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 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 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 The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2961
Author(s):  
José D. Jiménez-López ◽  
Rosa M. Fernández-Alcalá ◽  
Jesús Navarro-Moreno ◽  
Juan C. Ruiz-Molina
Keyword(s):  
Computational Cost ◽  
Linear Filter ◽  
Missing Observations ◽  
Widely Linear Processing ◽  
Insignificant Difference ◽  
Innovation Approach ◽  
Widely Linear ◽  
Mixed Uncertainties ◽  
Distributed Filter ◽  
Theoretical Results

This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under Tk-properness conditions. Observations from each sensor can be updated, delayed, or contain only noise, and a correlation is assumed between the state and the observation noises. Recursive algorithms for the optimal local linear filter at each sensor as well as both centralized and distributed linear fusion estimators are derived using an innovation approach. The Tk-properness assumption implies a reduction in the dimension of the augmented system, which yields computational savings in the previously mentioned algorithms compared to their counterparts, which are derived from real or widely linear processing. A numerical simulation example illustrates the obtained theoretical results and allows us to visualize, among other aspects, the insignificant difference in the accuracy of both fusion filters, which means that the distributed filter, although suboptimal, is preferable in practice as it implies a lower computational cost.

An Alternate Algorithm for (3x3) Median Filtering of Digital Images

2012 ◽  
Vol 2 (1) ◽  
pp. 7-9 ◽  
Author(s):  
Satinderjit Singh
Keyword(s):  
Median Filter ◽  
Computational Cost ◽  
Spatial Coherence ◽  
General Purpose ◽  
Median Filtering ◽  
Basic Algorithm ◽  
Temporal Complexity ◽  
Filter Kernel ◽  
One Step ◽  
High Computational Cost

Median filtering is a commonly used technique in image processing. The main problem of the median filter is its high computational cost (for sorting N pixels, the temporal complexity is O(N·log N), even with the most efficient sorting algorithms). When the median filter must be carried out in real time, the software implementation in general-purpose processorsdoes not usually give good results. This Paper presents an efficient algorithm for median filtering with a 3x3 filter kernel with only about 9 comparisons per pixel using spatial coherence between neighboring filter computations. The basic algorithm calculates two medians in one step and reuses sorted slices of three vertical neighboring pixels. An extension of this algorithm for 2D spatial coherence is also examined, which calculates four medians per step.

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.

Fractal Top for Contractive and Non-Contractive Transformations

2012 ◽  
Vol 3 (4) ◽  
pp. 49-65
Author(s):  
Sarika Jain ◽  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Iterated Function System ◽  
Function System ◽  
Feedback Process ◽  
Iterated Function ◽  
Spatial Part ◽  
One Step ◽  
The One ◽  
Definition Of

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to colour-render pictures produced by fractal top and stealing colours from a natural picture. Barnsley has used the one-step feed- back process to compute the fractal top. In this paper, the authors introduce a two-step feedback process to compute fractal top for contractive and non-contractive transformations.

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