2610005499
  • Open Access
  • Article

Receding Horizon Team Optimal Decentralized Filter for Discrete Multi-agent Systems with Delay

  • Xinrui Li 1,   
  • Junzhe Liu 1,   
  • Xiaohua Liu 2,   
  • Hongxia Guo 1 and 
  • Rong Gao 1,*

Received: 01 April 2026 | Revised: 18 June 2026 | Accepted: 15 October 2026 | Published: 26 October 2026

Abstract

We investigate the receding horizon team-optimal decentralized filter for discrete-time multi-agent systems subject to delayed information sharing. By minimizing the team estimation error covariance over a finite horizon under unbiasedness constraints, both batch and recursive implementations of the RHTODF are derived. It is shown that the resulting estimator admits a decomposed structure consisting of a common-information component and local innovation-based correction terms, which enables distributed implementation under delayed communication constraints. Numerical simulations demonstrate that the proposed RHTODF achieves improved estimation accuracy and smaller estimation error than the local Kalman filter, thereby illustrating the effectiveness of the proposed finite-horizon team-optimal filtering framework.

References 

  • 1.

    He, Y.; Wang, Q.G.; Wu, M.; et al. Delay-Dependent State Estimation for Delayed Neural Networks. IEEE Trans. Neural Netw. 2006, 17, 1077–1081. https://doi.org/10.1109/tnn.2006.875969.

  • 2.

    Weng, Z.; Djuric, P.M. Efficient Estimation of Linear Parameters from Correlated Node Measurements over Networks. IEEE Signal Process. Lett. 2014, 21, 1408–1412. https://doi.org/10.1109/LSP.2014.2334495.

  • 3.

    Alessandri, A.; Awawdeh, M. Moving-Horizon Estimation with Guaranteed Robustness for Discrete-Time Linear Systems and Measurements Subject to Outliers. Automatica 2016, 67, 85–93. https://doi.org/10.1016/j.automatica.2016.01.015.

  • 4.

    Farina, M.; Ferrari-Trecate, G.; Scattolini, R. Moving-Horizon Partition-Based State Estimation of Large-Scale Systems. Automatica 2010, 46, 910–918. https://doi.org/10.1016/j.automatica.2010.02.010.

  • 5.

    Zou, L.; Wang, Z.; Hu, J.; et al. Moving Horizon Estimation with Unknown Inputs under Dynamic Quantization Effects. IEEE Trans. Autom. Control. 2020, 65, 5368–5375. https://doi.org/10.1109/tac.2020.2968975.

  • 6.

    Zou, L.; Wang, Z.; Han, Q.L.; et al. Moving Horizon Estimation for Networked Time-Delay Systems under Round-Robin Protocol. IEEE Trans. Autom. Control. 2019, 64, 5191–5198. https://doi.org/10.1109/tac.2019.2910167.

  • 7.

    Caballero-Águila, R.; Frías-Bustamante, M.P.; Oya-Lechuga, A. Least-Squares Linear Estimation for Multirate Uncertain Systems Subject to DoS Attacks. Int. J. Netw. Dyn. Intell. 2025, 4, 100014. https://doi.org/10.53941/ijndi.2025.100014.

  • 8.

    Hu, Y.; Zhang, C.; Liu, S. Privacy-Preserving Distributed Recursive Filtering for State-Saturated Systems with Quantization Effects. Int. J. Netw. Dyn. Intell. 2025, 4, 100012. https://doi.org/10.53941/ijndi.2025.100012.

  • 9.

    Kalman, R.E. A New Approach to Linear Filtering and Prediction Problems. J. Basic Eng. 1960, 82, 35–45. https://doi.org/10.1115/1.3662552.

  • 10.

    Diwadkar, A.; Vaidya, U. Synchronization in Large-Scale Nonlinear Network Systems with Uncertain Links. Automatica 2019, 100, 194–199. https://doi.org/10.1016/j.automatica.2018.06.002.

  • 11.

    Bucy, R.S.; Joseph, P.D. Filtering for Stochastic Processes with Applications to Guidance; Interscience: New York, NY, USA, 1970.

  • 12.

