Least-Squares Linear Estimation for Multirate Uncertain Systems subject to DoS Attacks

Abstract

This paper investigates the least-squares linear estimation problem for multirate systems with stochastic parameter matrices, under the influence of random denial-of-service (DoS) attacks. These attacks can severely impair the performance of estimation algorithms by causing intermittent loss of measurement data. To counteract the adverse effect of DoS attacks, two compensation strategies-hold-input and prediction compensation- are used. For each of these strategies, specific recursive filtering and smoothing algorithms are designed. A key advantage of the proposed methodology is its ability to operate without requiring a detailed signal evolution model, relying only on the mean and covariance functions of the involved processes. The effectiveness of the proposed approaches is validated through numerical simulations, which highlight how common network-induced phenomena, such as missing observations, can be incorporated into the framework of systems with random parameter matrices and, additionally, they provide insights into estimation performance under different attack probabilities.

Keywords

multirate systems / least-squares estimation / random parameter matrices / DoS attacks / compensation strategies / hold-input / prediction compensation

References

[1] Liu Q.Y.; Wang Z.D.; He X. Stochastic Control and Filtering over Constrained Communication Networks; Springer: Cham, 2019. doi: 10.1007/978-3-030-00157-5.

[2] Liu W.; Xie X.P.; Qian W.; et al. Optimal linear filtering for networked control systems with random matrices, correlated noises, and packet dropouts. IEEE Access, 2020, 8: 59987-59997. doi: 10.1109/ACCESS.2020.2983122

[3] Hu J.; Jia C.Q.; Liu H.J.; et al. A survey on state estimation of complex dynamical networks. Int. J. Syst. Sci., 2021, 52: 3351-3367. doi: 10.1080/00207721.2021.1995528

[4] Caballero-Águila R.; Linares-Pérez J. Distributed fusion filtering for uncertain systems with coupled noises, random delays and packet loss prediction compensation. Int. J. Syst. Sci., 2023, 54: 371-390. doi: 10.1080/00207721.2022.2122905

[5] Wang Y.; Liu H.J.; Tan H.L. An overview of filtering for sampled-data systems under communication constraints. Int. J. Netw. Dyn. Intell., 2023, 2: 100011. doi: 10.53941/ijndi.2023.100011

[6] Sun S.L. Distributed optimal linear fusion predictors and filters for systems with random parameter matrices and correlated noises. IEEE Trans. Signal Process., 2020, 68: 1064-1074. doi: 10.1109/TSP.2020.2967180

[7] Caballero-Águila R.; Hermoso-Carazo A.; Linares-Pérez J. Networked fusion estimation with multiple uncertainties and time-correlated channel noise. Inf. Fusion, 2020, 54: 161-171. doi: 10.1016/j.inffus.2019.07.008

[8] Caballero-Águila R.; Linares-Pérez J. Centralized fusion estimation in networked systems: Addressing deception attacks and packet dropouts with a zero-order hold approach. Int. J. Netw. Dyn. Intell., 2024, 3: 100021. doi: 10.53941/ijndi.2024.100021

[9] Shen Y.X.; Wang Z.D.; Shen B.; et al. Outlier-resistant recursive filtering for multisensor multirate networked systems under weighted try-once-discard protocol. IEEE Trans. Cybern., 2021, 51: 4897-4908. doi: 10.1109/TCYB.2020.3021194

[10] Shen Y.X.; Wang Z.D.; Dong H.; et al. Multi-sensor multi-rate fusion estimation for networked systems: Advances and perspectives. Inf. Fusion, 2022, 82: 19-27. doi: 10.1016/j.inffus.2021.12.005

[11] Gao R.; Yang G.H. Distributed multi-rate sampled-data $H_{\infty}$ consensus filtering for cyber-physical systems under denial-of-service attacks. Inf. Sci., 2022, 587: 607-625. doi: 10.1016/j.ins.2021.12.046

[12] Shen Y.Q.; Sun S.L. Distributed recursive filtering for multi-rate uniform sampling systems with packet losses in sensor networks. Int. J. Syst. Sci., 2023, 54: 1729-1745. doi: 10.1080/00207721.2023.2209887

[13] Sánchez H.S.; Rotondo D.; Escobet T.; et al. Bibliographical review on cyber attacks from a control oriented perspective. Annu. Rev. Control, 2019, 48: 103-128. doi: 10.1016/j.arcontrol.2019.08.002

[14] Chen B.; Ho D.W.C.; Zhang W.A.; et al. Distributed dimensionality reduction fusion estimation for cyber-physical systems under DoS attacks. IEEE Trans. Syst., Man, Cybern.: Syst., 2019, 49: 455-468. doi: 10.1109/TSMC.2017.2697450

[15] Yang Y.; Li Y.F.; Yue D.; et al. Distributed secure consensus control with event-triggering for multiagent systems under DoS attacks. IEEE Trans. Cybern., 2021, 51: 2916-2928. doi: 10.1109/TCYB.2020.2979342

[16] Gu Z.; Ahn C.K.; Yue D.; et al. Event-triggered $H_{\infty}$ filtering for T-S fuzzy-model-based nonlinear networked systems with multisensors against DoS attacks. IEEE Trans. Cybern., 2022, 52: 5311-5321. doi: 10.1109/TCYB.2020.3030028

[17] Geng H.; Wang Z.D.; Hu J.; et al. Outlier-resistant sequential filtering fusion for cyber-physical systems with quantized measurements under denial-of-service attacks. Inf. Sci., 2023, 628: 488-503. doi: 10.1016/j.ins.2023.01.142

[18] Zhang L.; Sun S.L. Distributed $H_{\infty}$ fusion filtering for multi-sensor networked systems with DoS attacks and sensor saturations. Digit. Signal Process., 2023, 134: 103908. doi: 10.1016/j.dsp.2023.103908

[19] Zha L.; Guo Y.P.; Liu J.L.; et al. Protocol-based distributed security fusion estimation for time-varying uncertain systems over sensor networks: Tackling DoS attacks. IEEE Trans. Signal Inf. Proc. Netw., 2024, 10: 119-130. doi: 10.1109/TSIPN.2024.3356789

[20] Ma J.; Sun S.L. Optimal linear recursive estimators for stochastic uncertain systems with time-correlated additive noises and packet dropout compensations. Signal Process., 2020, 176: 107704. doi: 10.1016/j.sigpro.2020.107704

[21] Lin H.L.; Sun S.L. Estimator for multirate sampling systems with multiple random measurement time delays. IEEE Trans. Automat. Contr., 2022, 67: 1589-1596. doi: 10.1109/TAC.2021.3070299