Robust extended Kalman filtering for nonlinear stochastic systems with random sensor delays, packet dropouts and correlated noises

Abstract In this paper, the robust filtering problem is investigated for nonlinear stochastic systems with random sensor delays, packet dropouts and correlated noises. The stochastic multiplicative noises which enter into both state equation and measurement equation are modeled as random variables with bounded variance, and a Bernoulli distributed random sequence is introduced to describe the random delays and packet dropouts. Then, the system is converted to the stochastic parameterized one through introducing a group of new variables. Moreover, the two-step prediction framework is employed to achieve the goal of noise decoupling. The objective of the addressed estimation problem is to design a filter, such that in the presence of random delays, packet dropouts, multiplicative noises and correlated noises, the upper bounds for the prediction error and estimation error covariance can be guaranteed. Subsequently, the upper bounds are minimized by designing the optimal prediction gain and filter gain. Finally, the attitude estimation example is used to demonstrate the effectiveness of the proposed robust extended Kalman filter.

[1]  Jun Hu,et al.  Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements , 2012, Autom..

[2]  Mehrzad Namvar,et al.  Global attitude estimation using single delayed vector measurement and biased gyro , 2017, Autom..

[3]  Aurora Hermoso-Carazo,et al.  Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems , 2009 .

[4]  Myo-Taeg Lim,et al.  Unbiased Finite-Memory Digital Phase-Locked Loop , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Huijun Gao,et al.  Finite-Horizon $H_{\infty} $ Filtering With Missing Measurements and Quantization Effects , 2013, IEEE Transactions on Automatic Control.

[6]  Yuxin Zhao,et al.  Receding-Horizon $l_{2}{-}l_{\infty}$ FIR Filter With Embedded Deadbeat Property , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Robert E. Mahony,et al.  Recursive attitude estimation in the presence of multi-rate and multi-delay vector measurements , 2015, 2015 American Control Conference (ACC).

[8]  Peng Shi,et al.  Deadbeat Dissipative FIR Filtering , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Jun Hu,et al.  Gain-Constrained Recursive Filtering With Stochastic Nonlinearities and Probabilistic Sensor Delays , 2013, IEEE Transactions on Signal Processing.

[10]  Jun Hu,et al.  Recursive filtering with random parameter matrices, multiple fading measurements and correlated noises , 2013, Autom..

[11]  Huajing Fang,et al.  Minimum variance estimation for linear uncertain systems with one-step correlated noises and incomplete measurements , 2016, Digit. Signal Process..

[12]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[13]  Vladimir Stojanovic,et al.  Robust identification of OE model with constrained output using optimal input design , 2016, J. Frankl. Inst..

[14]  Raquel Caballero-Águila,et al.  Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements , 2015, Int. J. Gen. Syst..

[15]  Mehrzad Namvar,et al.  Delay compensation in global estimation of rigid-body attitude under biased velocity measurement , 2014, 53rd IEEE Conference on Decision and Control.

[16]  Reza Mahboobi Esfanjani,et al.  Improved robust finite-horizon Kalman filtering for uncertain networked time-varying systems , 2015, Inf. Sci..

[17]  X. Kai,et al.  Robust extended Kalman filtering for nonlinear systems with multiplicative noises , 2011 .

[18]  Myo-Taeg Lim,et al.  Switching Extensible FIR Filter Bank for Adaptive Horizon State Estimation With Application , 2016, IEEE Transactions on Control Systems Technology.

[19]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[20]  Myo Taeg Lim,et al.  A novel particle filter-based digital phase-locked loop robust against quantization error , 2017 .

[21]  Xiangning He,et al.  Power Conversion and Signal Transmission Integration Method Based on Dual Modulation of DC–DC Converters , 2015, IEEE Transactions on Industrial Electronics.

[22]  Quan Pan,et al.  A Gaussian approximation recursive filter for nonlinear systems with correlated noises , 2012, Autom..

[23]  Yuri B. Shtessel,et al.  Blood glucose regulation using higher‐order sliding mode control , 2008 .

[24]  Jing Ma,et al.  Optimal linear estimation for systems with multiplicative noise uncertainties and multiple packet dropouts , 2012, IET Signal Process..

[25]  Quan Pan,et al.  Gaussian filter for nonlinear systems with one-step randomly delayed measurements , 2013, Autom..

[26]  Peng Shi,et al.  Control of Nonlinear Networked Systems With Packet Dropouts: Interval Type-2 Fuzzy Model-Based Approach , 2015, IEEE Transactions on Cybernetics.

[27]  Aurora Hermoso-Carazo,et al.  Extended and unscented filtering algorithms using one-step randomly delayed observations , 2007, Appl. Math. Comput..

[28]  Zhenbao Liu,et al.  Square-root quaternion cubature Kalman filtering for spacecraft attitude estimation , 2012 .

[29]  Edwin Engin Yaz,et al.  Minimum variance generalized state estimators for multiple sensors with different delay rates , 2007, Signal Process..

[30]  Vladimir Stojanovic,et al.  Joint state and parameter robust estimation of stochastic nonlinear systems , 2016 .

[31]  Jun Hu,et al.  Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements , 2010, Signal Process..

[32]  Huajing Fang,et al.  Recursive estimation for nonlinear stochastic systems with multi-step transmission delays, multiple packet dropouts and correlated noises , 2015, Signal Process..

[33]  Ming Zeng,et al.  Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises , 2013, Inf. Fusion.

[34]  Huanshui Zhang,et al.  Linear optimal filtering for discrete-time systems with random jump delays , 2009, Signal Process..

[35]  Xiao Lu,et al.  Robust Kalman Filtering for Discrete-Time Systems With Measurement Delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[36]  Kamesh Subbarao,et al.  Adaptive Output Feedback Control for Spacecraft Rendezvous and Docking Under Measurement Uncertainty , 2006 .

[37]  Shu-Li Sun,et al.  Optimal Linear Filters for Discrete-Time Systems With Randomly Delayed and Lost Measurements With/Without Time Stamps , 2013, IEEE Transactions on Automatic Control.

[38]  Daniele Mortari,et al.  Norm-Constrained Kalman Filtering , 2009 .

[39]  Peng Shi,et al.  Two-Dimensional Dissipative Control and Filtering for Roesser Model , 2015, IEEE Transactions on Automatic Control.

[40]  Yeng Chai Soh,et al.  Adaptive Kalman Filtering in Networked Systems With Random Sensor Delays, Multiple Packet Dropouts and Missing Measurements , 2010, IEEE Transactions on Signal Processing.

[41]  Jing Ma,et al.  Linear estimation for networked control systems with random transmission delays and packet dropouts , 2014, Inf. Sci..

[42]  Qian Huaming,et al.  Robust extended Kalman filter for attitude estimation with multiplicative noises and unknown external disturbances , 2014 .

[43]  F. Markley.  Attitude Error Representations for Kalman Filtering , 2003 .

[44]  Raquel Caballero-Águila,et al.  Covariance-based estimation algorithms in networked systems with mixed uncertainties in the observations , 2014, Signal Process..

[45]  Sirish L. Shah,et al.  Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations , 2007, Int. J. Control.

[46]  Yunmin Zhu,et al.  Optimal Kalman filtering fusion with cross-correlated sensor noises , 2007, Autom..

[47]  Soon-Jo Chung,et al.  Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach , 2008, 0803.0170.