Mapping and planning are fundamental to robotic navigation in unknown environments. This work introduces a probabilistic framework that combines Gaussian processes (GPs) for 2.5D object modeling with an informative motion planner, using LiDAR-based measurements. The mapping approach employs a flexible, nonparametric representation to process 3D point cloud data to create compact volumetric representations through contours and heights, enabling robust shape estimation even from sparse data. Building on this, the GP representation-based informative motion planner incorporates information gain into the dynamic window approach (DWA) to enhance navigation performance. Simulations validate the framework by comparing its mapping accuracy with OctoMap and elevation map, and its planning efficiency with a baseline DWA.

In this paper, we consider the problem of tracking dynamic objects with unknown shapes using point cloud measurements generated by sensors such as lidars and radars. Specifically, our objective is to extend the Gaussian process-based extended object tracking (GPEOT) framework to encompass a broader class of objects. The derivation of the existing GPEOT algorithms is based on the assumption that the object of interest is star-convex. This assumption enables the modeling of the object’s extent through a radial distance function, which is described by a Gaussian process (GP). To enhance the flexibility of the resulting trackers, we propose the utilization of a potential function to indicate the unknown object extent. This approach enables the representation of objects with arbitrary shapes, including those that are non-convex and composed of disconnected components. Closely following the original formulation of GPEOT, the potential function is then modeled by a GP, which systematically accounts for the intrinsic spatial correlation of the extent. Furthermore, we develop a state-space model that incorporates both kinematic variables and an approximate description of the underlying GP model. The state vector can be estimated via a standard Bayesian technique, leading to an EOT algorithm. Through simulation experiments, we demonstrate the suggested method can satisfactorily estimate the kinematic variables of the objects while simultaneously learning their complex shapes.

In this work, we propose a new method to track extended targets of different shapes such as ellipses, rectangles and rhombi. We provide an analytical framework to express these shapes as superelliptical contours and propose a Bayesian filtering scheme that can handle measurements from the contour of the object. The method utilizes the Rao-Blackwellized particle filtering algorithm with novel sensor-object geometry constraints. The success of the algorithm is demonstrated using both simulations and real-data experiments, and the algorithm has been demonstrated to be of high performance in various challenging scenarios.

We present an alternative inference framework for the Gaussian process-based extended object tracking (GPEOT) models. The method provides an approximate solution to the Bayesian filtering problem in GPEOT by relying on a new measurement update, which we derive using variational Bayes techniques. The resulting algorithm effectively computes approximate posterior densities of the kinematic and the extent states. We conduct various experiments on simulated and real data and examine the performance compared with a reference method, which employs an extended Kalman filter for inference. The proposed algorithm significantly improves the accuracy of both the kinematic and the extent estimates and proves robust against model uncertainties.

In this paper, we consider the problem of extended target tracking, where the target extent cannot be represented by a single ellipse accurately. We model the target extent with multiple ellipses and solve the resulting inference problem, which involves data association between the measurements and sub-objects. We cast the inference problem into sequential Monte Carlo (SMC) framework and propose a simplified approach for the solution. Furthermore, we make use of the Rao-Blackwellization, aka marginalization, idea and derive an efficient filter to approximate the joint posterior density of the target kinematic states and target extent. Conditional analytical expressions, which are essential for Rao-Blackwellization, are not available in our problem. We use variational Bayes technique to approximate the conditional densities and enable Rao-Blackwellization. The performance of the method is demonstrated through simulations. A comparison with a recent method in the literature is performed.

In this study, we consider the challenging task of tracking dynamic 3D objects with unknown shapes by using sparse point cloud measurements gathered from the surface of the objects. We propose a Gaussian process based algorithm that is capable of tracking the dynamic behavior of the object and learn its shape in 3D simultaneously. Our solution does not require any parametric model assumption for the unknown shape. The shape of the objects is learned online via a Gaussian process. The proposed method can jointly estimate the position, orientation, and the shape of the object. The inference is performed by an extended Kalman filter which is suitable for online real-time applications. Lastly, we demonstrate the initial results of a promising approach, which aims at reducing the computational complexity.

Recent extended target tracking algorithms provide reliable shape estimates while tracking objects. The estimated extent of the objects can also be used for online classification. In this work, we propose to use a Bayesian classifier to identify different objects based on their contour estimates during tracking. The proposed method uses the uncertainty information provided by the estimation covariance of the tracker.

In this paper, marginal versions of the Bayesian Bhattacharyya lower bound (BBLB), which is a tighter alternative to the classical Bayesian Cramér- Rao bound, for discrete-time filtering are proposed. Expressions for the second and third-order marginal BBLBs are obtained and it is shown how these can be approximately calculated using particle filtering. A simulation example shows that the proposed bounds predict the achievable performance of the filtering algorithms better.

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.

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.

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.

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 Bayesian approach to estimate online both the state vector and the parameters representing the process noise statistics using a marginalized particle filter (MPF). Field tests show that the absolute radius can be estimated with submillimeter accuracy. The approach is tested in accordance with regulation 64 of the United Nations Economic Commission for Europe on a large data set (22 tests, using two vehicles and 12 different tire sets), where tire deflations are successfully detected, with high robustness, i.e., no false alarms. The proposed MPF approach outperforms common Kalman-filter-based methods used for joint state and parameter estimation when compared with respect to accuracy and robustness.

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 algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.

In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the state and the noise density is done via particle filters. Furthermore, the number of components and the noise statistics are allowed to vary in time. An extension of the method for the estimation of time varying noise characteristics is also introduced.

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 resulting representation, the number of formants is allowed to vary in time. The paper first presents an analysis on the continuity of the formants in the spectrum during the speech utterance. The analysis is based on a new state space representation of concatenated tube model. We show that the number of formants which appear in the spectrum is directly related to the location of the constriction of the vocal tract (i.e., the location of the excitation). Moreover, the disappearance of the formants in the spectrum is explained by “uncontrollable modes” of the state space model. Under the assumption of existence of varying number of formants in the spectrum, we propose the use of a DPM model based multi-target tracking algorithm for tracking unknown number of formants. The tracking algorithm defines a hierarchical Bayesian model for the unknown formant states and the inference is done via Rao–Blackwellized particle filter.