We present analytical expressions for predicting the mean square error (MSE) performance of the Kalman filter (KF) and Kalman smoother (KS) when applied to fixed, non-random state trajectories. Unlike the standard Bayesian setting, where the state is modeled as a random process, some practical applications-such as benchmark evaluations in target tracking-rely on deterministic state trajectories. In such cases, the KF and KS become biased and inconsistent (in a non-random/frequentist sense), and their standard covariance estimates no longer reflect actual estimation errors. To address this issue, we derive batch and horizon-recursive MSE expressions for KF and KS to predict their performance without relying on Monte Carlo simulations. Our approach also accounts for measurement model mismatch, allowing performance evaluation under model misspecification. Simulation results validate the accuracy of the proposed analytical expressions, demonstrating their agreement with empirical MSE values.

Bayesian filtering problem is considered in linear Gaussian systems with unknown inverse Wishart distributed process noise covariance. A Bayesian filter is formulated to approximate the joint posterior for the state and the process noise covariance. This involves utilizing moment matching and a scale Gaussian mixture approximation of the$\boldsymbol{t}$-distribution, The proposed filter distinguishes itself by being non-iterative, setting it apart from existing Bayesian solutions given in the literature. The algorithm's performance is demonstrated through its application to a scenario where a target is tracked in two dimensions. Simulation results indicate that the proposed filter achieves similar or better performance compared to state-of-the-art solutions while demanding a reduced computational load.

This paper presents a new state-space model and tracking filter for Riemannian angle tracking on the unit sphere. We consider a scenario where noisy angle-only measurements (azimuth and elevation) of a target, moving with nearly constant velocity, are obtained by a stationary sensor. The angular state, composed of the angular position vector constrained on the unit sphere and the angular velocity vector defined over the tangent plane at the angular position, is tracked. Since the target's nearly constant velocity motion in 3D space induces correlated acceleratory motion on the unit sphere, we develop a state-space model that accounts for this acceleration. A tracking filter based on the Riemannian generalization of the unscented Kalman filter (UKF) given in the literature is proposed and implemented using this model. Simulation results demonstrate that the developed angle tracker outperforms two benchmark Riemannian filters, one based on a (Riemannian generalization of) nearly constant velocity model and the other on a (Riemannian generalization of) nearly constant acceleration model, particularly for close-range and/or fast-moving targets.

Providing efficient yet accurate statistical models is a challenging problem in many applications. When elementary models are not sufficiently descriptive, mixtures of densities can be used. A complexity management issue arises when mixture models are employed: the number of components should be a trade-off between the complexity and the accuracy of the model. However, in general, it is not obvious how to determine the right number of mixture components for a specific application. In a previous work, theoretical foundations to address such a topic have been laid, grounded on the use of the Composite Transportation Dissimilarity between mixtures, and a preliminary criterion to manage the complexity of a mixture model has been proposed. In this paper, additional theoretical insights are provided that allow to formulate a novel adaptive mixture reduction algorithm. Numerical tests show that in most cases the new algorithm constitutes a significant improvement over the previous one.

In a sensor network compensation of the correlated information caused by previous communication is of utmost interest for distributed estimation. In this paper, we investigate different information decorrelation approaches that can be applied when using an interacting multiple model filter in a local sensor node. The related decorrelation and the corresponding fusion operations are discussed. The different approaches are compared on a simple distributed single maneuvering target tracking example.

In this paper, recursive Bobrovsky-Zakai bounds for filtering, prediction and smoothing of nonlinear dynamic systems are presented. The similarities and differences to an existing Bobrovsky-Zakai bound in the literature for the filtering case are highlighted. The tightness of the derived bounds are illustrated on a simple example where a linear system with non-Gaussian measurement likelihood is considered. The proposed bounds are also compared with the performance of some well-known filters/predictors/smoothers and other Bayesian bounds.

An approximate extended target tracking (ETT) measurement update is derived for random matrix extent representation with measurement noise. The derived update uses Taylor series approximations. The performance of the proposed update methodology is illustrated on a simple ETT scenario and compared to alternative updates in the literature.