Ondřej Straka

Tales Imbiriba, Ahmet Demirkaya, Jindřich Duník et al.

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.

Jan Krejčí, Oliver Kost, Yuxuan Xia et al.

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.

Nir Shlezinger, Guy Revach, Anubhab Ghosh et al.

The Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple state-space (SS) models, which may be crude and inaccurate descriptions of the underlying dynamics. Emerging data-centric artificial intelligence (AI) techniques tackle these tasks using deep neural networks (DNNs), which are model-agnostic. Recent developments illustrate the possibility of fusing DNNs with classic Kalman-type filtering, obtaining systems that learn to track in partially known dynamics. This article provides a tutorial-style overview of design approaches for incorporating AI in aiding KF-type algorithms. We review both generic and dedicated DNN architectures suitable for state estimation, and provide a systematic presentation of techniques for fusing AI tools with KFs and for leveraging partial SS modeling and data, categorizing design approaches into task-oriented and SS model-oriented. The usefulness of each approach in preserving the individual strengths of model-based KFs and data-driven DNNs is investigated in a qualitative and quantitative study, whose code is publicly available, illustrating the gains of hybrid model-based/data-driven designs. We also discuss existing challenges and future research directions that arise from fusing AI and Kalman-type algorithms.

Jan Krejčí, Oliver Kost, Ondřej Straka et al.

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.

Jan Krejčí, Oliver Kost, Ondřej Straka et al.

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.

Jan Krejčí, Oliver Kost, Yuxuan Xia et al.

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.

Ángel F. García-Fernández, Jinhao Gu, Lennart Svensson et al.

This paper introduces two quasi-metrics for performance assessment of multi-object tracking (MOT) algorithms. In particular, 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. These properties can be useful in MOT evaluation in certain applications. The performance of several Bayesian MOT algorithms is assessed with the T-GOSPA quasi-metric via simulations.

Jakub Prüher, Toni Karvonen, Chris J. Oates et al.

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.

Jakub Prüher, Filip Tronarp, Toni Karvonen et al.

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.

Jakub Prüher, Ondřej Straka

Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for Gaussian random variables which accounts for the error in the numerically computed mean. We employ an instance of Bayesian quadrature, called Gaussian process quadrature (GPQ), which allows us to treat the integral itself as a random variable, where the integral variance informs about the incurred integration error. Experiments on the coordinate transformation and nonlinear filtering examples show that the proposed GPQ moment transform performs better than the classical transforms.