The uncertainty of noise statistics in dynamic systems is one of the most important issues in engineering applications, and significantly affects the performance of state estimation. The optimal Bayesian Kalman filter (OBKF) is an important approach to solve this problem, as it is optimal over the posterior distribution of unknown noise parameters. However, it is not suitable for online estimation because the posterior distribution of unknown noise parameters at each time is derived from its prior distribution by incorporating the whole measurement sequence, which is computationally expensive. Additionally, when the system is subjected to large disturbances, its response is slow and the estimation accuracy deteriorates. To solve the problem, we improve the OBKF mainly in two aspects. The first is the calculation of the posterior distribution of unknown noise parameters. We derive it from the posterior distribution at a previous time rather than the prior distribution at the initial time. Instead of the whole measurement sequence, only the nearest fixed number of measurements are used to update the posterior distribution of unknown noise parameters. Using the sliding window technique reduces the computational complexity of the OBKF and enhances its robustness to jump noise. The second aspect is the estimation of unknown noise parameters. The posterior distribution of an unknown noise parameter is represented by a large number of samples by the Markov chain Monte Carlo approach. In the OBKF, all samples are equivalent and the noise parameter is estimated by averaging the samples. In our approach, the weights of samples, which are proportional to their likelihood function values, are taken into account to improve the estimation accuracy of the noise parameter. Finally, simulation results show the effectiveness of the proposed method.
Data loss is ubiquitous in practical engineering applications due to communication delay or congestion. Data loss rate is a key metric to evaluate the reliability of state estimation. To jointly estimate system state and data loss rate, we propose a class of Gaussian-Beta filters for linear and moderate nonlinear Gaussian state-space models with unknown probability of measurement loss. In the filters, the arrival of the measurement at each time is formulated as a binary random variable, which is determined by the classical threshold technology. In addition, the hidden state and the unknown probability of measurement loss are modeled as a product of Gaussian and Beta distributions, and the form remains unchanged through recursive operations. Simulation results verify the effectiveness of the proposed Gaussian-Beta filters compared with the existing filtering algorithms.INDEX TERMS State-space model, measurement loss, threshold technology, Gaussian-Beta filter.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.