I discuss models which allow the local level model, which rationalised exponentially weighted moving averages, to have a time-varying signal/noise ratio. I call this a martingale component model. This makes the rate of discounting of data local. I show how to handle such models effectively using an auxiliary particle filter which deploys M Kalman filters run in parallel competing against one an...

This paper describes a Kalman filter for the real-time estimation of a rigid body orientation from measurements of acceleration, angular velocity and magnetic field strength. A quaternion representation of the orientation is computationally effective and avoids problems with singularities. The nonlinear relationship between estimated orientation and expected measurement prevent the usage of a c...

Bayesian particle filters have become popular for tracking human motion in cluttered scenes. The most commonly used filters suffer from two drawbacks. First, the prior used for the filtering step is often poor due to relatively large, poorly modelled inter-frame motion. Second, the use of the prior as an importance function results in inefficient sampling of the posterior. The use of the auxili...

This paper presents filtering solutions for estimating the relative trajectory of a spin stabilized satellite. The SPHERES satellites have been selected as the hardware testbed for implementing a Multiplicative Extended Kalman Filter and novel Multiplicative Unscented Kalman Filter. Relative state measurements are provided by imaging fiducial markers on the target. The results from this analysi...

Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) integrated system involves nonlinear motion state and measurement models. However, the extended Kalman filter (EKF) is commonly used as the estimation filter, which might lead to solution divergence. This is usually encountered during GPS outages, when low-cost micro-electro-mechanical sensors (MEMS) inertial se...

Particle filtering is probably the most widely accepted methodology for general nonlinear applications. The performance of a particle filter critically depends on choice proposal distribution. In this paper, we propose using wrapped normal distribution as angular data, i.e. data within finite range (-π,π]. We then use same method to derive density filter, in place standard ...