The Bayesian inference of phase

Performance Characterization of AOA Geolocation Systems Using the Von Mises Distribution

“…It is not immediately clear if the parameter, ρ l , defined as h(κ l ), admits a similar interpretation. We next show that ρ l in fact can also be expressed as the inverse of the variance of φ l , now computed using (5).…”

“…4). Since the variance of the von Mises distribution (1) is computed by (5), it also follows from (33) that the variance of φ l , also denoted by v φ l here, is closely approximated by 1 κ l , provided that the standard deviation of φ l is less than 1 radian, or 180 π ≈ 57 degrees, which can be assumed to be satisfied for virtually all useful DF systems. Thus, for all practical purposes, we can safely write…”

“…where v φ l is the variance of φ l , computed using either (5) or (29), depending on whether the von Mises distribution (7) or the Gaussian distribution (26) is used to model the AOA measurements φ l , 1 ≤ l ≤ n:…”

Machine-Learning-Based Parameter Estimation of Gaussian Quantum States

“…Similar to the displacement estimation scenario, we assume that multiple independent measurements are obtained and then our proposed machine learning based method is used on the observed data to obtain the phase estimate. Unlike the previous work [8] that considered a uniform prior for the phase parameter, in this work we consider a von Mises prior that is widely used for modelling directional parameters [48]- [53]. Under a uniform prior assumption on the phase, the Bayesian estimate proposed in [8] is the same as the maximum likelihood estimate since the prior is an uninformed prior with uniform distribution of θ in [−π, π].…”

“…We assume a von Mises prior on θ, which is a circular distribution that has been widely used in classical signal processing applications to model directional parameters [48]- [53]. In quantum phase estimation, a recent work assumed a wrapped Gaussian prior for qubit phase estimation [54].…”