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

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.

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

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

The Generalized Sidelobe Canceller Based on Quaternion Widely Linear Processing

We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array’s quaternion model, we propose the general expression of a quaternionsemiwidelylinear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array’s gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal’s direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC.