Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing

摘要

Widely linear estimation plays an important role in quaternion signal processing, as it caters for both proper\udand improper quaternion signals. However, widely linear algorithms are computationally expensive owing to the\uduse of augmented variables and statistics. To reduce the computation cost while maintaining the performance\udlevel, we propose a four-channel estimation framework as an efficient alternative to quaternion widely linear\udestimation. This is achieved by using four linear models to estimate the four components of quaternion signals.\udWe also show that any of the four channels is able to replace a strictly linear quaternion estimator when\udestimating strictly linear systems. The proposed method is shown to reduce computational complexity and\udprovide more flexible algorithms, while preserving the physical meaning inherent in the quaternion domain.\udThe proposed framework is next applied to quaternion minimum mean square error estimation to yield the\udreduced-complexity versions of the quaternion least mean square (QLMS), quaternion recursive least squares\ud(QRLS), and quaternion nonlinear gradient decent (QNGD) algorithms. For the proposed QLMS algorithm, an\udadaptive step-size strategy is also explored. The effectiveness of the so introduced estimation techniques is\udvalidated by simulations on synthetic and real-world signals.