The widely linear quaternion recursive total least squares
Constantinides, Anthony G.
Mandic, Danilo P.
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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Thanthawaritthisai, T., Tobar, F., Constantinides, A. G., & Mandic, D. P. (2015). The widely linear quaternion recursive total least squares. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 3357-3361. https://doi.org/10.1109/ICASSP.2015.7178593
This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICASSP.2015.7178593
A widely linear quaternion recursive total least squares (WLQRTLS) algorithm is introduced for the processing of Q- improper processes contaminated by noise. The total least squares for quaternions (QTLS) is a generalisation of the real-valued total least squares and is introduced rigorously, starting from the existence condition for low-rank approximation of quaternion matrices. Then, a quaternion Rayleigh quotient (QRQ) is defined to establish the link between the QTLS solution and the minimisation of the QRQ. Finally, the rank-one update formula is employed to allow for fast iterative solution based on the QRQ. Through simulations, the WL-QRTLS was shown to exhibit superior performance, under perturbations on both input and output signals, to other adaptive filtering of the same class - the widely linear quaternion least mean squares (WL-QLMS) and the widely linear quaternion recursive least squares (WL-QRLS). The experiments on both synthetic and real-world Q-improper processes supported the analysis.
widely linear QRTLS, total least squares, Rayleigh quotient, low-rank approximation, quaternions
External DOI: https://doi.org/10.1109/ICASSP.2015.7178593
This record's URL: https://www.repository.cam.ac.uk/handle/1810/248033