Nonlinear least squares algorithm for canonical polyadic decomposition using low-rank weights

The canonical polyadic decomposition (CPD) is an important tensor tool in signal processing with various applications in blind source separation and sensor array processing. Many algorithms have been developed for the computation of a CPD using a least squares cost function. Standard least-squares methods assumes that the residuals are uncorrelated and have equal variances which is often not true in practice, rendering the approach suboptimal. Weighted least squares allows one to explicitly accommodate for general (co)variances in the cost function. In this paper, we develop a new nonlinear least-squares algorithm for the computation of a CPD using low-rank weights which enables efficient weighting of the residuals. We briefly illustrate our algorithm for direction-of-arrival estimation using an array of sensors with varying quality.