arXiv subjects

Ondřej Straka

Publications and source records attributed to Ondřej Straka.

At least 19 recordsLinked to original sources

arXiv2026

Fixed-structure Gaussian Mixture Filtering with Robust Measurement Updates under Outliers

Bayesian state estimation for discrete-time nonlinear stochastic systems is considered in the presence of measurement outliers. Building on a fixed-structure Gaussian mixture filtering framework, this paper proposes a robust measurement-update variant in which the predictive density structure is determined by an offline decomposition of the transition density into axis-aligned Gaussian components. This construction maintains the Gaussian mixture structure as deterministic and tunable via the chosen decomposition fidelity. Measurement components affected by outliers are modeled using a Student's-t distribution, and the corresponding update of each Gaussian mixture component is approximated by a variational Bayes procedure. The resulting filter is evaluated in a three-dimensional tracking scenario with range and bearing measurements, where the bearing channel is affected by outliers, modeled as heavy-tailed noise.

eess.SY↗

arXiv2026

GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms

This paper introduces two quasi-metrics for performance assessment of multi-object tracking (MOT) algorithms. One quasi-metric is an extension of the generalised optimal subpattern assignment (GOSPA) metric and measures the discrepancy between sets of objects. The other quasi-metric is an extension of the trajectory GOSPA (T-GOSPA) metric and measures the discrepancy between sets of trajectories. Similar to the GOSPA-based metrics, these quasi-metrics include costs for localisation error for properly detected objects, the number of false objects and the number of missed objects. The T-GOSPA quasi-metric also includes a track switching cost. Differently from the GOSPA and T-GOSPA metrics, the proposed quasi-metrics have the flexibility of penalising missed and false objects with different costs, and the localisation costs are not required to be symmetric. We also explain how to obtain similarity score functions based on these quasi-metrics. The performance of several Bayesian MOT algorithms is assessed with the T-GOSPA quasi-metric via simulations.

cs.CV↗

arXiv2026

Occlusion-Aware Multi-Object Tracking via Expected Probability of Detection

This paper addresses multi-object systems, where objects may occlude one another relative to the sensor. The standard point-object model for detection-based sensors is enhanced so that the probability of detection considers the presence of all objects. A principled tracking method is derived, assigning each object an expected probability of detection, where the expectation is taken over the reduced Palm density, which means conditionally on the object's existence. The assigned probability thus considers the object's visibility relative to the sensor, under the presence of other objects. Unlike existing methods, the proposed method systematically accounts for uncertainties related to all objects in a clear and manageable way. The method is demonstrated through a visual tracking application using the multi-Bernoulli mixture (MBM) filter with marks.

eess.SY↗

arXiv2025

Revisiting Functional Derivatives in Multi-object Tracking

Probability generating functionals (PGFLs) are efficient and powerful tools for tracking independent objects in clutter. It was shown that PGFLs could be used for the elegant derivation of practical multi-object tracking algorithms, e.g., the probability hypothesis density (PHD) filter. However, derivations using PGFLs use the so-called functional derivatives whose definitions usually appear too complicated or heuristic, involving Dirac delta ``functions''. This paper begins by comparing different definitions of functional derivatives and exploring their relationships and implications for practical applications. It then proposes a rigorous definition of the functional derivative, utilizing straightforward yet precise mathematics for clarity. Key properties of the functional derivative are revealed and discussed.

eess.SY↗

arXiv2025

TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking

Multi-object tracking algorithms are deployed in various applications, each with different performance requirements. For example, track switches pose significant challenges for offline scene understanding, as they hinder the accuracy of data interpretation. Conversely, in online surveillance applications, their impact is often minimal. This disparity underscores the need for application-specific performance evaluations that are both simple and mathematically sound. The trajectory generalized optimal sub-pattern assignment (TGOSPA) metric offers a principled approach to evaluate multi-object tracking performance. It accounts for localization errors, the number of missed and false objects, and the number of track switches, providing a comprehensive assessment framework. This paper illustrates the effective use of the TGOSPA metric in computer vision tasks, addressing challenges posed by the need for application-specific scoring methodologies. By exploring the TGOSPA parameter selection, we enable users to compare, comprehend, and optimize the performance of algorithms tailored for specific tasks, such as target tracking and training of detector or re-ID modules.

eess.SY↗

arXiv2025

Model-based Multi-object Visual Tracking: Identification and Standard Model Limitations

