Two-stage particle filtering

An effective way to address non-Gaussian estimation problems with measurement fading


The advancement of wireless communication technologies involves extensive research on the networked systems comprising sensors and processing units. Typically, bandwidth limitation and measurement fading are the most encountered phenomena in wireless transmission. The two, along with other network-induced phenomena like transmission delays, packet dropouts, and signal quantization, must be taken into consideration to ensure accurate state estimation. Among the available tools for solving various state estimation problems, the Kalman filter and its variants, analytical or approximate solutions to the sequential Bayesian filtering problem, are commonly used. Unfortunately, the analytical solutions of the sequential Bayesian filtering do not exist for general non-Gaussian models. This has resulted in numerical solutions such as the particle filter for tracking the non-Gaussian probability density function (PDF) problems.

On the other hand, measurement fading, which describes the distortion of transmitted raw signals, is a major challenge in wireless communication. This can be attributed to the complexity caused by the non-Gaussianity of the fading models, which has remained underexplored despite its significance in networked systems. Currently, hard-decoding and soft-decoding are two schemes used to describe channel fading. The latter does not require a detector and is thus easy to realize. Nonetheless, the state estimation under fading measurements remains a challenge owing to numerous drawbacks that hinder obtaining accurate measurements.

Recently, Dr. Wenshuo Li and Professor Lei Guo from Beihang University, Professor Zidong Wang from Shandong University of Science and Technology, and Professor Yuan Yuan from Northwestern Polytechnic University developed a two-stage particle filtering to address the non-Gaussian filtering problems in systems with fading measurements. Taking into consideration the practical advantages of the cascade structure of the system, the two-stage algorithm was expected to achieve state estimation and measurement recovery simultaneously. Their work is currently published in the research journal, Automatica.

In their approach, the original problem was decomposed into two cascaded subproblems: measurements recovery from the faded ones and state estimation based on the recovered measurements. The decomposition was made possible by decentralization of the particle filter that provided an alternative means of estimating the augmented state of the model. The two subproblems were solved by first- and second-stage particle filters, respectively, using the proposed two-step particle filter algorithm. The feasibility of the proposed algorithm was validated using two examples in which the first case involved tackling the nonlinear filtering, while the second case involved tracking object problem in which the measured signals were distorted using the communication channels. The authors also investigated the relationship between the proposed algorithmand existing schemessuch as brute-force particle filter and decentralized particle filter.

Results showed that the second-stage resampling procedure could be implemented simultaneously and in parallel resulting in a significant reduction in the algorithm execution time. The parallelized architecture further proved suitable for implementing distributed systems resulting in a further improvement in the execution efficiency. Moreover, the two-stage particle filter outperformed the brute force particle filter as it was capable of striking a better balance between the execution time and tracking accuracy, owing to the advantage of the cascaded model structure.

In summary, the research team proposed a two-stage particle filter to solve the non-Gaussian state estimation problems with fading measurements. The algorithm was reportedly suitable for distributed implementations with reduced execution time and improved accuracy and efficiency. Moreover, it outperformed a majority of the existing schemes indicating its potential practical applications. In a statement to Advances in Engineering, Professor Lei Guo admitted that the proposed algorithm could be extended to solve more complicated problems, thus cementing its significance in the research field.

About the author

Wenshuo Li received the B.Eng. degree in automation from Shandong University, China and the Ph.D. degree in control theory and control engineering from Beihang University, China, in 2012 and 2020 respectively. He is currently a Postdoctoral Research Fellow with Hangzhou Innovation Institute, Beihang University, Hangzhou, China. From Jan.~2016 to Jan.~2017, he was an international researcher in the Department of Computer Science, Brunel University London, UK.

His research interests include nonlinear filtering, anti-disturbance control and filtering, networked control systems, and Bayesian estimation. He is an active reviewer for many international journals.

About the author

Zidong Wang was born in Jiangsu, China, in 1966. He received the B.Sc. degree in mathematics in 1986 from Suzhou University, Suzhou, China, and the M.Sc. degree in applied mathematics in 1990 and the Ph.D. degree in electrical engineering in 1994, both from Nanjing University of Science and Technology, Nanjing, China.

He is currently Professor of Dynamical Systems and Computing in the Department of Information Systems and Computing, Brunel University London, U.K. From 1990 to 2002, he held teaching and research appointments in universities in China, Germany and the UK. Prof. Wang’s research interests include dynamical systems, signal processing, bioinformatics, control theory and applications. He has published more than 400 papers in refereed international journals. He is a holder of the Alexander von Humboldt Research Fellowship of Germany, the JSPS Research Fellowship of Japan, William Mong Visiting Research Fellowship of Hong Kong.

Prof. Wang serves (or has served) as the Editor-in-Chief for Neurocomputing, the Deputy Editor-in-Chief for International Journal of Systems Science, and an Associate Editor for 12 international journals, including IEEE Transactions on Automatic Control, IEEE Transactions on Control Systems Technology, IEEE Transactions on Neural Networks, IEEE Transactions on Signal Processing, and IEEE Transactions on Systems, Man, and Cybernetics – Part C. He is a Fellow of the IEEE, a Fellow of the Royal Statistical Society and a member of program committee for many international conferences.

About the author

Yuan Yuan was born in Xi’an, China, in 1986. He received his B.Sc.~degree in the School of Instrumental Science and Opto-electronics Engineering, Beihang University, Beijing, China in 2009. In 2015, he received his Ph.D. degree in computer science and technology from Department of Computer Science and Technology, Tsinghua University, Beijing, China. He is currently a research fellow in the Department of Computer Science, Brunel University London, Uxbridge, U.K. His research interests include anti-disturbance control, stochastic control, and game theoretic control with their applications to the aerospace systems.

About the author

Lei Guo was born in Qufu, China, in 1966. He received the B.S. and M.S. degrees in mathematics from the Qufu Normal University, Qufu, China, in 1988 and 1991, respectively, and the Ph.D. degree in control engineering from the Southeast University, Nanjing, China, in 1997. From 1991 to 1994, he was a Lecturer with the Qingdao University, Qingdao, China.

From 1997 to 1999, he was a Postdoctoral Fellow with the Southeast University. From 1999 to 2000, he was a Research Fellow with IRCCyN, Nantes, France. From 2000 to 2003, he was a Research Fellow with the University of Glasgow, Glasgow, U.K.; Loughborough University, Loughborough, U.K.; and the University of Manchester Institute of Science and Technology, Manchester, U.K. In 2004, he joined the Institute of Automation, Southeast University, as a Professor. In 2006, he became a Professor with the School of Instrumentation and Opto-Electronics Engineering, Beihang University, Beijing, China, where he is currently with the School of Automation Science and Electronic Engineering. He has authored/coauthored more than 120 papers and one monograph and served as an Editor for five journals. His research interests include anti-disturbance control and filtering, stochastic control, and fault detection with their applications to aerospace systems.

Prof. Guo was a recipient of the National Science Fund for Distinguished Young Scholars of China and a Changjiang Distinguished Professor of the Ministry of Education of China.


Li, W., Wang, Z., Yuan, Y., & Guo, L. (2020). Two-stage particle filtering for non-Gaussian state estimation with fading measurements. Automatica, 115, 108882.

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