Kalman filtering for state delay systems with multiplicative noises and random one-step sensor delay

2014 ◽  
Author(s):  
Long Xu ◽  
Jun Hu ◽  
Dongyan Chen
Keyword(s):  
Kalman Filtering ◽  
Delay Systems ◽  
State Delay ◽  
Multiplicative Noises ◽  
One Step

Robust Kalman filtering for discrete state-delay systems

2000 ◽  
Vol 147 (6) ◽  
pp. 613-618 ◽  
Author(s):  
M.S. Mahmoud ◽  
L. Xie ◽  
Y.C. Soh
Keyword(s):  
Kalman Filtering ◽  
Delay Systems ◽  
State Delay ◽  
Discrete State

scholarly journals Optimal Kalman Filtering for a Class of State Delay Systems with Randomly Multiple Sensor Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dongyan Chen ◽  
Long Xu
Keyword(s):  
Kalman Filtering ◽  
Stochastic Systems ◽  
Random Variable ◽  
Delay Systems ◽  
State Delay ◽  
Discrete State ◽  
Measurement Delay ◽  
Multiple Sensor ◽  
Recursive Matrix ◽  
Filtering Problem

The optimal Kalman filtering problem is investigated for a class of discrete state delay stochastic systems with randomly multiple sensor delays. The phenomenon of measurement delay occurs in a random way and the delay rate for each sensor is described by a Bernoulli distributed random variable with known conditional probability. Based on the innovative analysis approach and recursive projection formula, a new linear optimal filter is designed such that, for the state delay and randomly multiple sensor delays with different delay rates, the filtering error is minimized in the sense of mean square and the filter gain is designed by solving the recursive matrix equation. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed filtering scheme.

scholarly journals Optimal Linear Estimators for Time-Delay Systems with Fading Measurements and Correlated Noises

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yazhou Li ◽  
Jiayi Li ◽  
Xin Wang
Keyword(s):  
Time Delay ◽  
Minimum Variance ◽  
Delay Systems ◽  
Multiplicative Noises ◽  
Linear Estimators ◽  
Discrete Linear Systems ◽  
Estimation Problems ◽  
Optimal Linear ◽  
State Augmentation ◽  
Correlated Noises

The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.

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