Consistent motion estimation is fundamental for all mobile autonomous systems. While this sounds like an easy task, often, it is not the case because of changing environmental conditions affecting odometry obtained from vision, Lidar, or the wheels themselves. Unsusceptible to challenging lighting and weather conditions, radar sensors are an obvious alternative. Usually, automotive radars return a sparse point cloud, representing the surroundings. Utilizing this information to motion estimation is challenging due to unstable and phantom measurements, which result in a high rate of outliers. We introduce a credible and robust probabilistic approach to estimate the ego-motion based on these challenging radar measurements; intended to be used within a loosely-coupled sensor fusion framework. Compared to existing solutions, evaluated on the popular nuScenes dataset and others, we show that our proposed algorithm is more credible while not depending on explicit correspondence calculation.

Robust and reliable online 3D multi-object tracking is an essential component of autonomous driving. Recent research follows the tracking-by-detection paradigm and focuses mainly on lidar sensors, due to their superior range, resolution and depth accuracy compared to other automotive sensors. This simplifies the challenging data association in crowded urban road scenes, resulting in a predominant status of laser based methods. In contrast, we propose an online 3D multi-object tracker based solely on mono camera images and radar data to promote non-lidar based tracking research. By representing all detections of one frame as a Gaussian mixture model (GMM), we are able to avoid a fixed data association, which may include wrong assumptions. Instead, we assign the GMM to each tracked object and solve the data association implicitly and jointly by estimating the full 3D object tracks in our factor graph based optimization back end. By including all available information from the object detector, our algorithm achieves accurate, robust and reliable tracking results. We conduct real world experiments on the nuScenes tracking data set improving the state-of-the-art for non-lidar based methods from 17.7% to 34.1 % AMOTA.

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set registration or tracking. However, using them with common least squares solvers is still difficult. Existing approaches are either approximations of the true mixture or prone to convergence issues due to their strong nonlinearity. We propose a novel least squares representation of a Gaussian mixture, which is an exact and almost linear model of the corresponding log-likelihood. Our approach provides an efficient, accurate and flexible model for many probabilistic estimation problems and can be used as cost function for least squares solvers. We demonstrate its superior performance in various Monte Carlo experiments, including different kinds of point set registration. Our implementation is available as open source code for the state-of-the-art solvers Ceres and GTSAM.

Factor graph optimization (FGO) recently has attracted attention as an alternative to the extended Kalman filter (EKF) for GNSS-INS integration. This study evaluates both loosely and tightly coupled integrations of GNSS code pseudorange and INS measurements for real-time positioning, using both conventional EKF and FGO with a dataset collected in an urban canyon in Hong Kong. The FGO strength is analyzed by degenerating the FGO-based estimator into an “EKF-like estimator.” In addition, the effects of window size on FGO performance are evaluated by considering both the GNSS pseudorange error models and environmental conditions. We conclude that the conventional FGO outper-forms the EKF because of the following two factors: (1) FGO uses multiple iterations during the estimation to achieve a robust estimation; and (2) FGO better explores the time correlation between the measurements and states, based on a batch of historical data, when the measurements do not follow the Gaussian noise assumption.

Accurate and globally referenced positioning is crucial to autonomous systems with navigation requirements, such as unmanned aerial vehicles (UAV) and autonomous driving vehicles (ADV). GNSS/LiDAR integration is a popular sensor pair that can provide outstanding positioning performance in open areas. However, the accuracy is significantly degraded in urban canyons, due to the excessive unmodeled non-Gaussian GNSS outliers caused by multipath effects and none-line-of-sight (NLOS) receptions. As a result, the violation of the Gaussian assumption can severely distort the sensor fusion process, such as the extended Kalman filter (EKF). To mitigate the effects of these non-Gaussian GNSS outliers, this paper proposes to leverage the Gaussian mixture model (GMM) to describe the potential noise of GNSS positioning and apply it to further sensor fusion. Instead of relying on excessive offline parameterization and tuning, the parameters of the GMM are estimated simultaneously based on the residuals of the GNSS measurements using an expectation-maximization (EM) algorithm. Then the state-of-the-art factor graph optimization (FGO) is applied to integrate the GNSS positioning and LiDAR odometry based on the estimated GMM. The experiment in a typical urban canyon is conducted to validate the performance of the proposed method. The result shows that the GMM can effectively mitigate the effects of GNSS outliers and improves positioning performance.

