Polynomial extended kalman filtering for discrete-time nonlinear stochastic systems

2004 ◽  
Author(s):  
A. Germani ◽  
C. Manes ◽  
P. Palumbo
Keyword(s):  
Discrete Time ◽  
Kalman Filtering ◽  
Stochastic Systems ◽  
Extended Kalman Filtering ◽  
Nonlinear Stochastic Systems

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.

Fixed-Interval Kalman Smoother for Non-Square Descriptor Systems with Correlated Noise

2012 ◽  
Vol 433-440 ◽  
pp. 3601-3607
Author(s):  
Hang Wei Tian ◽  
Ying Shi
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Stochastic Systems ◽  
Fixed Interval ◽  
Descriptor Systems ◽  
Correlated Noise ◽  
Filtering Theory ◽  
Numerical Examples ◽  
Kalman Smoother

Based on the classical Kalman filtering theory, the state estimation problem is considered for non-square descriptor discrete time stochastic systems. Under Assumptions 1~3, a fixed-Interval Kalman smoother for non-square descriptor systems with correlated noise is given. Some numerical examples illustrate the effectiveness of the proposed algorithm.

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