Implementation of a square‐root filtering approach in marginalized particle filters for mixed linear/nonlinear state‐space models

Abstract

Marginalized particle filter (MPF) takes advantage of both Kalman filter and particle filter frameworks to estimate nonlinear state-space models with reduced number of calculations in comparison to particle filter. However, due to existence of Kalman filter framework inside MPF, some limitations are introduced in implementation of MPF especially in embedded systems with finite numerical accuracies. In this paper, for the first time, we propose a novel square-root filtering strategy for MPFs to alleviate these restrictions using modified  factorization. Typical square-root Kalman filters cannot be employed inside MPF due to the presence of minus operations in some equations of MPF. However, our method can be easily implemented inside the MPF structure. The proposed method can be used in any application that employs MPFs to estimate the mixed linear/nonlinear state-space models. In order to demonstrate its usefulness, we employed the proposed square-root filtering method inside a marginalized particle extended Kalman filter (MP-EKF) structure, which was specifically designed for ECG denoising. The experimental results showed that, in the field of ECG denoising, the square-root MP-EKF performs more consistently than MP-EKF in white Gaussian noises. KEYWORDSmarginalized particle filtering, model-based filtering, square-root filtering,  factorization(1a) and (1b) are called the state dynamic and measurement models, respectively. In the above models, f and h are general nonlinear functions. x k and y k are state and measurement vectors at time step k. w k and e k are noise vectors defined by Int J Adapt Control Signal Process. 2019;33:493-511. wileyonlinelibrary.com/journal/acs

Stochastic filtering based transmissibility estimation of novel coronavirus

“…Several parametric Bayesian methods are useful for the parameter estimation of Gaussian and non-Gaussian systems in which states are Markov process. Different parametric Bayesian estimation methods are available in the literature [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] are described in Table 1 . For the non-Gaussian systems, Bayesian computation of conditional probabilities has been used for updating the weights involved in the state estimation.…”

“… (i) Particle degradation results in estimation error. (i) Electrocardiogram denoising [17] . (ii) Cancer patient treatment systems [18] (iii) Heart rate estimation [19] .…”