Accurate and reliable tracking of multiple moving objects in 3D space is an essential component of urban scene understanding. This is a challenging task because it requires the assignment of detections in the current frame to the predicted objects from the previous one. Existing filter-based approaches tend to struggle if this initial assignment is not correct, which can happen easily. We propose a novel optimization-based approach that does not rely on explicit and fixed assignments. Instead, we represent the result of an off-the-shelf 3D object detector as Gaussian mixture model, which is incorporated in a factor graph framework. This gives us the flexibility to assign all detections to all objects simultaneously. As a result, the assignment problem is solved implicitly and jointly with the 3D spatial multi-object state estimation using non-linear least squares optimization. Despite its simplicity, the proposed algorithm achieves robust and reliable tracking results and can be applied for offline as well as online tracking. We demonstrate its performance on the real world KITTI tracking dataset and achieve better results than many state-of-the-art algorithms. Especially the consistency of the estimated tracks is superior offline as well as online.

The recently proposed factor graph optimization (FGO) is adopted to integrate GNSS/INS attracted lots of attention and improved the performance over the existing EKF-based GNSS/INS integrations. However, a comprehensive comparison of those two GNSS/INS integration schemes in the urban canyon is not available. Moreover, the performance of the FGO-based GNSS/INS integration rely heavily on the size of the window of optimization. Effectively tuning the window size is still an open question. To fill this gap, this paper evaluates both loosely and tightly-coupled integrations using both EKF and FGO via the challenging dataset collected in the urban canyon. The detailed analysis of the results for the advantages of the FGO is also given in this paper by degenerating the FGO-based estimator to an EKF like estimator. More importantly, we analyze the effects of window size against the performance of FGO, by considering both the GNSS pseudorange error distribution and environmental conditions.

The integration of the global navigation satellite system (GNSS) and inertial navigation systems (INS) is extensively studied in the past decades for vehicular navigations, such as unmanned aerial vehicles (UAV) and autonomous driving vehicles (ADV). Conventionally, the two most common integration solutions are the loosely-coupled and the tightly-coupled integration using the extended Kalman filter (EKF). The recently proposed factor graph optimization (FGO) is adopted to integrate GNSS/INS which attracted lots of attention and improved the performance over the existing EKF-based GNSS/INS integrations. However, a comprehensive comparison of those two GNSS/INS integration schemes in the urban canyon is not available. Moreover, the accuracy and efficiency of the FGO-based GNSS/INS integration rely heavily on the size of the window of optimization. Effectively tuning the window size is still an open question. To fill this gap, this paper first evaluates both loosely and tightly-coupled integrations using both EKF and FGO via the challenging dataset collected in the urban canyon of Hong Kong.The results show that the FGO-based tightly-coupled GNSS/INS integration obtains the best performance. The detailed analysis of the results for the advantages of the FGO is also given in this paper by degenerating the FGO-based estimator to an EKF like estimator. More importantly, we analyze the effects of window size against the performance of FGO based on the validated dataset, by considering both the GNSS pseudorange error distribution and environmental conditions.

Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their robustness depends on a close approximation of the real error distribution, their parametrization is crucial. We propose a novel approach that allows to adapt a multimodal Gaussian mixture model to the error distribution of a sensor fusion problem. By combining expectation-maximization and non-linear least squares optimization, we are able to provide a computationally efficient solution with well-behaved convergence properties. We demonstrate the performance of these algorithms on several real-world GNSS and indoor localization datasets. The proposed adaptive mixture algorithm outperforms state-of-the-art approaches with static parametrization. Source code and datasets are available under https://mytuc.org/libRSF.

GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding distributions in the sensor fusion algorithm. However, these approaches require prior knowledge about the sensor's distribution, which is often not available. We introduce a novel sensor fusion algorithm based on variational Bayesian inference, that is able to approximate the true distribution with a Gaussian mixture model and to learn its parametrization online. The proposed Incremental Variational Mixture algorithm automatically adapts the number of mixture components to the complexity of the measurement's error distribution. We compare the proposed algorithm against current state-of-the-art approaches using a collection of open access real world datasets and demonstrate its superior localization accuracy.

A fundamental problem of non-linear state estimation in robotics is the violation of assumptions about the sensors' error distribution. State of the art approaches reduce the impact of these violations with robust cost functions or predefined non-Gaussian error models. Both require extensive parameter tuning and fail if the sensors' error characteristic changes over time, due to environmental changes, ageing or sensor malfunctions. We demonstrate how the error distribution itself can be part of the state estimation process. Based on an efficient approximation of a Gaussian mixture, we optimize the sensor model simultaneously during the standard state estimation. Due to an implicit expectation-maximization approach, we achieve a fast convergence without prior knowledge of the true distribution parameters. We implement this self-tuning algorithm in a least-squares optimization framework and demonstrate its real time capability on a real world dataset for satellite localization of a driving vehicle. The resulting estimation quality is superior to previous robust algorithms.

