Stochastic Nonlinear Filtering in Absolute Phase Acquisition and Tracking

24 11/2015

Tuesday, 24 Nov. 2015, 13:00 - 14:00

Presenter: José Leitao; Institute of Telecommunications, Lisbon, P
Host: M. Aspelmeyer
Where: Schrödingerroom, 4th floor, Boltzmanng. 5, 1090 Wien

Stochastic nonlinear filtering is essentially a Bayesian approach to the problem of estimating the evolution of a stochastic process from its noisy observations. Accordingly, all the information about the process to be estimated is contained in its conditional probability density function (filtering density), which, in phase estimation problems, is in general multimodal.

In (absolute and cyclic) phase tracking, the strategy usualy followed is to linearize the model's nonlinearities arround the current estimates and assume Gaussian initial conditions. The resulting estimator is the so-called extended Kalman-Bucy filter (EKB-F), which, on account of those simplifications, may loose important information, tending to exhibit poor performance or to diverge in certain situations. If the relevant shape of the filtering density is preserved, better performance is expected; this is what we look for with sochastic nonlinear filtering implementations.

In absolute phase acquisition the initial phase ambiguity overlaps a multiple of 2pi intervals in terms of a multimodal density function; the problem is to recursively transform this density into a practicaly unimodal form, thus making the phase estimate converge to the actual phase value. Once the acquisition has been performed, a tracking period begins. Absolute phase acquisition is inherently a global optimal nonlinear filtering problem, where a local estimator (such as the EKB-F) cannot even provide a suboptimal solution.

Based on published work, we will present our approach to a set of problems: ranging in radar/sonar systems (absolute phase acquisition); broadband reflectometry in fusion plasma density profile evaluation (absolute phase and phase-rate tracking); detection and estimation in mobile communications in fading channels with large carrier variations (phase detection while tracking); combining absolute phase tracking with pseudorange estimation in global navigation satellite systems; interferometric imaging reconstruction (phase unwrapping); adaptive carrier tracking in mobile communications: an innovations-based appoach.

As for quantum metrology, there is a refererence ([2]) to our work on acquisition and tracking in "Local and Global Distinguishability in Quantum Interferometry", by Durkin and Dowling: "...The tasks of global phase acquisition and local phase tracking are both important challenges. Classically, the distinction is well-understood, for example in implementations of Radar/Sonar [2]". As far as I can understand, there are other aspects of our work and experience that could be also of interest in quantum experiments, namely optomechanics or quantum technologies in space.