o...

The Iterated Extended Kalman smoother (IEKS) is shown to be equivalent to one iteration of the Expectation Maximisation (EM)-based SAGE algorithm for the class of nonlinear signal models containing polynomial dynamics. Thus the IEKS is a maximum a posteriori (MAP) state sequence estimator for this class of systems. The Iterated Extended Kalman filter (IEKF) can be thought of as a heuristic, onl...

This article presents the winning solution to the CATS time series prediction competition. The solution is based on classical optimal linear estimation theory. The proposed method models the long and short term dynamics of the time series as stochastic linear models. The computation is based on a Kalman smoother, in which the noise densities are estimated by cross-validation. In time series pre...

In this paper, a new nonlinear adaptive filter is presented. This filter consists of three main parts. In the first part, the input space is mapped into the high dimensional space, HDS, using the RBF kernel. The second part employs the Kalman filter as a smoother in HDS. The RLS adaptation algorithm is used for weight updating in the third part. The innovation of this work lies in using Kalman ...

The performance of a non-linear lter hinges in the end on the accuracy of the assumed non-linear model of the process. In particular, the process noise covariance Q is hard to get by physical modeling and dedicated system identi cation experiments. We propose a variant of the expectation maximization (EM) algorithm which iteratively estimates the unobserved state sequence and Q based on the obs...

The performance of a non-linear filter hinges in the end on the accuracy of the assumed non-linear model of the process. In particular, the process noise covariance Q is hard to get by physical modeling and dedicated system identification experiments. We propose a variant of the expectation maximization (EM) algorithm which iteratively estimates the unobserved state sequence and Q based on the ...

The mobile robot localization problem is decomposed into two stages; attitude estimation followed by position estimation. The innovation of our method is the use of a smoother, in the attitude estimation loop that outperforms other Kalman ter based techniques in estimate accuracy. The smoother exploits the special nature of the data fused; high frequency inertial sensor (gyroscope) data and low...

In this paper we consider the problem of localizing a mobile robot on uneven terrain. The localization problem is decomposed into two stages; attitude estimation followed by position estimation. The innovation of our method is the use of a smoother, in the attitude estimation loop that outperforms other Kalman lter based techniques in estimate accuracy. The smoother exploits the special nature ...

Data assimilation has traditionally been employed to provide initial conditions for numerical weather prediction (NWP). A multi{year time sequence of objective analyses produced by data assimilation can also be used as an archival record from which to carry out a variety of atmospheric process studies. For this latter purpose, NWP analyses are not as accurate as they could be, for each analysis...