    Jazwinski, A. Limited Memory Optimal Filtering. IEEE Trans. Autom. Control. 1968, 13, 558–563. https://doi.org/10.1109/tac.1968.1098981.

  • 13.

    Fagiano, L.; Novara, C. A Combined Moving Horizon and Direct Virtual Sensor Approach for Constrained Nonlinear Estimation. Automatica 2013, 49, 193–199. https://doi.org/10.1016/j.automatica.2012.09.009.

  • 14.

    Pearson, R.K. Outliers in Process Modeling and Identification. IEEE Trans. Control. Syst. Technol. 2002, 10, 55–63. https://doi.org/10.1109/87.974338.

  • 15.

    Sandell, N.; Varaiya, P.; Athans, M.; et al. Survey of Decentralized Control Methods for Large Scale Systems. IEEE Trans. Autom. Control. 1978, 23, 108–128. https://doi.org/10.1109/tac.1978.1101704.

  • 16.

    Vadigepalli, R.; Doyle, F.J. A Distributed State Estimation and Control Algorithm for Plantwide Processes. IEEE Trans. Control. Syst. Technol. 2003, 11, 119–127. https://doi.org/10.1109/tcst.2002.806462.

  • 17.

    Bruckstein, A.; Kailath, T. Recursive Limited Memory Filtering and Scattering Theory (Corresp.). IEEE Trans. Inf. Theory 1985, 31, 440–443. https://doi.org/10.1109/tit.1985.1057031.

  • 18.

    Kwon, W.H.; Lee, K.S.; Kwon, O.K. Optimal FIR Filters for Time-Varying State-Space Models. IEEE Trans. Aerosp. Electron. Syst. 1990, 26, 1011–1021. https://doi.org/10.1109/7.62253.

  • 19.

    Kwon, W.H.; Kim, P.S.; Han, S.H. A Receding Horizon Unbiased FIR Filter for Discrete-Time State Space Models. Automatica 2002, 38, 545–551. https://doi.org/10.1016/s0005-1098(01)00242-4.

  • 20.

    Alessandri, A.; Baglietto, M.; Battistelli, G. Receding-Horizon Estimation for Discrete-Time Linear Systems. IEEE Trans. Autom. Control. 2003, 48, 473–478. https://doi.org/10.1109/TAC.2003.809155.

  • 21.

    Saif, M.; Guan, Y. Decentralized State Estimation in Large-Scale Interconnected Dynamical Systems. Automatica 1992, 28, 215–219. https://doi.org/10.1016/0005-1098(92)90024-a.

  • 22.

    Siljak, D.D.; Vukcevic, M. Decentralization, Stabilization, and Estimation of Large-Scale Linear Systems. IEEE Trans. Autom. Control. 1976, 21, 363–366. https://doi.org/10.1109/tac.1976.1101235.

  • 23.

    Liu, H.; Yu, H. Decentralized State Estimation for a Large-Scale Spatially Interconnected System. ISA Trans. 2018, 74, 67–76. https://doi.org/10.1016/j.isatra.2018.01.007.

  • 24.

    Venkategowda, N.K.D.; Narayana, B.B.; Jagannatham, A.K. Precoding for Robust Decentralized Estimation in Coherent-MAC-Based Wireless Sensor Networks. IEEE Signal Process. Lett. 2017, 24, 240–244. https://doi.org/10.1109/lsp.2017.2647984.

  • 25.

    Li, W.; Jia, Y.; Du, J. Distributed Kalman Consensus Filter with Intermittent Observations. J. Frankl. Inst. 2015, 352, 3764–3781. https://doi.org/10.1016/j.jfranklin.2015.01.002.

  • 26.

    Olfati-Saber, R. Kalman-Consensus Filter : Optimality, Stability, and Performance. In Proceedings of the 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC), Shanghai, China, 15–18 December 2009; pp. 7036–7042. https://doi.org/10.1109/cdc.2009.5399678.

  • 27.

    Cattivelli, F.S.; Sayed, A.H. Diffusion Strategies for Distributed Kalman Filtering and Smoothing. IEEE Trans. Autom. Control. 2010, 55, 2069–2084. https://doi.org/10.1109/tac.2010.2042987.

