Robert Piché

Henri Nurminen, Tohid Ardeshiri, Robert Piché et al.

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation. Although the variational update is done suboptimally using an expectation propagation algorithm, our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm. Consequently, the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low-complexity alternatives in accuracy and speed. We present both simulations and tests based on real-world navigation data, in particular GPS data in an urban area, to demonstrate the performance of the novel methods. Moreover, the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew-$t$ is outlined. Finally, the paper presents a study of theoretical performance bounds for the proposed algorithms.

Henri Nurminen, Laura Suomalainen, Simo Ali-Löytty et al.

We propose modeling an angle-of-arrival (AOA) positioning measurement as a von Mises-Fisher (VMF) distributed unit vector instead of the conventional normally distributed azimuth and elevation measurements. Describing the 2-dimensional AOA measurement with three numbers removes discontinuities and reduces nonlinearity at the poles of the azimuth-elevation coordinate system. Our computer simulations show that the proposed VMF measurement noise model based filters outperform the normal distribution based algorithms in accuracy in a scenario where close-to-pole measurements occur frequently.

Henri Nurminen, Tohid Ardeshiri, Robert Piché et al.

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-t-distributed measurement noise. The proposed filter and smoother are compared with conventional low-complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

Marko Järvenpää, Robert Piché

A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The model is based on the characterisation of the Laplace density prior as a scale mixture of Gaussians. With different priors on the mixture variable, other total variation like regularisations e.g. a prior that is related to t-distribution, are also obtained. An approximation of the resulting posterior mean is found using a variational Bayes method. In addition, an iterative alternating sequential algorithm for computing the maximum a posteriori estimate is presented. The methods are illustrated with examples of image deblurring. Results show that the proposed model can be used for automatic edge-preserving inversion in the case of image deblurring. Despite promising results, some difficulties with the model were encountered and are subject to future work.