Adaptive Algorithms to Track the PARAFAC Decomposition of a Third-Order Tensor

Abstract

Abstract-The PARAFAC decomposition of a higher-order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode-both serious drawbacks for on-line applications. When the data are serially acquired, or the underlying model changes with time, adaptive PARAFAC algorithms that can track the sought decomposition at low complexity would be highly desirable. This is a challenging task that has not been addressed in the literature, and the topic of this paper. Given an estimate of the PARAFAC decomposition of a tensor at instant t, we propose two adaptive algorithms to update the decomposition at instant t + 1, the new tensor being obtained from the old one after appending a new slice in the 'time' dimension. The proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state-of-art batch algorithms, at orders of magnitude lower complexity. The effectiveness of the proposed algorithms is illustrated using a MIMO radar application (tracking of directions of arrival and directions of departure) as an example.

A PARAFAC-based algorithm for multidimensional parameter estimation in polarimetric bistatic MIMO radar

“…The definition of PARAFAC quadrilinear decomposition model can be derivatively described from the trilinear decomposition model [19][20][21]. …”

“…In recent years, PARAFAC has become a new research means in MIMO radar [19][20][21]. The PARAFAC analysis algorithms [19,20] and adaptive PARAFAC algorithm [21] have been developed for the estimation of DOAs and DODs of multiple targets.…”

“…Despite the fact that several PARAFAC-based methods have been proposed for DOA and DOD estimation in bistatic MIMO radars, trilinear decomposition algorithms [17][18][19][20][21] with trilinear alternating least square (TALS) are commonly used to fit PARAFAC model. In this article, we investigate joint estimation of DOD, DOA, Doppler frequency and polarization.…”

Multiple target three-dimensional coordinate estimation for bistatic MIMO radar with uniform linear receive array

“…Also, bistatic MIMO radar has the particular advantage of being able to obtain the target angles with respect to the transmit array (direction of departure) by processing the received data [3]. Several publications have studied direction of departure and direction of arrival estimation for bistatic MIMO radar [5][6][7][8][9]. Multiple target localization without range information can be achieved by using the estimated angles.…”

Constrained Trilinear Decomposition With Application to Array Signal Processing

“…They applied PARAFAC model to estimate the azimuth and elevation angles from different sources in a uniform square array. Beamforming [14,15], polarization sensitive array processing [16][17][18] and MIMO radar location [19,20] have also been linked to trilinear analysis. The common characteristic of tensor modeling approach in these applications is that baseband signals and array response vectors, which are always involved in data model, are treated as pure 'double-precision' or 'complex' data during trilinear decomposition.…”