  • 28.

    Song, E.; Xu, J.; Zhu, Y. Optimal Distributed Kalman Filtering Fusion with Singular Covariances of Filtering Errors and Measurement Noises. IEEE Trans. Autom. Control. 2014, 59, 1271–1282. https://doi.org/10.1109/tac.2014.2308451.

  • 29.

    Venkategowda, N.K.D.; Jagannatham, A.K. Optimal Minimum Variance Distortionless Precoding (MVDP) for Decentralized Estimation in MIMO Wireless Sensor Networks. IEEE Signal Process. Lett. 2015, 22, 696–700. https://doi.org/10.1109/lsp.2014.2368253.

  • 30.

    Zhou, J.; Gu, G.; Chen, X. Distributed Kalman Filtering over Wireless Sensor Networks in the Presence of Data Packet Drops. IEEE Trans. Autom. Control. 2019, 64, 1603–1610. https://doi.org/10.1109/tac.2018.2854644.

  • 31.

    Qian, J.; Duan, P.; Duan, Z.; et al. Event-Triggered Distributed State Estimation: A Conditional Expectation Method. IEEE Trans. Autom. Control. 2023, 68, 6361–6368. https://doi.org/10.1109/tac.2023.3234453.

  • 32.

    Ma, Y.; Ma, Z.; Li, Y.; et al. Event-Triggered Distributed Cubature Kalman Filtering Algorithm with Stealthy Attacks over Sensor Networks. IEEE Trans. Signal Inf. Process. over Netw. 2025, 11, 124–135. https://doi.org/10.1109/tsipn.2025.3525977.

  • 33.

    Lyu, X.; Wen, G.; Shi, L.; et al. Performance Analysis of Distributed Filtering under Misspecified Noise Covariances. IEEE Trans. Autom. Control. 2025, 70, 6735–6750. https://doi.org/10.1109/tac.2025.3565956.

  • 34.

    Afshari, M.; Mahajan, A. Team Optimal Decentralized State Estimation. In Proceedings of the 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, 17–19 December 2018; pp. 5044–5050. https://doi.org/10.1109/cdc.2018.8619493.

  • 35.

    Afshari, M.; Mahajan, A. Multi-Agent Estimation and Filtering for Minimizing Team Mean-Squared Error. IEEE Trans. Signal Process. 2021, 69, 5206–5221. https://doi.org/10.1109/tsp.2021.3104981.

  • 36.

    Sayin, M.O.; Kozat, S.S.; Başar, T. Team-Optimal Distributed MMSE Estimation in General and Tree Networks. Digit. Signal Process. 2017, 64, 83–95. https://doi.org/10.1016/j.dsp.2017.02.007.

  • 37.

    Battistelli, G. Distributed Moving-Horizon Estimation with Arrival-Cost Consensus. IEEE Trans. Autom. Control. 2019, 64, 3316–3323. https://doi.org/10.1109/tac.2018.2879598.

  • 38.

    Farina, M.; Ferrari-Trecate, G.; Scattolini, R. Distributed Moving Horizon Estimation for Linear Constrained Systems. IEEE Trans. Autom. Control. 2010, 55, 2462–2475. https://doi.org/10.1109/tac.2010.2046058.

  • 39.

    Yu, D.; Xia, Y.; Zhai, D.H. Distributed Moving-Horizon Estimation with Event-Triggered Communication over Sensor Networks. IEEE Trans. Autom. Control. 2023, 68, 7982–7988. https://doi.org/10.1109/tac.2023.3255201.

Share this article:
How to Cite
Li, X.; Liu, J.; Liu, X.; Guo, H.; Gao, R. Receding Horizon Team Optimal Decentralized Filter for Discrete Multi-agent Systems with Delay. International Journal of Network Dynamics and Intelligence 2026, 5 (3), 22. https://doi.org/10.53941/ijndi.2026.100022.
RIS
BibTex
Copyright & License
article copyright Image
Copyright (c) 2026 by the authors.
Article Metrics
41
Article Views
0
Citations