This paper uses multi-object tracking methods known from the radar tracking community to address the problem of pedestrian tracking using 2D bounding box detections. The standard point-object (SPO) model is adopted, and the posterior density is computed using the Poisson multi-Bernoulli mixture (PMBM) filter. The selection of the model parameters rooted in continuous time is discussed, including the birth and survival probabilities. Some parameters are selected from the first principles, while others are identified from the data, which is, in this case, the publicly available MOT-17 dataset. Although the resulting PMBM algorithm yields promising results, a mismatch between the SPO model and the data is revealed. The model-based approach assumes that modifying the problematic components causing the SPO model-data mismatch will lead to better model-based algorithms in future developments.

eess.SY↗

arXiv2025

Dual Approach to Inverse Covariance Intersection Fusion

Linear fusion of estimates under the condition of no knowledge of correlation of estimation errors has reached maturity. On the other hand, various cases of partial knowledge are still active research areas. A frequent motivation is to deal with "common information" or "common noise", whatever it means. A fusion rule for a strict meaning of the former expression has already been elaborated. Despite the dual relationship, a strict meaning of the latter one has not been considered so far. The paper focuses on this area. The assumption of unknown "common noise" is formulated first, analysis of theoretical properties and illustrations follow. Although the results are disappointing from the perspective of a single upper bound of mean square error matrices, the partial knowledge demonstrates improvement over no knowledge in suboptimal cases and from the perspective of families of upper bounds.

eess.SP↗

arXiv2025

Interpretable Augmented Physics-Based Model for Estimation and Tracking

State-space estimation and tracking rely on accurate dynamical models to perform well. However, obtaining an vaccurate dynamical model for complex scenarios or adapting to changes in the system poses challenges to the estimation process. Recently, augmented physics-based models (APBMs) appear as an appealing strategy to cope with these challenges where the composition of a small and adaptive neural network with known physics-based models (PBM) is learned on the fly following an augmented state-space estimation approach. A major issue when introducing data-driven components in such a scenario is the danger of compromising the meaning (or interpretability) of estimated states. In this work, we propose a novel constrained estimation strategy that constrains the APBM dynamics close to the PBM. The novel state-space constrained approach leads to more flexible ways to impose constraints than the traditional APBM approach. Our experiments with a radar-tracking scenario demonstrate different aspects of the proposed approach and the trade-offs inherent in the imposed constraints.

eess.SY↗

arXiv2025

Aspects of density approximation by tensor trains

Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the number of the grid points can be mitigated by application of low-rank approximations of multidimensional arrays. Tensor train decompositions represent individual values by the product of matrices. This paper focuses on selected issues that are substantial in state estimation. Namely, the contamination of the density approximations by negative values is discussed first. Functional decompositions of quadratic functions are compared with decompositions of discretised Gaussian densities next. In particular, the connection of correlation with tensor train ranks is explored. Last, the consequences of interpolating the density values from one grid to a new grid are analysed.

eess.SP↗

arXiv2024

Pedestrian Tracking with Monocular Camera using Unconstrained 3D Motion Model

A first-principle single-object model is proposed for pedestrian tracking. It is assumed that the extent of the moving object can be described via known statistics in 3D, such as pedestrian height. The proposed model thus need not constrain the object motion in 3D to a common ground plane, which is usual in 3D visual tracking applications. A nonlinear filter for this model is implemented using the unscented Kalman filter (UKF) and tested using the publicly available MOT-17 dataset. The proposed solution yields promising results in 3D while maintaining perfect results when projected into the 2D image. Moreover, the estimation error covariance matches the true one. Unlike conventional methods, the introduced model parameters have convenient meaning and can readily be adjusted for a problem.

cs.CV↗

arXiv2024

Design of Unitless Normalized Measure of Nonlinearity for State Estimation

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or parameters, or iii) to indicate the possible effect of strong nonlinearity that leads to estimate credibility loss. This paper summarizes the state of the art of nonlinearity measures, focusing on the mean-square-error-based measure of nonlinearity. Its weak point related to unit selection is illustrated, and based on this, requirements for a new measure of nonlinearity are formulated. A new nonlinearity measure that is both unitless and normalized is designed. Its properties are demonstrated using numerical tracking experiments.

eess.SY↗

arXiv2024

Trajectory Tracking for UAVs: An Interpolating Control Approach

Building on our previous work, this paper investigates the effectiveness of interpolating control (IC) for real-time trajectory tracking. Unlike prior studies that focused on trajectory tracking itself or UAV stabilization control in simulation, we evaluate the performance of a modified extended IC (eIC) controller compared to Model Predictive Control (MPC) through both simulated and laboratory experiments with a remotely controlled UAV. The evaluation focuses on the computational efficiency and control quality of real-time UAV trajectory tracking compared to previous IC applications. The results demonstrate that the eIC controller achieves competitive performance compared to MPC while significantly reducing computational complexity, making it a promising alternative for resource-constrained platforms.

