Finite-time mean-square boundedness, H2, and H∞-properties of the discrete-time extended Kalman filter for systems with independent sensor failures

2017 ◽  
Author(s):  
Jennifer L. Bonniwell ◽  
Susan C. Schneider ◽  
Edwin E. Yaz
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Finite Time ◽  
Mean Square ◽  
Sensor Failures

SYNCHRONIZATION THROUGH FILTERING

2000 ◽  
Vol 10 (04) ◽  
pp. 763-775 ◽  
Author(s):  
C. CRUZ ◽  
H. NIJMEIJER
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Private Communication ◽  
Extended Kalman Filtering ◽  
Extensive Simulation ◽  
Synchronization Problem

We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an EKF that is driven by a noisy drive signal from a noisy transmitter dynamics. The convergence of the filter dynamics towards the transmitter dynamics is rigorously shown using recent results in extended Kalman filtering. Two extensive simulation examples show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to private communication is also given.

A novel cubature statistically linearized Kalman filter for fractional-order nonlinear discrete-time stochastic systems

2017 ◽  
Vol 24 (24) ◽  
pp. 5880-5897 ◽  
Author(s):  
Hamed Torabi ◽  
Naser Pariz ◽  
Ali Karimpour
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Fractional Order ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Taylor Series Expansion ◽  
The State ◽  
Nonlinear Functions ◽  
Measurement Models

In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.

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