The Hybrid Density Filter for Nonlinear Estimation based on Hybrid Conditional Density

In nonlinear Bayesian estimation it is generally inevitable to incorporate approximate descriptions of the exact estimation algorithm. There are two possible ways to involve approximations: Approximating the nonlinear stochastic system model or approximating the prior probability density function. The key idea of the introduced novel estimator called Hybrid Density Filter relies on approximating the nonlinear system, thus approximating conditional densities. These densities nonlinearly relate the current system state to the future system state at predictions or to potential measurements at measurement updates. A hybrid density consisting of both Dirac delta functions and Gaussian densities is used for an optimal approximation. This paper addresses the optimization problem for treating the conditional density approximation. Furthermore, efficient estimation algorithms are derived based upon the special structure of the hybrid density, which yield a Gaussian mixture representation of the system state\u27s density

Simultaneous State and Parameter Estimation of Distributed-Parameter Physical Systems based on Sliced Gaussian Mixture Filter

This paper presents a method for the simultaneous state and parameter estimation of finite-dimensional models of distributed systems monitored by a sensor network. In the first step, the distributed system is spatially and temporally decomposed leading to a linear finite-dimensional model in state space form. The main challenge is that the simultaneous state and parameter estimation of such systems leads to a high-dimensional nonlinear problem. Thanks to the linear substructure contained in the resulting finite-dimensional model, the development of an overall more efficient estimation process is possible. Therefore, in the second step, we propose the application of a novel density representation - sliced Gaussian mixture density - in order to decompose the estimation problem into a (conditionally) linear and a nonlinear problem. The systematic approximation procedure minimizing a certain distance measure allows the derivation of (close to) optimal and deterministic results. The proposed estimation process provides novel prospects in sensor network applications. The performance is demonstrated by means of simulation results

The Sliced Gaussian Mixture Filter for Efficient Nonlinear Estimation

This paper addresses the efficient state estimation for mixed linear/nonlinear dynamic systems with noisy measurements. Based on a novel density representation - sliced Gaussian mixture density - the decomposition into a (conditionally) linear and nonlinear estimation problem is derived. The systematic approximation procedure minimizing a certain distance measure allows the derivation of (close to) optimal and deterministic estimation results. This leads to high-quality representations of the measurement-conditioned density of the states and, hence, to an overall more efficient estimation process. The performance of the proposed estimator is compared to state-of-the-art estimators, like the well-known marginalized particle filter

A Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper