Robust Gaussian Filtering using a Pseudo Measurement

Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, all estimation algorithms belonging to the family of Gaussian filters (such as the widely-used extended Kalman filter and unscented Kalman filter) are inherently incompatible with such fat-tailed sensor models. The contribution of this paper is to show that any Gaussian filter can be made compatible with fat-tailed sensor models by applying one simple change: Instead of filtering with the physical measurement, we propose to filter with a pseudo measurement obtained by applying a feature function to the physical measurement. We derive such a feature function which is optimal under some conditions. Simulation results show that the proposed method can effectively handle measurement outliers and allows for robust filtering in both linear and nonlinear systems

Tracking the Warhead Among Objects Separation from the Reentry Vehicle in a Clear Environment

Separating a reentry vehicle into warhead, main body, and debris is a conventional and efficient means of producing a huge decoy and increasing the kinetic energy of the warhead. This procedure causes the radar to track the main body and debris, which radar cross section are large, and ignore the warhead, is the most important part of the reentry vehicle. The warhead is difficult to identify after separation using standard tracking criteria. This study presents a novel tracking algorithm by integrating input estimation and modified probabilistic data association filter to identify warhead among objects separation from the reentry vehicle in a clear environment. The proposed algorithm provides a good tracking capability for the warhead ignoring the radar cross section. Simulation results reveal that the errors between the updated and warhead trajectories are reduced to a small interval in a short time. Therefore, the radar can generate a beam to illuminate the right area and keep tracking the warhead all the time. This algorithm is worthy of further study and application.Defence Science Journal, 2009, 59(2), pp.113-125, DOI:http://dx.doi.org/10.14429/dsj.59.149

A partially linearized sigma point filter for latent state estimation in nonlinear time series models

A new technique for the latent state estimation of a wide class of nonlinear time series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process

A new algorithm for latent state estimation in nonlinear time series models

We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples