A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student’s t-inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN.
AgamennoniGNietoJINebotEM (2012) Approximate inference in state-space models with heavy-tailed noise. IEEE Transactions on Signal Processing60(10): 5024–5037.
2.
ChenSY (2012) Kalman filter for robot vision: A survey. IEEE Transactions on Industrial Electronics59(11): 4409–4420.
3.
DanS (2006) Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches. New York: John Wiley & Sons.
4.
DingDHanQLGeX, et al. (2021) Secure state estimation and control of cyber-physical systems: A survey. IEEE Transactions on Systems, Man, and Cybernetics: Systems51(1): 176–190.
5.
FengYNieXHChenX (2020) Robust optimal filtering over lossy networks. IEEE Transactions on Automatic Control65(5): 2272–2277.
6.
HartikainenSSJ (2013) Variational Bayesian adaptation of noise covariances in non-linear Kalman filtering. Arxiv. Available at: https://arxiv.org/abs/1302.0681
7.
HuangYLJiaGLChenBD, et al. (2020) A new robust Kalman filter with adaptive estimate of time-varying measurement bias. IEEE Signal Processing Letters27: 700–704.
8.
HuangYLZhangYGLiN, et al. (2016a) A robust Gaussian approximate fixed-interval smoother for nonlinear systems with heavy-tailed process and measurement noises. IEEE Signal Processing Letters23(4): 468–472.
9.
HuangYLZhangYGLiN, et al. (2016b) Robust student’s t based nonlinear filter and smoother. IEEE Transactions on Aerospace and Electronic Systems52(5): 2586–2596.
10.
HuangYLZhangYGXuB, et al. (2017) A new outlier-robust student’s t based Gaussian approximate filter for cooperative localization. IEEE-ASME Transactions on Mechatronics22(5): 2380–2386.
11.
HuangYLZhangYGZhaoYX, et al. (2019) A novel robust Gaussian-student’s t mixture distribution based Kalman filter. IEEE Transactions on Signal Processing67(13): 3606–3620.
12.
JiaGLHuangYLZhangYG, et al. (2019) A novel adaptive Kalman filter with unknown probability of measurement loss. IEEE Signal Processing Letters26(12): 1862–1866.
13.
JiaGLZhangYGHuangYL, et al. (2018) A new robust student’s t based SINS/GPS integrated navigation method. In: Proceedings of the 2018 international conference on control, automation and information sciences, Hangzhou, China, 24–27 October, pp. 285–290. New York: IEEE.
14.
MaoJYSunYYiXJ, et al. (2021) Recursive filtering of networked nonlinear systems: A survey. International Journal of Systems Science52(6): 1110–1128.
15.
RohrERMarelliDFuM (2014) Kalman filtering with intermittent observations: On the boundedness of the expected error covariance. IEEE Transactions on Automatic Control59(10): 2724–2738.
16.
SchenatoL (2008) Optimal estimation in networked control systems subject to random delay and packet drop. IEEE Transactions on Automatic Control53(5): 1311–1317.
17.
ShiLEpsteinMMurrayRM (2010) Kalman filtering over a packet-dropping network: A probabilistic perspective. IEEE Transactions on Automatic Control55(3): 594–604.
18.
SinopoliBSchenatoLFranceschettiM, et al. (2004) Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control49(9): 1453–1464.
19.
SunSLDengZL (2004) Multi-sensor optimal information fusion Kalman filter*. Automatica40(6): 1017–1023.
20.
TzikasDGLikasACGalatsanosNP (2008) The variational approximation for Bayesian inference life after the EM algorithm. IEEE Signal Processing Magazine25(6): 131–146.
21.
XuLMaKMFanHX (2018) Unscented Kalman filtering for nonlinear state estimation with correlated noises and missing measurements. International Journal of Control Automation and Systems16(3): 1011–1020.
22.
YounWHuangYLMyungH (2020) Outlier-robust student’s-t-based IMM-VB localization for manned aircraft using TDOA measurements. IEEE-ASME Transactions on Mechatronics25(3): 1646–1658.
23.
ZhouJMGuGXChenX (2019) Distributed Kalman filtering over wireless sensor networks in the presence of data packet drops. IEEE Transactions on Automatic Control64(4): 1603–1610.
