Fritsche, Carsten
Orguner, Umut
Özkan, Emre
Gustafsson, Fredrik
In this paper, marginal versions of the Bayesian Bhattacharyya lower bound (BBLB), which is a tighter alternative to the classical Bayesian Cramer-Rao bound, for discrete-time filtering are proposed. Expressions for the second and third-order marginal BBLBs are obtained and it is shown how these can be approximately calculated using particle filtering. A simulation example shows that the proposed bounds predict the achievable performance of the filtering algorithms better.


Fritsche, Carsten; Özkan, Emre; Orguner, Umut; Gustafsson, Fredrik (2015-04-24)
A marginal version of the Weiss-Weinstein bound (WWB) is proposed for discrete-time nonlinear filtering. The proposed bound is calculated analytically for linear Gaussian systems and approximately for nonlinear systems using a particle filtering scheme. Via simulation studies, it is shown that the marginal bounds are tighter than their joint counterparts.
The Marginal Enumeration Bayesian Cramer-Rao Bound for Jump Markov Systems
FRITSCHE, Carsten; Orguner, Umut; Svensson, Lennart; Gustafsson, Fredrik (2014-04-01)
A marginal version of the enumeration Bayesian Cramer-Rao Bound (EBCRB) for jump Markov systems is proposed. It is shown that the proposed bound is at least as tight as EBCRB and the improvement stems from better handling of the nonlinearities. The new bound is illustrated to yield tighter results than BCRB and EBCRB on a benchmark example.
Some Inequalities Between Pairs of Marginal and Joint Bayesian Lower Bounds
Bacharach, Lucien; Chaumette, Eric; Fritsche, Carsten; Orguner, Umut (2019-01-01)
In this paper, tightness relations (or inequalities) between Bayesian lower bounds (BLBs) on the mean-squared-error are derived which result from the marginalization of a joint probability density function (pdf) depending on both parameters of interest and extraneous or nuisance parameters. In particular, it is shown that for a large class of BLBs, the BLB derived from the marginal pdf is at least as tight as the corresponding BLB derived from the joint pdf. A Bayesian linear regression example is used to i...
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...
Fritsche, Carsten; Orguner, Umut; Gustafsson, Fredrik (2016-03-25)
Parametric Cramer-Rao lower bounds (CRLBs) are given for discrete-time systems with non-zero process noise. Recursive expressions for the conditional bias and mean-square-error (MSE) (given a specific state sequence) are obtained for Kalman filter estimating the states of a linear Gaussian system. It is discussed that Kalman filter is conditionally biased with a non-zero process noise realization in the given state sequence. Recursive parametric CRLBs are obtained for biased estimators for linear state esti...
Citation Formats
C. Fritsche, U. Orguner, E. Özkan, and F. Gustafsson, “MARGINAL BAYESIAN BHATTACHARYYA BOUNDS FOR DISCRETE-TIME FILTERING,” presented at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, CANADA, 2018, Accessed: 00, 2020. [Online]. Available: