Using Bayesian probability theory we demonstrate that the Lomb-Scargle periodogram may be generalized in a straightforward manner to nonuniformly nonsimultaneously sampled quadrature data when the sinusoid has arbitrary amplitude modulation. This generalized Lomb-Scargle periodogram is the sufficient statistic for single frequency estimation in a wide class of problems ranging from stationary f...

This paper discusses modeling and automatic feedback control of (postural and rest) tremor for adaptive-control-methodology-based estimation of deep brain stimulation (DBS) parameters. The simplest linear oscillator-based tremor model, between stimulation amplitude and tremor, is investigated by utilizing input-output knowledge. Further, a nonlinear generalization of the oscillator-based tremor...

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshape...

In a companion paper [1], we studied amplitude estimation of one-dimensional (1-D) sinusoidal signals from measurements corrupted by possibly colored observation noise. We herein extend the results for twodimensional (2-D) amplitude estimation, which is of interest in various applications, including medical imaging, synthetic aperture radar (SAR), seismology, and many others. In particular, we ...