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.

This paper presents a distributed online method for joint state and parameter estimation in a Jump Markov NonLinear System based on a distributed recursive Expectation Maximization algorithm. State inference is enabled via the use of Rao-Blackwellized Particle Filter and, for the parameter estimation, the E-step is performed independently at each sensor with the calculation of local sufficient statistics. An average consensus algorithm is used to diffuse local sufficient statistics to neighbors and approximate the global sufficient statistics throughout the network. The evaluation of the proposed algorithm is carried out on a Terrain Based Navigation problem where the unknown parameters of the observation noise model contain relevant information about the terrain properties.

In this paper, we propose using Gaussian processes to track an extended object or group of objects, that generates multiple measurements at each scan. The shape and the kinematics of the object are simultaneously estimated, and the shape is learned online via a Gaussian process. The proposed algorithm is capable of tracking different objects with different shapes within the same surveillance region. The shape of the object is expressed analytically, with well-defined confidence intervals, which can be used for gating and association. Furthermore, we use an efficient recursive implementation of the algorithm by deriving a state space model in which the Gaussian process regression problem is cast into a state estimation problem.

In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.

In this paper, a semi-parametric model for RSS measurements is introduced that can be used to predict coverage in cellular radio networks. The model is composed of an empirical log-distance model and a deterministic antenna gain model that accounts for possible non-uniform base station antenna radiation. A least-squares estimator is proposed to jointly estimate the path loss and antenna gain model parameters. Simulation as well as experimental results verify the efficacy of this approach. The method can provide improved accuracy compared to conventional path loss based estimation methods. 

A marginal version of the Weiss-Weinstein bound (WWB) is proposed for discrete-time nonlinear filtering. The proposed bound is calculated analytically for linear Gaussian systems and approximately for nonlinear systems using a particle filtering scheme. Via simulation studies, it is shown that the marginal bounds are tighter than their joint counterparts.

Cramér-Rao lower bounds (CRLBs) are proposed for deterministic parameter estimation under model mismatch conditions where the assumed data model used in the design of the estimators differs from the true data model. The proposed CRLBs are defined for the family of estimators that may have a specified bias (gradient) with respect to the assumed model. The resulting CRLBs are calculated for a linear Gaussian measurement model and compared to the performance of the maximum likelihood estimator for the corresponding estimation problem.

The commercial interest in proximity services is increasing. Application examples include location-based information and advertisements, logistics, social networking, file sharing, etc. In this paper, we consider positioning of devices based on time series proximity reports from a mobile device to a network node. This corresponds to nonlinear measurements with respect to the device position in relation to the network nodes. Therefore, particle filtering is applicable for positioning. Positioning performance is evaluated in a typical office area with Bluetooth-low-energy beacons deployed for proximity detection and report. Accuracy is concluded to vary spatially over the office floor, and in relation to the beacon deployment density.

We present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide range of non-linear models. To exploit the inherent structure of JMNLS, we design a Rao-Blackwellized particle filter (RBPF) where the discrete mode is marginalized out analytically. This results in an efficient implementation of the algorithm and reduces the estimation error variance. The proposed RBPF is then used to compute, recursively in time, smoothed estimates of complete data sufficient statistics. Together with the online expectation maximization algorithm, this enables recursive identification of unknown model parameters including the transition probability matrix. The method is also applicable to online identification of jump Markov linear systems(JMLS). The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.

In this technical report, some derivations for the smoother proposed in [1] are presented. More specifically, the derivations for the cyclic iteration needed to solve the variational Bayes smoother for linear state-space models with unknownprocess and measurement noise covariances in [1] are presented. Further, the variational iterations are compared with iterations of the Expectation Maximization (EM) algorithm for smoothing linear state-space models with unknown noise covariances.

[1] T. Ardeshiri, E. Özkan, U. Orguner, and F. Gustafsson, ApproximateBayesian smoothing with unknown process and measurement noise covariances, submitted to Signal Processing Letters, 2015.