In robotics, non-linear least squares estimation is a common technique for simultaneous localization and mapping. One of the remaining challenges are measurement outliers leading to inconsistency or even divergence within the optimization process. Recently, several approaches for robust state estimation dealing with outliers inside the optimization back-end were presented, but all of them include at least one arbitrary tuning parameter that has to be set manually for each new application. Under changing environmental conditions, this can lead to poor convergence properties and erroneous estimates. To overcome this insufficiency, we propose a novel robust algorithm based on a parameter free probabilistic foundation called Dynamic Covariance Estimation. We derive our algorithm directly from the probabilistic formulation of a Gaussian maximum likelihood estimator. Through including its covariance in the optimization problem, we empower the optimizer to approximate these to the sensor's real properties. Finally, we prove the robustness of our approach on a real world wireless localization application where two similar state-of-the-art algorithms fail without extensive parameter tuning.

—Localization and navigation are two key factors for our globalized world. Driven by cost-effective end-user devices, position estimation using Global Navigation Satellite Systems (GNSS) is common sense. Using the pseudorange measurements as input, many research groups developed their own approaches for estimating position information and evaluated it in simulation or real-world scenarios. Surprisingly, a common publicly available dataset for comparing such algorithms against each other has not been established. We pursue the idea of a uniform, free to use dataset collected by a low-cost receiver in conjunction with associated reference data originating from a high-precision device. For creating representative datasets, we chose four challenging scenarios within two different cities with various influences of urban canyons and surroundings. Based on this, we present first preliminary results from our Factor Graph approach. Our datasets are associated with the smartLoc project and are available online at: www.mytuc.org/GNSS

The SpaceBot Cup 2015 was a national robotics contest among 10 German universities and research institutes. It was organized by the German Aerospace Agency DLR and required 60 minutes of autonomous operation in a challenging environment. The robots had to explore and map the environment, find, transport and manipulate two objects, and navigate back to the landing site without global position information like GPS under very restricted communication. This paper describes our concept, the used systems and algorithms, and our experiences in terms of lessons learned.

While many applications of sensor fusion suffer from the occurrence of outliers, a broad range of outlier robust graph optimization techniques has been developed for simultaneous localization and mapping. In this paper we investigate the performance of some of the most advanced algorithms for a simulated wireless localization setting affected by non-Gaussian errors. With this first analysis we can show some of the advantages and disadvantages that are connected with the different concepts behind Max-Mixture, Generalized iSAM, Switchable Constraints and Dynamic Covariance Scaling.

A standardized characterization method for solar cells is only available for outdoor use. For the supply of wireless sensor nodes with energy harvesting also indoor applications are of interest. Without comparable values it is difficult to select the proper cell for defined environmental conditions. Therefore it is necessary to make an investigation on their behavior individually to be able to make a selection. The work presented here shows the characterization of solar cells according to their spectral behavior, the influence of illumination and the usage of this information about the maximum power to design an energy management. Therefore a test structure with a monochromator, different light sources, source measure units and instruments for measuring intensity and spectra has been developed. The measurements help to select the best solar cell out of a repertory for indoor energy harvesting applications. As for indoor applications also the ability to make use of weak light and a high efficiency is important, the energy management has been improved using a dual DC/DC strategy that allows it to make efficient use of solar cells within difficult situations.

Localization and navigation are two key factors for our globalized world. Driven by cost-effective end-user devices, position estimation using Global Navigation Satellite Systems (GNSS) is common sense. Using the pseudorange measurements as input, many research groups developed their own approaches for estimating position information and evaluated it in simulation or real-world scenarios. Surprisingly, a common publicly available dataset for comparing such algorithms against each other has not been established. We pursue the idea of a uniform, free to use dataset collected by a low-cost receiver in conjunction with associated reference data originating from a high-precision device. For creating representative datasets, we chose four challenging scenarios within two different cities with various influences of urban canyons and surroundings. Based on this, we present first preliminary results from our Factor Graph approach. Our datasets are associated with the smartLoc project and are available online at: www.mytuc.org/GNSS Keywords–GNSS; Low-cost Sensor; NLOS; Reference Data; Urban Canyon