Abstract
In this letter, we develop a partial update Kalman filtering (PUKF) algorithm to solve the state of a discrete-time linear stochastic dynamical system. In the proposed algorithm, only a subset of the state vector is updated at every iteration, which reduces its computational complexity, compared to the original KF algorithm. The required conditions for the stability of the algorithm are discussed. A closed-form expression for steady-state mean-square deviation is also derived. Numerical examples are used to validate the correctness of the provided analysis. They also reveal the PUKF algorithm exhibits a trade-off between the estimation accuracy and the computational load which is extremely profitable in practical applications.
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References
R. Arablouei, S. Werner, K. Dogancay, Partial-diffusion recursive least-squares estimation over adaptive networks. In Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
R. Arablouei, S. Werner, Y.-F. Huang, K. Dogancay, Distributed least mean-square estimation with partial diffusion. IEEE Trans. Signal Process. 62(2), 472–484 (2014)
R. Claser, V.H. Nascimento, Low-complexity approximation to the kalman filter using convex combinations of adaptive filters from different families (2017), pp. 2630–2633
F.S.C. Dobarro, Distributed collaborative processing over adaptive networks (University of California, Los Angeles, 2010)
S.C. Douglas, Adaptive filters employing partial updates. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 44(3), 209–216 (1997)
H. Fang, G. Zhu, V. Stojanovic, R. Nie, S. He, X. Luan, F. Liu, Adaptive optimization algorithm for nonlinear markov jump systems with partial unknown dynamics. Int. J. Robust Nonlinear Control 31(6), 2126–2140 (2021)
M. Godavarti, A.O. Hero, Partial update lms algorithms. IEEE Trans. Signal Process. 53(7), 2382–2399 (2005)
J.B. Jorgensen, P.G. Thomsen, H. Madsen, M.R. Kristensen, A computationally efficient and robust implementation of the continuous-discrete extended Kalman filter (2007), pp. 3706–3712
T. Kailath, A.H. Sayed, B. Hassibi, Linear estimation (Prentice Hall, Number BOOK, 2000)
M. Katzfuss, J.R. Stroud, C.K. Wikle, Ensemble kalman methods for high-dimensional hierarchical dynamic space-time models. J. Am. Stat. Assoc. 115(530), 866–885 (2020)
A. Khalili, V. Vahidpour, A. Rastegarnia, W.M. Bazzi, S. Sanei, Partial diffusion kalman filter with adaptive combiners. IEEE Trans. Aerosp. Electron. Syst. 57, 1972 (2020)
C. Li, S. Chu, S. Tsai, Improved variable step-size partial update lms algorithm (2016), pp. 17–19
K. Mayyas, L. Afeef, A variable step-size partial-update normalized least mean square algorithm for second-order adaptive volterra filters. Circuits Syst. Signal Process. 39, 6073–6097 (2020)
J. Minglu, Partial updating rls algorithm. In Proceedings 7th International Conference on Signal Processing, 2004. Proceedings. ICSP ’04. 2004. 1, 392–395 (2004)
M. Raitoharju, R. Piché, On computational complexity reduction methods for Kalman filter extensions. IEEE Aerosp. Electron. Syst. Mag. 34(10), 2–19 (2019)
M. Roth, G. Hendeby, C. Fritsche, F. Gustafsson, The ensemble Kalman filter: a signal processing perspective. EURASIP J. Adv. Signal Process (2017). https://doi.org/10.1186/s13634-017-0492-x
V. Stojanovic, D. Prsic, Robust identification for fault detection in the presence of non-gaussian noises: application to hydraulic servo drives. Nonlinear Dyn. 100, 2299–2313 (2020)
V. Stojanovic, S. He, B. Zhang, State and parameter joint estimation of linear stochastic systems in presence of faults and non-gaussian noises. Int. J. Robust Nonlinear Control 30(16), 6683–6700 (2020)
X. Sun, M. Medvedovic, Model reduction and parameter estimation of non-linear dynamical biochemical reaction networks. IET Syst. Biol. 10(1), 10–16 (2016)
V. Vahidpour, A. Rastegarnia, A. Khalili, S. Sanei, Partial diffusion Kalman filtering for distributed state estimation in multiagent networks (2019a)
V. Vahidpour, A. Rastegarnia, A. Khalili, W.M. Bazzi, S. Sanei, Analysis of partial diffusion lms for adaptive estimation over networks with noisy links. IEEE Trans. Network Sci. Eng. 5(2), 101–112 (2017a)
V. Vahidpour, A. Rastegarnia, A. Khalili, S. Sanei, Analysis of partial diffusion recursive least squares adaptation over noisy links. IET Signal Proc. 11(6), 749–757 (2017b)
V. Vahidpour, A. Rastegarnia, M. Latifi, A. Khalili, S. Sanei, Performance analysis of distributed Kalman filtering with partial diffusion over noisy network. IEEE Trans. Aerosp. Electron. Syst. 56, 1767 (2019b)
V. Vahidpour, A. Rastegarnia, A. Khalili, W.M. Bazzi, S. Sanei, Variants of partial update augmented clms algorithm and their performance analysis. IEEE Trans. Signal Process. 68, 3146–3157 (2020)
S. Werner, M.L. De Campos, P.S. Diniz, Partial-update NLMS algorithms with data-selective updating. IEEE Trans. Signal Process. 52(4), 938–949 (2004)
B. Xie, T. Bose, Partial update least-square adaptive filtering. Synth. Lect. Commun. 7(1), 1–115 (2014)
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Pourasad, Y., Vahidpour, V., Rastegarnia, A. et al. State Estimation in Linear Dynamical Systems By Partial Update Kalman Filtering. Circuits Syst Signal Process 41, 1188–1200 (2022). https://doi.org/10.1007/s00034-021-01815-5
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DOI: https://doi.org/10.1007/s00034-021-01815-5