arXiv subjects

Emre Özkan

Publications and source records attributed to Emre Özkan.

11 recordsLinked to original sources

arXiv2025

GPL-SLAM: A Laser SLAM Framework with Gaussian Process Based Extended Landmarks

We present a novel Simultaneous Localization and Mapping (SLAM) method that employs Gaussian Process (GP) based landmark (object) representations. Instead of conventional grid maps or point cloud registration, we model the environment on a per object basis using GP based contour representations. These contours are updated online through a recursive scheme, enabling efficient memory usage. The SLAM problem is formulated within a fully Bayesian framework, allowing joint inference over the robot pose and object based map. This representation provides semantic information such as the number of objects and their areas, while also supporting probabilistic measurement to object associations. Furthermore, the GP based contours yield confidence bounds on object shapes, offering valuable information for downstream tasks like safe navigation and exploration. We validate our method on synthetic and real world experiments, and show that it delivers accurate localization and mapping performance across diverse structured environments.

cs.RO↗

arXiv2025

A Rao-Blackwellized Particle Filter for Superelliptical Extended Target Tracking

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.

eess.SP↗

arXiv2021

Three-Dimensional Extended Object Tracking and Shape Learning Using Gaussian Processes

In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position, orientation and velocities, together with the shape of the object for online and offline applications. We describe the unknown shape by a radial function in 3D, and induce a correlation structure via a Gaussian process. Furthermore, we propose an efficient algorithm to reduce the computational complexity of working with 3D data. This is accomplished by casting the tracking problem into projection planes which are attached to the object's local frame. The resulting algorithms can process 3D point cloud data and accomplish tracking of a dynamic object. Furthermore, they provide analytical expressions for the representation of the object shape in 3D, together with confidence intervals. The confidence intervals, which quantify the uncertainty in the shape estimate, can later be used for solving the gating and association problems inherent in object tracking. The performance of the methods is demonstrated both on simulated and real data. The results are compared with an existing random matrix model, which is commonly used for extended object tracking in the literature.

eess.SP↗

arXiv2021

Random Matrix Based Extended Target Tracking with Orientation: A New Model and Inference

In this study, we propose a novel extended target tracking algorithm which is capable of representing the extent of dynamic objects as an ellipsoid with a time-varying orientation angle. A diagonal positive semi-definite matrix is defined to model objects' extent within the random matrix framework where the diagonal elements have inverse-Gamma priors. The resulting measurement equation is non-linear in the state variables, and it is not possible to find a closed-form analytical expression for the true posterior because of the absence of conjugacy. We use the variational Bayes technique to perform approximate inference, where the Kullback-Leibler divergence between the true and the approximate posterior is minimized by performing fixed-point iterations. The update equations are easy to implement, and the algorithm can be used in real-time tracking applications. We illustrate the performance of the method in simulations and experiments with real data. The proposed method outperforms the state-of-the-art methods when compared with respect to accuracy and robustness.

stat.ML↗

arXiv2020

Comments on "Spatio-Temporal Gaussian Process Models for Extended and Group Object Tracking with Irregular Shapes"

In the study "Spatio-temporal Gaussian process models for extended and group object tracking with irregular shapes" (IEEE Trans. Veh. Tech., vol. 68, no. 3, pp. 2137-2151, Mar. 2019), the extended object tracking problem was tackled by an approach based on spatio-temporal Gaussian processes (STGP). The performance of the proposed STGP-based trackers was comparatively evaluated through simulations and real data together with another state-of-the-art method (referred to as GP-EKF) proposed in "Extended target tracking using Gaussian processes" (IEEE Trans. Signal Process., vol. 63, no. 16, pp. 4165-4178, Aug. 2015). Unfortunately, we recognized that there are major errors in the implementation of the experiments presented in the STGP paper, which led to incorrect performance evaluation results. In this correspondence, our aim is to share the correct results of these experiments and to respond to some claims regarding GP-EKF, which we believe, would contribute to a better understanding of the methods.

