A new robust Kalman filter with measurement loss based on mixing distribution

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.

An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics

Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.

Robust Kalman Filter Soil Moisture Inversion Model Using GPS SNR Data—A Dual-Band Data Fusion Approach

This article aims to attempt to increase the number of satellites that can be used for monitoring soil moisture to obtain more precise results using GNSS-IR (Global Navigation Satellite System-Interferometric Reflectometry) technology to estimate soil moisture. We introduce a soil moisture inversion model by using GPS SNR (Signal-to-Noise Ratio) data and propose a novel Robust Kalman Filter soil moisture inversion model based on that. We validate our models on a data set collected at Lamasquère, France. This paper also compares the precision of the Robust Kalman Filter model with the conventional linear regression method and robust regression model in three different scenarios: (1) single-band univariate regression, by using only one observable feature such as frequency, amplitude, or phase; (2) dual-band data fusion univariate regression; and (3) dual-band data fusion multivariate regression. First, the proposed models achieve higher accuracy than the conventional method for single-band univariate regression, especially by using the phase as the input feature. Second, dual-band univariate data fusion achieves higher accuracy than single-band and the result of the Robust Kalman Filter model correlates better to the in situ measurement. Third, multivariate variable fusion improves the accuracy for both models, but the Robust Kalman Filter model achieves better improvement. Overall, the Robust Kalman Filter model shows better results in all the scenarios.

Online Dynamic Response Reconstruction in the Presence of Observation Outliers

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.