eess.SY↗

arXiv2024

UAV Trajectory Planning with Path Processing

This paper examines the influence of initial guesses on trajectory planning for Unmanned Aerial Vehicles (UAVs) formulated in terms of Optimal Control Problem (OCP). The OCP is solved numerically using the Pseudospectral collocation method. Our approach leverages a path identified through Lazy Theta* and incorporates known constraints and a model of the UAV's behavior for the initial guess. Our findings indicate that a suitable initial guess has a beneficial influence on the planned trajectory. They also suggest promising directions for future research.

cs.RO↗

arXiv2024

Mission Planner for UAV Battery Replacement

The paper presents a mission planner for an autonomous unmanned aerial vehicle (UAV) battery management system. The objective of the system is to plan replacements of the UAV's battery on the static battery management stations. The plan ensures that UAVs have sufficient energy to fulfill their long-term mission, which would otherwise be impossible. The paper provides a detailed description of the mission planner and all of its components. The functionality of the planner is successfully demonstrated in simulated multi-UAV multi-station scenarios.

cs.RO↗

arXiv2022

Hybrid Neural Network Augmented Physics-based Models for Nonlinear Filtering

In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come into play or the physics-based model is insufficient (or incomplete) to properly describe the latent phenomenon. One advantage of the APBMs and our estimation procedure is the capability of maintaining the physical interpretability of estimated states. Furthermore, we propose a constraint filtering approach to control the neural network contributions to the overall model. We also exploit assumed density filtering techniques and cubature integration rules to present a flexible estimation strategy that can easily deal with nonlinear models and high-dimensional latent spaces. Finally, we demonstrate the efficacy of our methodology by leveraging a target tracking scenario with nonlinear and incomplete measurement and acceleration models, respectively.

cs.LG↗

arXiv2020

Expectation-Maximization Algorithm for Identification of Mesh-based Compartment Thermal Model of Power Modules

Accurate knowledge of temperatures in power semiconductor modules is crucial for proper thermal management of such devices. Precise prediction of temperatures allows to operate the system at the physical limit of the device avoiding undesirable over-temperatures and thus improve reliability of the module. Commonly used thermal models can be based on detailed expert knowledge of the device's physical structure or on precise and complete temperature distribution measurements. The latter approach is more often used in the industry. Recently, we have proposed a linear time invariant state-space thermal model based on a compartment representation and its identification procedure that is based on the Expectation-Maximization algorithm from incomplete temperature data. However, the model still requires to measure temperatures of all active elements. In this contribution, we aim to relax the need for all measurements. Therefore, we replace the previous dark gray-box approach with a structured compartment model. The structure of the model is designed by a mesh-based discretization of the physical layout of the module. All compartments are assumed to share parameters that are identified from the data of the measured elements. Temperatures of the unmeasured elements are predicted using the shared parameters. Identification of the parameters is possible only with suitable regularization due to limited amount of the data. In particular, the model tightening is accomplished by sharing parameters among compartments and by constraining the process covariance matrix of the model in this contribution. Applicability of the proposed identification procedure is discussed in terms of growing state-space and therefore speeding up of the identification algorithm is suggested. Performance of the proposed approach is tested and demonstrated on simulated data.

eess.SP↗

arXiv2020

Improved Calibration of Numerical Integration Error in Sigma-Point Filters

The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF. The classical quadrature rules used in the sigma-point filters are motivated via polynomial approximation of the integrand, however in the applied context these assumptions cannot always be justified. As a result, quadrature error can introduce bias into estimated moments, for which there is no compensatory mechanism in the classical sigma-point filters. This can lead in turn to estimates and predictions that are poorly calibrated. In this article, we investigate the Bayes-Sard quadrature method in the context of sigma-point filters, which enables uncertainty due to quadrature error to be formalised within a probabilistic model. Our first contribution is to derive the well-known classical quadratures as special cases of the Bayes-Sard quadrature method. Then a general-purpose moment transform is developed and utilised in the design of novel sigma-point filters, so that uncertainty due to quadrature error is explicitly quantified. Numerical experiments on a challenging tracking example with misspecified initial conditions show that the additional uncertainty quantification built into our method leads to better-calibrated state estimates with improved RMSE.

stat.ML↗

arXiv2017

Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise

The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable whose variance provides information about the incurred integration error. Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error. The moment transform is applied in nonlinear sigma-point filtering and evaluated on two numerical examples, where it is shown to outperform the state-of-the-art moment transforms.

stat.ME↗