Bobrovsky-Zakai Bound for Filtering, Prediction and Smoothing of Nonlinear Dynamic Systems

2018-07-13
Fritsche, Carsten
Orguner, Umut
Gustafsson, Fredrik
In this paper, recursive Bobrovsky-Zakai bounds for filtering, prediction and smoothing of nonlinear dynamic systems are presented. The similarities and differences to an existing Bobrovsky-Zakai bound in the literature for the filtering case are highlighted. The tightness of the derived bounds are illustrated on a simple example where a linear system with non-Gaussian measurement likelihood is considered. The proposed bounds are also compared with the performance of some well-known filters/predictors/smoothers and other Bayesian bounds.

Suggestions

Online state estimation for discrete nonlinear dynamic systems with nonlinear noise and interference
Demirbaş, Kerim (2015-01-01)
This paper presents a real-time recursive state filtering and prediction scheme (PR) for discrete nonlinear dynamic systems with nonlinear noise and random interference, such as undesired random jamming or clutter. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple composite hypothesis testing. The PR outperforms both the sampling importance resampling (SIR) particle filter and auxiliary sampling importance resampling (ASIR) particle filter; wh...
Recent results on Bayesian Cramér-Rao bounds for jump Markov systems
Fritsche, Carsten; Orguner, Umut; Svensson, Lennart; Gustafsson, Fredrik (2016-07-08)
In this paper, recent results on the evaluation of the Bayesian Cramer-Rao bound for jump Markov systems are presented. In particular, previous work is extended to jump Markov systems where the discrete mode variable enters into both the process and measurement equation, as well as where it enters exclusively into the measurement equation. Recursive approximations are derived with finite memory requirements as well as algorithms for checking the validity of these approximations are established. The tightnes...
A new real-time suboptimum filtering and prediction scheme for general nonlinear discrete dynamic systems with Gaussian or non-Gaussian noise
Demirbaş, Kerim (Informa UK Limited, 2011-01-01)
A new suboptimum state filtering and prediction scheme is proposed for nonlinear discrete dynamic systems with Gaussian or non-Gaussian disturbance and observation noises. This scheme is an online estimation scheme for real-time applications. Furthermore, this scheme is very suitable for state estimation under either constraints imposed on estimates or missing observations. State and observation models can be any nonlinear functions of the states, disturbance and observation noises as long as noise samples ...
Expectation propagation for state estimation with discrete-valued hidden random variables
Sarıtaş, Elif; Orguner, Umut; Department of Electrical and Electronics Engineering (2023-2-21)
In this thesis, the expectation propagation (EP) approach of Minka is considered for the estimation problems in dynamical systems with discrete hidden random variables where optimal posteriors are usually intractable. The concept of context adjustment is introduced to avoid/alleviate indefinite covariance problems encountered in standard EP implementations in a systematic way. Additionally, the moment projection (Mprojection) problem involving pseudo-Gaussian likelihoods as factors is solved to be used in t...
Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem
Koc, S; Song, JM; Chew, WC (Society for Industrial & Applied Mathematics (SIAM), 1999-04-29)
The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate-but fast-methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtain...
Citation Formats
C. Fritsche, U. Orguner, and F. Gustafsson, “Bobrovsky-Zakai Bound for Filtering, Prediction and Smoothing of Nonlinear Dynamic Systems,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38070.