scholarly journals Optimal Fusion Filtering in Multisensor Stochastic Systems with Missing Measurements and Correlated Noises

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
R. Caballero-Águila ◽  
I. García-Garrido ◽  
J. Linares-Pérez
Keyword(s):  
Stochastic Systems ◽  
Linear Filter ◽  
Missing Measurements ◽  
Process Noise ◽  
Estimation Algorithms ◽  
Optimal Linear ◽  
One Step ◽  
Optimal Fusion ◽  
Innovation Approach ◽  
Correlated Noises

The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with missing measurements and autocorrelated and cross-correlated noises. The stochastic uncertainties in the measurements coming from each sensor (missing measurements) are described by scalar random variables with arbitrary discrete probability distribution over the interval[0,1]; hence, at each single sensor the information might be partially missed and the different sensors may have different missing probabilities. The noise correlation assumptions considered are (i) the process noise and all the sensor noises are one-step autocorrelated; (ii) different sensor noises are one-step cross-correlated; and (iii) the process noise and each sensor noise are two-step cross-correlated. Under these assumptions and by an innovation approach, recursive algorithms for the optimal linear filter are derived by using the two basic estimation fusion structures; more specifically, both centralized and distributed fusion estimation algorithms are proposed. The accuracy of these estimators is measured by their error covariance matrices, which allow us to compare their performance in a numerical simulation example that illustrates the feasibility of the proposed filtering algorithms and shows a comparison with other existing filters.

scholarly journals T-proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

2021 ◽  
Author(s):  
Rosa M. Fernández-Alcalá ◽  
Jesús Navarro-Moreno ◽  
Juan C. Ruiz-Molina
Keyword(s):  
Fixed Point ◽  
Stochastic Systems ◽  
Computational Cost ◽  
Linear Estimators ◽  
Widely Linear Processing ◽  
Multiple Sensor ◽  
One Step ◽  
Optimal Estimators ◽  
Widely Linear ◽  
Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

scholarly journals \({\mathbb{T}}\)-Proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5729
Author(s):  
Rosa Fernández-Alcalá ◽  
Jesús Navarro-Moreno ◽  
Juan Ruiz-Molina
Keyword(s):  
Fixed Point ◽  
Stochastic Systems ◽  
Computational Cost ◽  
Linear Estimators ◽  
Widely Linear Processing ◽  
Multiple Sensor ◽  
One Step ◽  
Optimal Estimators ◽  
Widely Linear ◽  
Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or a widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

scholarly journals Distributed Fusion Filtering in Networked Systems with Random Measurement Matrices and Correlated Noises

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Raquel Caballero-Águila ◽  
Irene García-Garrido ◽  
Josefa Linares-Pérez
Keyword(s):  
Mean Squared Error ◽  
Current System ◽  
Unified Framework ◽  
Missing Measurements ◽  
Network Systems ◽  
Process Noise ◽  
Random Measurement ◽  
One Step ◽  
Sensor Measurement ◽  
Distributed Fusion

The distributed fusion state estimation problem is addressed for sensor network systems with random state transition matrix and random measurement matrices, which provide a unified framework to consider some network-induced random phenomena. The process noise and all the sensor measurement noises are assumed to be one-step autocorrelated and different sensor noises are one-step cross-correlated; also, the process noise and each sensor measurement noise are two-step cross-correlated. These correlation assumptions cover many practical situations, where the classical independence hypothesis is not realistic. Using an innovation methodology, local least-squares linear filtering estimators are recursively obtained at each sensor. The distributed fusion method is then used to form the optimal matrix-weighted sum of these local filters according to the mean squared error criterion. A numerical simulation example shows the accuracy of the proposed distributed fusion filtering algorithm and illustrates some of the network-induced stochastic uncertainties that can be dealt with in the current system model, such as sensor gain degradation, missing measurements, and multiplicative noise.

scholarly journals Covariance-Based Estimation from Multisensor Delayed Measurements with Random Parameter Matrices and Correlated Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
R. Caballero-Águila ◽  
A. Hermoso-Carazo ◽  
J. Linares-Pérez
Keyword(s):  
Stochastic Systems ◽  
State Space Model ◽  
Binary Sequence ◽  
Random Parameter ◽  
Signal Process ◽  
Covariance Functions ◽  
Error Covariance ◽  
Delayed Measurements ◽  
Innovation Approach ◽  
Correlated Noises

The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems subject to randomly delayed measurements with different delay rates. For each sensor, a different binary sequence is used to model the delay process. The measured outputs are perturbed by both random parameter matrices and one-step autocorrelated and cross correlated noises. Using an innovation approach, computationally simple recursive algorithms are obtained for the prediction, filtering, and smoothing problems, without requiring full knowledge of the state-space model generating the signal process, but only the information provided by the delay probabilities and the mean and covariance functions of the processes (signal, random parameter matrices, and noises) involved in the observation model. The accuracy of the estimators is measured by their error covariance matrices, which allow us to analyze the estimator performance in a numerical simulation example that illustrates the feasibility of the proposed algorithms.

scholarly journals Adaptive Kalman Estimation in Target Tracking Mixed with Random One-Step Delays, Stochastic-Bias Measurements, and Missing Measurements

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Sujuan Chen ◽  
Yinya Li ◽  
Guoqing Qi ◽  
Andong Sheng
Keyword(s):  
Target Tracking ◽  
Discrete Time ◽  
Adaptive Filter ◽  
Stochastic Systems ◽  
Tracking System ◽  
Random Variables ◽  
Design Approach ◽  
Missing Measurements ◽  
One Step ◽  
Mixed Uncertainties

The objective of this paper is concerned with the estimation problem for linear discrete-time stochastic systems with mixed uncertainties involving random one-step sensor delay, stochastic-bias measurements, and missing measurements. Three Bernoulli distributed random variables are employed to describe the uncertainties. All the three uncertainties in the measurement have certain probability of occurrence in the target tracking system. And then, an adaptive Kalman estimation is proposed to deal with this problem. The adaptive filter gains can be obtained in terms of solutions to a set of recursive discrete-time Riccati equations. Examples in three scenarios of target tracking are exploited to show the effectiveness of the proposed design approach.

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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