scholarly journals A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems

Automatica ◽  
2016 ◽  
Vol 63 ◽  
pp. 321-329 ◽  
Author(s):  
Sze Zheng Yong ◽  
Minghui Zhu ◽  
Emilio Frazzoli
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Simultaneous Input

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.

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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