Isaac Skog

Magnus Malmström, Isaac Skog, Daniel Axehill et al.

Classifiers based on neural networks (NN) often lack a measure of uncertainty in the predicted class. We propose a method to estimate the probability mass function (PMF) of the different classes, as well as the covariance of the estimated PMF. First, a local linear approach is used during the training phase to recursively compute the covariance of the parameters in the NN. Secondly, in the classification phase another local linear approach is used to propagate the covariance of the learned NN parameters to the uncertainty in the output of the last layer of the NN. This allows for an efficient Monte Carlo (MC) approach for: (i) estimating the PMF; (ii) calculating the covariance of the estimated PMF; and (iii) proper risk assessment and fusion of multiple classifiers. Two classical image classification tasks, i.e., MNIST, and CFAR10, are used to demonstrate the efficiency the proposed method.

Magnus Malmström, Anton Kullberg, Isaac Skog et al.

This paper considers the problem of detecting and tracking objects in a sequence of images. The problem is formulated in a filtering framework, using the output of object-detection algorithms as measurements. An extension to the filtering formulation is proposed that incorporates class information from the previous frame to robustify the classification, even if the object-detection algorithm outputs an incorrect prediction. Further, the properties of the object-detection algorithm are exploited to quantify the uncertainty of the bounding box detection in each frame. The complete filtering method is evaluated on camera trap images of the four large Swedish carnivores, bear, lynx, wolf, and wolverine. The experiments show that the class tracking formulation leads to a more robust classification.

Anton Kullberg, Frida Viset, Isaac Skog et al.

Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and straightforward model to use, they suffer from quadratic computational complexity in the number of BFs if the predictive variance is to be computed. We develop a method to automatically select the most important BFs for prediction in a sub-domain of the model domain. This significantly reduces the computational complexity of computing predictions while maintaining predictive accuracy. The proposed method is demonstrated using two numerical examples, where reductions up to 50-75% are possible without significantly reducing the predictive accuracy.

Chuan Huang, Gustaf Hendeby, Isaac Skog

Spatially inhomogeneous magnetic fields offer a valuable, non-visual information source for positioning. Among systems leveraging this, magnetic field-based simultaneous localization and mapping (SLAM) systems are particularly attractive. These systems execute positioning and magnetic field mapping tasks simultaneously, and they have bounded positioning error within previously visited regions. However, state-of-the-art magnetic-field SLAM methods typically require low-drift odometry data provided by visual odometry, a wheel encoder, or pedestrian dead-reckoning technology. To address this limitation, this work proposes loosely coupled and tightly coupled inertial magnetic SLAM (IM-SLAM) systems, which use only low-cost sensors: an inertial measurement unit (IMU), 30 magnetometers, and a barometer. Both systems are based on a magnetic-field-aided inertial navigation system (INS) and use error-state Kalman filters for state estimation. The key difference between the two systems is whether the navigation state estimation is done in one or two steps. These systems are evaluated in real-world indoor environments with multi-floor structures. The results of the experiment show that the tightly coupled IM-SLAM system achieves lower positioning errors than the loosely coupled system in most scenarios, with typical errors on the order of meters per 100 meters traveled. These results demonstrate the feasibility of developing a full 3D IM-SLAM system using low-cost sensors. A potential application of the proposed systems is for the positioning of emergency response officers.

Chuan Huang, Gustaf Hendeby, Isaac Skog

This paper presents a new approach for jointly calibrating magnetometers and inertial measurement units, focusing on improving calibration accuracy and computational efficiency. The proposed method formulates the calibration problem as a maximum a posteriori estimation problem, treating both the calibration parameters and orientation trajectory of the sensors as unknowns. This formulation enables efficient optimization with closed-form derivatives. The method is compared against two state-of-the-art approaches in terms of computational complexity and estimation accuracy. Simulation results demonstrate that the proposed method achieves lower root mean square error in calibration parameters while maintaining competitive computational efficiency. Further validation through real-world experiments confirms the practical benefits of our approach: it effectively reduces position drift in a magnetic field-aided inertial navigation system by more than a factor of two on most datasets. Moreover, the proposed method calibrated 30 magnetometers in less than 2 minutes. The contributions include a new calibration method, an analysis of existing methods, and a comprehensive empirical evaluation. Datasets and algorithms are made publicly available to promote reproducible research.

Håkan Carlsson, Isaac Skog, Gustaf Hendeby et al.

We present a comprehensive framework for fusing measurements from multiple and generally placed accelerometers and gyroscopes to perform inertial navigation. Using the angular acceleration provided by the accelerometer array, we show that the numerical integration of the orientation can be done with second-order accuracy, which is more accurate compared to the traditional first-order accuracy that can be achieved when only using the gyroscopes. Since orientation errors are the most significant error source in inertial navigation, improving the orientation estimation reduces the overall navigation error. The practical performance benefit depends on prior knowledge of the inertial sensor array, and therefore we present four different state-space models using different underlying assumptions regarding the orientation modeling. The models are evaluated using a Lie Group Extended Kalman filter through simulations and real-world experiments. We also show how individual accelerometer biases are unobservable and can be replaced by a six-dimensional bias term whose dimension is fixed and independent of the number of accelerometers.

Johan Wahlström, Isaac Skog, João G. P. Rodrigues et al.

We present a particle-based framework for estimating the position of a vehicle using map information and measurements of speed. Two measurement functions are considered. The first is based on the assumption that the lateral force on the vehicle does not exceed critical limits derived from physical constraints. The second is based on the assumption that the driver approaches a target speed derived from the speed limits along the upcoming trajectory. Performance evaluations of the proposed method indicate that end destinations often can be estimated with an accuracy in the order of $100\,[m]$. These results expose the sensitivity and commercial value of data collected in many of today's insurance telematics programs, and thereby have privacy implications for millions of policyholders. We end by discussing the strengths and weaknesses of different methods for anonymization and privacy preservation in telematics programs.

Johan Wahlström, Isaac Skog, Peter Händel

Just like it has irrevocably reshaped social life, the fast growth of smartphone ownership is now beginning to revolutionize the driving experience and change how we think about automotive insurance, vehicle safety systems, and traffic research. This paper summarizes the first ten years of research in smartphone-based vehicle telematics, with a focus on user-friendly implementations and the challenges that arise due to the mobility of the smartphone. Notable academic and industrial projects are reviewed, and system aspects related to sensors, energy consumption, cloud computing, vehicular ad hoc networks, and human-machine interfaces are examined. Moreover, we highlight the differences between traditional and smartphonebased automotive navigation, and survey the state-of-the-art in smartphone-based transportation mode classification, driver classification, and road condition monitoring. Future advances are expected to be driven by improvements in sensor technology, evidence of the societal benefits of current implementations, and the establishment of industry standards for sensor fusion and driver assessment

John-Olof Nilsson, Dave Zachariah, Isaac Skog et al.

The implementation challenges of cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging are discussed and work on the subject is reviewed. System architecture and sensor fusion are identified as key challenges. A partially decentralized system architecture based on step-wise inertial navigation and step-wise dead reckoning is presented. This architecture is argued to reduce the computational cost and required communication bandwidth by around two orders of magnitude while only giving negligible information loss in comparison with a naive centralized implementation. This makes a joint global state estimation feasible for up to a platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion for the considered setup, based on state space transformation and marginalization, is presented. The transformation and marginalization are used to give the necessary flexibility for presented sampling based updates for the inter-agent ranging and ranging free fusion of the two feet of an individual agent. Finally, characteristics of the suggested implementation are demonstrated with simulations and a real-time system implementation.