Discrete‐time invariant extended Kalman filter on matrix Lie groups

2020 ◽  
Vol 30 (12) ◽  
pp. 4449-4462
Author(s):  
Karmvir Singh Phogat ◽  
Dong Eui Chang
Keyword(s):  
Kalman Filter ◽  
Lie Groups ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Time Invariant

Estimation of Steady-State Optimal Filter Gain From Nonoptimal Kalman Filter Residuals

1994 ◽  
Vol 116 (3) ◽  
pp. 550-553 ◽  
Author(s):  
Chung-Wen Chen ◽  
Jen-Kuang Huang
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Finite Number ◽  
Discrete Time ◽  
Stochastic System ◽  
Moving Average ◽  
Ar Model ◽  
Numerical Example ◽  
Measurement Noises ◽  
Time Invariant

This paper proposes a new algorithm to estimate the optimal steady-state Kalman filter gain of a linear, discrete-time, time-invariant stochastic system from nonoptimal Kalman filter residuals. The system matrices are known, but the covariances of the white process and measurement noises are unknown. The algorithm first derives a moving average (MA) model which relates the optimal and nonoptimal residuals. The MA model is then approximated by inverting a long autoregressive (AR) model. From the MA parameters the Kalman filter gain is calculated. The estimated gain in general is suboptimal due to the approximations involved in the method and a finite number of data. However, the numerical example shows that the estimated gain could be near optimal.

Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise

2008 ◽  
Vol 22 (6) ◽  
pp. 1132-1139 ◽  
Author(s):  
Jin Zhu ◽  
Junhong Park ◽  
Kwan-Soo Lee ◽  
Maksym Spiryagin
Keyword(s):  
Kalman Filter ◽  
Nonlinear System ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Markovian Jump

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.

Inverse optimal controller based on extended Kalman filter for discrete-time nonlinear systems

2017 ◽  
Vol 39 (1) ◽  
pp. 19-34 ◽  
Author(s):  
Moayed Almobaied ◽  
Ibrahim Eksin ◽  
Mujde Guzelkaya
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Optimal Controller
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