eess.SP↗

arXiv2020

Extended Target Tracking and Classification Using Neural Networks

Extended target/object tracking (ETT) problem involves tracking objects which potentially generate multiple measurements at a single sensor scan. State-of-the-art ETT algorithms can efficiently exploit the available information in these measurements such that they can track the dynamic behaviour of objects and learn their shapes simultaneously. Once the shape estimate of an object is formed, it can naturally be utilized by high-level tasks such as classification of the object type. In this work, we propose to use a naively deep neural network, which consists of one input, two hidden and one output layers, to classify dynamic objects regarding their shape estimates. The proposed method shows superior performance in comparison to a Bayesian classifier for simulation experiments.

eess.SP↗

arXiv2017

Robust Bayesian Filtering and Smoothing Using Student's t Distribution

State estimation in heavy-tailed process and measurement noise is an important challenge that must be addressed in, e.g., tracking scenarios with agile targets and outlier-corrupted measurements. The performance of the Kalman filter (KF) can deteriorate in such applications because of the close relation to the Gaussian distribution. Therefore, this paper describes the use of Student's t distribution to develop robust, scalable, and simple filtering and smoothing algorithms. After a discussion of Student's t distribution, exact filtering in linear state-space models with t noise is analyzed. Intermediate approximation steps are used to arrive at filtering and smoothing algorithms that closely resemble the KF and the Rauch-Tung-Striebel (RTS) smoother except for a nonlinear measurement-dependent matrix update. The required approximations are discussed and an undesirable behavior of moment matching for t densities is revealed. A favorable approximation based on minimization of the Kullback-Leibler divergence is presented. Because of its relation to the KF, some properties and algorithmic extensions are inherited by the t filter. Instructive simulation examples demonstrate the performance and robustness of the novel algorithms.

stat.ME↗

arXiv2016

Distributed Localization of Tree-structured Scattered Sensor Networks

Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or communications among computational agents. Furthermore, some of these distributed algorithms put a considerable computational demand on the agents. In this paper, we show that for tree-structured scattered sensor networks, which are networks that their inter-sensor range measurement graphs have few edges (few range measurements among sensors) and can be represented using a tree, it is possible to devise an efficient distributed localization algorithm that solely relies on second-order methods. Particularly, we apply a state-of-the-art primal-dual interior-point method to a semidefinite relaxation of the maximum-likelihood formulation of the localization problem. We then show how it is possible to exploit the tree-structure in the network and use message-passing or dynamic programming over trees, to distribute computations among different computational agents. The resulting algorithm requires far fewer iterations and communications among agents to converge to an accurate estimate. Moreover, the number of required communications among agents, seems to be less sensitive and more robust to the number of sensors in the network, the number of available measurements and the quality of the measurements. This is in stark contrast to distributed algorithms that rely on first-order methods. We illustrate the performance of our algorithm using experiments based on simulated and real data.

math.OC↗

arXiv2015

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.

eess.SY↗

arXiv2015

Gaussian Mixture Reduction Using Reverse Kullback-Leibler Divergence

We propose a greedy mixture reduction algorithm which is capable of pruning mixture components as well as merging them based on the Kullback-Leibler divergence (KLD). The algorithm is distinct from the well-known Runnalls' KLD based method since it is not restricted to merging operations. The capability of pruning (in addition to merging) gives the algorithm the ability of preserving the peaks of the original mixture during the reduction. Analytical approximations are derived to circumvent the computational intractability of the KLD which results in a computationally efficient method. The proposed algorithm is compared with Runnalls' and Williams' methods in two numerical examples, using both simulated and real world data. The results indicate that the performance and computational complexity of the proposed approach make it an efficient alternative to existing mixture reduction methods.

stat.ML↗

arXiv2013

Recursive maximum likelihood identification of jump Markov nonlinear systems

In this contribution, 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. The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.

stat.CO↗