A Widely Linear Complex Unscented Kalman Filter

Abstract

Abstract-Conventional complex valued signal processing algorithms assume rotation invariant (circular) signal distributions, and are thus suboptimal for real world processes which exhibit rotation dependent distributions (noncircular). In nonlinear sequential state space estimation, noncircularity can arise from the data, state transition model, and state and observation noises. We provide further insight by revisiting the augmented complex unscented Kalman filter (ACUKF) and illuminating its operation in such scenarios. The analysis establishes a relationship between the estimation error and the degree of second order noncircularity (improperness) in the system for the conventional complex unscented Kalman filter (CUKF), and is supported by simulations on both synthetic and real world proper and improper signals.

A Kalman filter for stereophonic acoustic echo cancellation

“…We assume that the variance of the noise, σ 2 v , is available in all the simulations. The performance measures is the normalized misalignment (in dB), which is computed based on (12). In order to evaluate the tracking capabilities of the algorithms, the impulse responses in the near-end location are shifted to the right by 12 samples in the middle of each experiment.…”

“…The main motivation behind this work is the appealing performance of the Kalman filter for echo cancellation [8], [9], [10], [11]. Also, the WL complex Kalman filters [12], [13], [14] were found to be attractive for many applications. The WL-GKF has inherited some similarities with the WL augmented complex Kalman filter presented in [13].…”

Adaptive cubature Kalman filter based on the variance-covariance components estimation

“…In practical engineering, two nonlinear methods named the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are most widely used (Gao et al 2014;Dini et al 2011;Vaccarella et al 2013;Masazade et al 2012). In the EKF, the nonlinear system can be linearized utilizing the Taylor series expansion for variance propagation while the prediction of the state vector and measurement vector are conducted using the nonlinear system (Gao et al 2014;Arasaratnam & Haykin 2009).…”

“…Although this method is used in many nonlinear systems for its simplicity, the precision is limited in the systems with strong nonlinearity and the fussy Jacobian matrix should be calculated which will inevitably increase the computational load. With the Unscented Transformation (UT), the UKF method can approximate the mean and the variance of the Gaussian state distribution using the nonlinear function to avoid the local linearization and the calculation of the Jacobian matrix effectively (Gao et al 2014;Dini et al 2011). However, the covariance matrix sometimes is easy non-positive in high-dimensional systems which will lead to filtering divergence.…”

Complex-Valued Gaussian Sum Filter for Nonlinear Filtering of Non-Gaussian/Non-Circular Noise

“…Recently [21]- [24], there has been a surge of interest in developing widely-linear implementations of the KF [21], [22] for linear systems and KF-based algorithms [23] for systems with non-linear dynamics. However, in scenarios where the underlying system exhibits significant non-Gaussian behaviour, e.g., due to presence of non-Gaussian measurement…”