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

Abstract

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.

Multisensor Fusion Estimation for Systems with Uncertain Measurements, Based on Reduced Dimension Hypercomplex Techniques

“…Alternatively, the multisensor fusion estimation problem has also been analyzed by using 4D hypercomplex algebras [16][17][18][19][20][21][22][23]. These algebras appear to be a natural extension of complex algebras comprising a real part and three imaginary parts, which gives rise to ideal structures for describing phenomena in the real physical world.…”

“…In this field, quaternions have been the most common 4D hypercomplex algebra in signal processing, since they have the desirable property of being a normed division algebra. Unlike quaternions, tessarines constitute a commutative algebra which facilitates the extension of the main results obtained in the real and complex fields to the four-dimensional case, and the use of tessarines as a signal processing tool has been gaining popularity in the last few years [22,23,28].…”

“…In the tessarine domain, two types of properness have recently been introduced, namely T 1 and T 2 -properness [24,32], and they have been satisfactorily applied in multisensor fusion estimation problems with uncertainties in the measurements [22,23]. In [22], T k -proper, k = 1, 2, centralized fusion algorithms of reduced dimension are proposed for the computation of the optimal (in the least-squares sense) filter, predictor, and fixedpoint smoother of the state in systems with random one-step delays and correlated noises. In [23], a more general problem with random sensor delays and missing measurements is analyzed.…”

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

“…It should be highlighted that quaternion processing is not always the most appropriate methodology. In fact, the use of tessarine signals can bring, under certain conditions, a better performance of the estimators, as has been tested in [41][42][43].…”

“…Later, the T 2 -properness definition is established in [42], obtaining the same result for the TWL and T 2 estimation errors. These types of T k -properness have been used in [43] to approach the LS linear centralized fusion estimation problem of signals from multi-sensor observations with random delays.…”