arXiv subjects

Robert Piche

Publications and source records attributed to Robert Piche.

4 recordsLinked to original sources

arXiv2016

Automatic numerical differentiation by maximum likelihood estimation of state-space model

A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements and non-equally spaced abscissas, and can compute state estimates at points between the data abscissas. The state space model's parameters, including driving noise intensity, measurement variance, and initial state, are determined from the given data sequence using maximum likelihood estimation computed using a expectation maximisation iteration. In tests with synthetic biomechanics data, the algorithm has equivalent or better accuracy compared to other automatic numerical differentiation algorithms.

stat.ME↗

arXiv2016

Skew-t inference with improved covariance matrix approximation

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field variational Bayes approximation of the posterior distribution to a skew-t likelihood and normal prior. Our simulations show that the proposed variational Bayes approximation gives a more accurate approximation of the posterior covariance matrix than our earlier proposed method. Furthermore, the novel filter and smoother outperform our earlier proposed methods and conventional low complexity alternatives in accuracy and speed.

eess.SY↗

arXiv2015

An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the twisted particle filtering methodology, establish accessible theoretical results which convey its rationale, and provide a demonstration of its practical performance within particle Markov chain Monte Carlo for estimating static model parameters. We derive twisted particle filters that incorporate systematic or multinomial resampling and information from historical particle states, and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise and we apply such approximations to two examples: a range and bearing tracking problem and an indoor positioning problem with Bluetooth signal strength measurements. We demonstrate improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time, and improved tracking performance using estimated parameters.

stat.CO↗

arXiv2014

An empirical-parametric gamma calibration algorithm

A method to determine the gamma correction curves for displays is presented. An empirical model is first constructed from exhaustive measurements of a few representative units. The model parameters for the remaining units are then fitted using only a few measurements. The method uses standard least-squares algorithms and is computationally light. Experimental results for a small sample of LCD displays are presented.

physics.optics↗