scholarly journals Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Dongyan Chen ◽  
Yonglong Yu ◽  
Long Xu ◽  
Xiaohui Liu
Keyword(s):  
Kalman Filtering ◽  
Data Transmission ◽  
Stochastic Systems ◽  
Minimum Mean Square Error ◽  
Multiplicative Noises ◽  
Augmented System ◽  
Analysis Technique ◽  
State Augmentation ◽  
Innovation Analysis ◽  
Filtering Problem

This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method.

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.

scholarly journals An Ultra-Short Baseline Underwater Positioning System with Kalman Filtering

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 143
Author(s):  
Qinghua Luo ◽  
Xiaozhen Yan ◽  
Chunyu Ju ◽  
Yunsai Chen ◽  
Zhenhua Luo
Keyword(s):  
Phase Difference ◽  
Kalman Filtering ◽  
Negative Impact ◽  
Minimum Mean Square Error ◽  
Acoustic Signals ◽  
Positioning System ◽  
Short Baseline ◽  
Positioning Accuracy ◽  
Wrong Decision ◽  
Underwater Positioning

The ultra-short baseline underwater positioning is one of the most widely applied methods in underwater positioning and navigation due to its simplicity, efficiency, low cost, and accuracy. However, there exists environmental noise, which has negative impacts on the positioning accuracy during the ultra-short baseline (USBL) positioning process, which results in a large positioning error. The positioning result may lead to wrong decision-making in the latter processing. So, it is necessary to consider the error sources, and take effective measurements to minimize the negative impact of the noise. In our work, we propose a USBL positioning system with Kalman filtering to improve the positioning accuracy. In this system, we first explore a new kind of element array to accurately capture the acoustic signals from the object. We then organically combine the Kalman filters with the array elements to filter the acoustic signals, using the minimum mean-square error rule to obtain accurate acoustic signals. We got the high-precision phase difference information based on the non-equidistant quaternary original array and the phase difference acquisition mechanism. Finally, on account of the obtained accurate phase difference information and position calculation, we determined the coordinates of the underwater target. Comprehensive evaluation results demonstrate that our proposed USBL positioning method based on the Kalman filter algorithm can effectively enhance the positioning accuracy.

scholarly journals OPTIMAL FILTERING IN DISCRETE-TIME SYSTEMS WITH TIME DELAYS AND MARKOVIAN JUMP PARAMETERS

2009 ◽  
Vol 51 (2) ◽  
pp. 218-233 ◽  
Author(s):  
CHUNYAN HAN ◽  
HUANSHUI ZHANG
Keyword(s):  
Discrete Time ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
Markovian Jump ◽  
Free System ◽  
Markovian Jump Parameters ◽  
Markovian Jump Linear Systems ◽  
Measurement Delay ◽  
Innovation Analysis ◽  
Delayed Measurements

AbstractThis paper investigates the linear minimum mean-square error estimation for discrete-time Markovian jump linear systems with delayed measurements. The key technique applied for treating the measurement delay is reorganization innovation analysis, by which the state estimation with delayed measurements is transformed into a standard linear mean-square filter of an associated delay-free system. The optimal filter is derived based on the innovation analysis method together with geometric arguments in an appropriate Hilbert space. The solution is given in terms of two Riccati difference equations. Finally, a simulation example is presented to illustrate the efficiency of the proposed method.

scholarly journals Quadratic Filtering for Discrete-Time Systems with Measurement Delay and Packet Dropping

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ling Li ◽  
Lei Tan ◽  
Xinmin Song ◽  
Xuehua Yan
Keyword(s):  
Lyapunov Equation ◽  
Delay System ◽  
Free System ◽  
Augmented System ◽  
Multichannel Systems ◽  
Measurement Delay ◽  
Reorganized Innovation ◽  
Innovation Analysis ◽  
Remote Estimation ◽  
Time Systems

We consider the problem of remote estimation with time delay and multiplicative noise for multichannel systems. First, we apply the reorganized innovation analysis approach to construct the original delay system into a new delay-free system. Secondly, the delay-free system will be reconstructed by the quadratic filtering method to obtain an augmented system. Then, Kalman filtering theory and projection formula are used to solve two Riccati equations and one Lyapunov equation for the augmented system, and the quadratic filter for the measurement delay system on the packet loss network can be obtained. Finally, we use a numerical example to illustrate the effectiveness of the method.

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