Tessarine signal processing under the T-properness condition

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

“…These properties make each algebra more appropriate for every specific problem. With this in mind, in [21][22][23][24] the application of these two isodimensional algebras is compared with the objective of showing how the choice of a particular algebra may determine the proposed method performance.…”

“…In general, the use of tessarines in estimation problems has been limited by the fact that it is not being a normed division algebra. This drawback was successfully overcome in [23] by introducing a metric that guarantees the existence and unicity of the optimal estimator. Moreover, although the optimal processing in the tessarine field is the WL processing, under properness conditions, it is possible to get the optimal solution from estimation algorithms with lower computational costs.…”

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

“…(1) Definition 1. A tessarine random signal x(t) ∈ T n is a stochastic process of the form [22] x(t) = x r (t) + ηx η (t) + η x η (t) + η x η (t), t ∈ Z…”

“…the following properness conditions in the tessarine domain has been recently introduced 149 in [22] and [23]. Definition 4.…”

“…Nevertheless, this drawback has been overcome in [22] by defining a suitable metric 247 which assures the existence the existence and uniqueness of these projections.…”