Tobit Kalman filter with fading measurements

Abstract This paper is concerned with the Tobit Kalman filtering problem for a class of discrete time-varying systems with both censored and fading measurements. The censored measurements are described by the Tobit measurement model and the fading measurements are characterized by the L th-order Rice fading channel model capable of accounting for not only the packet dropout but also the communication phenomenon. The measurement fading occurs in a random way where the fading probabilities are regulated by a set of mutually independent Gaussian random variables. By resorting to the state augmentation technique and the orthogonality projection principle, the Tobit Kalman filter (TKF) is designed in the presence of fading measurements. In the course of filter design, several state-augmentation-induced terms are introduced, all of which can be calculated recursively or off-line. A numerical example concerning the estimation of ballistic roll rates is provided to illustrate the usefulness of the proposed filter.

[1]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[2]  Zidong Wang,et al.  $H_\infty$ Fuzzy Control With Randomly Occurring Infinite Distributed Delays and Channel Fadings , 2014, IEEE Transactions on Fuzzy Systems.

[3]  Tao Wang,et al.  Method to improve convergence performance of iterative learning control systems over wireless networks in presence of channel noise , 2014 .

[4]  Michael J. Piovoso,et al.  Estimation of mobile vehicle range & position using the tobit Kalman filter , 2014, 53rd IEEE Conference on Decision and Control.

[5]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Quan Pan,et al.  Joint estimation of target state and ionospheric height bias in over-the-horizon radar target tracking , 2016 .

[7]  Nan Xiao,et al.  Feedback Stabilization of Discrete-Time Networked Systems Over Fading Channels , 2012, IEEE Transactions on Automatic Control.

[8]  Shu-Li Sun,et al.  H∞ filtering for multiple channel systems with varying delays, consecutive packet losses and randomly occurred nonlinearities , 2014, Signal Process..

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

[10]  Zidong Wang,et al.  Envelope-constrained H∞ filtering with fading measurements and randomly occurring nonlinearities: The finite horizon case , 2015, Autom..

[11]  Yan Liang,et al.  Linear-minimum-mean-square-error observer for multi-rate sensor fusion with missing measurements , 2014 .

[12]  Hamid Reza Karimi,et al.  Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays , 2014, Signal Process..

[13]  Fei Ren,et al.  A Novel Emulator for Discrete-Time MIMO Triply Selective Fading Channels , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  P.J. Zufiria,et al.  A Kalman filter with censored data , 2005, IEEE International Workshop on Intelligent Signal Processing, 2005..

[15]  Raquel Caballero-Águila,et al.  Fusion estimation using measured outputs with random parameter matrices subject to random delays and packet dropouts , 2016, Signal Process..

[16]  Mark Ilg,et al.  Ballistic Roll Estimation using EKF Frequency Tracking and Adaptive Noise Cancellation , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[17]  Michael J. Piovoso,et al.  Nonlinear estimators for censored data: A comparison of the EKF, the UKF and the Tobit Kalman filter , 2015, 2015 American Control Conference (ACC).

[18]  James Lam,et al.  Finite-Horizon ${\cal H}_{\infty}$ Control for Discrete Time-Varying Systems With Randomly Occurring Nonlinearities and Fading Measurements , 2015, IEEE Transactions on Automatic Control.

[19]  John B. Hampshire,et al.  Tobit maximum-likelihood estimation for stochastic time series affected by receiver saturation , 1992, IEEE Trans. Inf. Theory.

[20]  Shlomo Shamai,et al.  Fading Channels: Information-Theoretic and Communication Aspects , 1998, IEEE Trans. Inf. Theory.

[21]  Fuad E. Alsaadi,et al.  Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays , 2016, Neurocomputing.

[22]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

[23]  J. Tobin.  Estimation of Relationships for Limited Dependent Variables , 1958 .

[24]  Yurong Liu,et al.  Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects , 2016, Neurocomputing.

[25]  Michael V. Basin,et al.  Mean-square H∞ filtering for stochastic systems: Application to a 2DOF helicopter , 2012, Signal Process..

[26]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[27]  Yuanqing Xia,et al.  UKF-based nonlinear filtering over sensor networks with wireless fading channel , 2015, Inf. Sci..

[28]  Gongjian Zhou,et al.  Constant turn model for statically fused converted measurement Kalman filters , 2015, Signal Process..

[29]  Michael J. Piovoso,et al.  Estimation of saturated data using the Tobit Kalman filter , 2014, 2014 American Control Conference.

[30]  Guisong Yang,et al.  Distributed H∞ filtering for a class of sensor networks with uncertain rates of packet losses , 2014, Signal Process..

[31]  Zidong Wang,et al.  Fuzzy Filtering With Randomly Occurring Parameter Uncertainties, Interval Delays, and Channel Fadings , 2014, IEEE Transactions on Cybernetics.

[32]  Douglas L. Jones,et al.  Decentralized Detection With Censoring Sensors , 2008, IEEE Transactions on Signal Processing.

[33]  Andrea J. Goldsmith,et al.  LQG Control for MIMO Systems Over Multiple Erasure Channels With Perfect Acknowledgment , 2012, IEEE Transactions on Automatic Control.

[34]  Junping Du,et al.  Tobit Kalman filter with time-correlated multiplicative measurement noise , 2017 .

[35]  I. James,et al.  Linear regression with censored data , 1979 .

[36]  Richard T. Carson,et al.  The Tobit Model With a Non-Zero Threshold , 2005 .

[37]  Nicola Elia,et al.  Remote stabilization over fading channels , 2005, Syst. Control. Lett..

[38]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[39]  Farrokh Janabi-Sharifi,et al.  A Robust Vision-Based Sensor Fusion Approach for Real-Time Pose Estimation , 2014, IEEE Transactions on Cybernetics.

[40]  Y. Bar-Shalom,et al.  Censoring sensors: a low-communication-rate scheme for distributed detection , 1996, IEEE Transactions on Aerospace and Electronic Systems.

[41]  Bruce F. Cockburn,et al.  Modeling and Hardware Implementation Aspects of Fading Channel Simulators , 2008, IEEE Transactions on Vehicular Technology.

[42]  Michael J. Piovoso,et al.  The Tobit Kalman Filter: An Estimator for Censored Measurements , 2016, IEEE Transactions on Control Systems Technology.

[43]  Richard M. Murray,et al.  To Drop or Not to Drop: Design Principles for Kalman Filtering Over Wireless Fading Channels , 2009, IEEE Transactions on Automatic Control.

[44]  Konrad Reif,et al.  Stochastic Stability of the Extended Kalman Filter With Intermittent Observations , 2010, IEEE Transactions on Automatic Control.

[45]  Takeshi Amemiya,et al.  Regression Analysis when the Dependent Variable is Truncated Normal , 1973 .

[46]  Peng Shi,et al.  Event-triggered fuzzy filtering for a class of nonlinear networked control systems , 2015, Signal Process..

[47]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[48]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[49]  Huijun Gao,et al.  On H-infinity Estimation of Randomly Occurring Faults for A Class of Nonlinear Time-Varying Systems With Fading Channels , 2016, IEEE Transactions on Automatic Control.