This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under ${\mathbb{T}}_k$-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 ${\mathbb{T}}_k$-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.

The prediction and smoothing fusion problems in multisensor systems with mixed uncertainties and correlated noises are addressed in the tessarine domain, under ${\mathbb{T}}_k$-properness conditions. Bernoulli distributed random tessarine processes are introduced to describe one-step randomly delayed and missing measurements. Centralized and distributed fusion methods are applied in a ${\mathbb{T}}_k$-proper setting, $k=1,2$, which considerably reduce the dimension of the processes involved. As a consequence, efficient centralized and distributed fusion prediction and smoothing algorithms are devised with a lower computational cost than that derived from a real formalism. The performance of these algorithms is analyzed by using numerical simulations where different uncertainty situations are considered: updated/delayed and missing measurements.

This paper analyses the centralized fusion linear estimation problem in multi-sensor systems with multiple packet dropouts and correlated noises. Packet dropouts are modeled by independent Bernoulli distributed random variables. This problem is addressed in the tessarine domain under conditions of ${\mathbb{T}}_1$ and ${\mathbb{T}}_2$-properness, which entails a reduction in the dimension of the problem and, consequently, computational savings. The methodology proposed enables us to provide an optimal (in the least-mean-squares sense) linear fusion filtering algorithm for estimating the tessarine state with a lower computational cost than the conventional one devised in the real field. Simulation results illustrate the performance and advantages of the solution proposed in different settings.