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We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new(More)
Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear(More)
The particle filter provides a general solution to the nonlinear filtering problem with arbitrarily accuracy. However, the curse of dimensionality prevents its application in cases where the state dimensionality is high. Further, estimation of stationary parameters is a known challenge in a particle filter framework. We suggest a marginalization approach(More)
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(More)
In this paper, we propose a new approach for dynamic speech spectrum representation and tracking vocal tract resonance (VTR) frequencies. The method involves representing the spectral density of the speech signals as a mixture of Gaussians with unknown number of components for which time-varying Dirichlet process mixture model (DPM) is utilized. In the(More)
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(More)
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(More)
In this paper, the measurements of individual wheel speeds and the absolute position from a global positioning system are used for high-precision estimation of vehicle tire radii. The radii deviation from its nominal value is modeled as a Gaussian random variable and included as noise components in a simple vehicle motion model. The novelty lies in a(More)
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(More)
In this paper, we explore the potential of networked microphone arrays for multiple target tracking. Tracking is accomplished by using the direction-of-arrival (DOA) estimates of multiple microphone arrays. Each microphone array obtains the DOA estimates by using the wideband extensions of the multiple signal classification (MUSIC) technique. Based on these(More)