Xiang M, Scalzo Dees B, Mandic DP. Multiple-Model Adaptive Estimation for 3-D and 4-D Signals: A Widely Linear Quaternion Approach.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019;
30:72-84. [PMID:
29993725 DOI:
10.1109/tnnls.2018.2829526]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quaternion state estimation techniques have been used in various applications, yet they are only suitable for dynamical systems represented by a single known model. In order to deal with model uncertainty, this paper proposes a class of widely linear quaternion multiple-model adaptive estimation (WL-QMMAE) algorithms based on widely linear quaternion Kalman filters and Bayesian inference. The augmented second-order quaternion statistics is employed to capture complete second-order statistical information in improper quaternion signals. Within the WL-QMMAE framework, a widely linear quaternion interacting multiple-model algorithm is proposed to track time-variant model uncertainty, while a widely linear quaternion static multiple-model algorithm is proposed for time-invariant model uncertainty. A performance analysis of the proposed algorithms shows that, as expected, the WL-QMMAE reduces to semiwidely linear QMMAE for [Formula: see text]-improper signals and further reduces to strictly linear QMMAE for proper signals. Simulation results indicate that for improper signals, the proposed WL-QMMAE algorithms exhibit an enhanced performance over their strictly linear counterparts. The effectiveness of the proposed recursive performance analysis algorithm is also validated.
Collapse