Robust Inference for State-Space Models with Skewed Measurement Noise

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.Comment: 5 pages, 7 figures. Accepted for publication in IEEE Signal Processing Letter

Морфонологія українських віддієслівних словотвірних гнізд

(uk) У статті окреслено перспективу дослідження девербативів у сучасній українській мові в контексті теоретичних здобутків сучасної лінгвістики, з’ясовано морфонологічні характеристики словотвірних гнізд девербативів різних структурних типів.(en) The article outlines the perspective of the research of verbal derivatives in modern Ukrainian language in the context of theoretical achievements of modern linguistics, the morphological characteristics of wordbuilding units of verbal derivatives with different structure types

Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.Comment: Derivations for the smoother can found here: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-12070

Maximum entropy properties of discrete-time first-order stable spline kernel

The first order stable spline (SS-1) kernel is used extensively in regularized system identification. In particular, the stable spline estimator models the impulse response as a zero-mean Gaussian process whose covariance is given by the SS-1 kernel. In this paper, we discuss the maximum entropy properties of this prior. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling schemes, we also explicitly derive the special structure underlying the SS-1 kernel (e.g. characterizing the tridiagonal nature of its inverse), also giving to it a maximum entropy covariance completion interpretation. Along the way similar maximum entropy properties of the Wiener kernel are also given

Sharp Gaussian Approximation Bounds for Linear Systems with α-stable Noise

We report the results of several theoretical studies into the convergence rate for certain random series representations of α-stable random variables, which are motivated by and find application in modelling heavy-tailed noise in time series analysis, inference, and stochastic processes. The use of α-stable noise distributions generally leads to analytically intractable inference problems. The particular version of the Poisson series representation invoked here implies that the resulting distributions are “conditionally Gaussian,” for which inference is relatively straightforward, although an infinite series is still involved. Our approach is to approximate the residual (or “tail”) part of the series from some point, c > 0, say, to ∞, as a Gaussian random variable. Empirically, this approximation has been found to be very accurate for large c. We study the rate of convergence, as c → ∞, of this Gaussian approximation. This allows the selection of appropriate truncation parameters, so that a desired level of accuracy for the approximate model can be achieved. Explicit, nonasymptotic bounds are obtained for the Kolmogorov distance between the relevant distribution functions, through the application of probability-theoretic tools. The theoretical results obtained are found to be in very close agreement with numerical results obtained in earlier work

An adaptive PHD filter for tracking with unknown sensor characteristics

In multi-target tracking, the discrepancy between the nominal and the true values of the model parameters might result in poor performance. In this paper, an adaptive Probability Hypothesis Density (PHD) filter is proposed which accounts for sensor parameter uncertainty. Variational Bayes technique is used for approximate inference which provides analytic expressions for the PHD recursions analogous to the Gaussian mixture implementation of the PHD filter. The proposed method is evaluated in a multi-target tracking scenario. The improvement in the performance is shown in simulations