arXiv subjects

Isaac Skog

Publications and source records attributed to Isaac Skog.

35 records · Page 2Linked to original sources

arXiv2023

Extended target tracking utilizing machine-learning software -- with applications to animal classification

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.

cs.CV↗

arXiv2023

Unified Linearization-based Nonlinear Filtering

This letter shows that the following three classes of recursive state estimation filters: standard filters, such as the extended Kalman filter; iterated filters, such as the iterated unscented Kalman filter; and dynamically iterated filters, such as the dynamically iterated posterior linearization filters; can be unified in terms of a general algorithm. The general algorithm highlights the strong similarities between specific filtering algorithms in the three filter classes and facilitates an in-depth understanding of the pros and cons of the different filter classes and algorithms. We end with a numerical example showing the estimation accuracy differences between the three classes of filters when applied to a nonlinear localization problem.

eess.SP↗

arXiv2023

Iterated Filters for Nonlinear Transition Models

A new class of iterated linearization-based nonlinear filters, dubbed dynamically iterated filters, is presented. Contrary to regular iterated filters such as the iterated extended Kalman filter (IEKF), iterated unscented Kalman filter (IUKF) and iterated posterior linearization filter (IPLF), dynamically iterated filters also take nonlinearities in the transition model into account. The general filtering algorithm is shown to essentially be a (locally over one time step) iterated Rauch-Tung-Striebel smoother. Three distinct versions of the dynamically iterated filters are especially investigated: analogues to the IEKF, IUKF and IPLF. The developed algorithms are evaluated on 25 different noise configurations of a tracking problem with a nonlinear transition model and linear measurement model, a scenario where conventional iterated filters are not useful. Even in this "simple" scenario, the dynamically iterated filters are shown to have superior root mean-squared error performance as compared with their respective baselines, the EKF and UKF. Particularly, even though the EKF diverges in 22 out of 25 configurations, the dynamically iterated EKF remains stable in 20 out of 25 scenarios, only diverging under high noise.

eess.SP↗

arXiv2023

Tightly Integrated Motion Classification and State Estimation in Foot-Mounted Navigation Systems

A framework for tightly integrated motion mode classification and state estimation in motion-constrained inertial navigation systems is presented. The framework uses a jump Markov model to describe the navigation system's motion mode and navigation state dynamics with a single model. A bank of Kalman filters is then used for joint inference of the navigation state and the motion mode. A method for learning unknown parameters in the jump Markov model, such as the motion mode transition probabilities, is also presented. The application of the proposed framework is illustrated via two examples. The first example is a foot-mounted navigation system that adapts its behavior to different gait speeds. The second example is a foot-mounted navigation system that detects when the user walks on flat ground and locks the vertical position estimate accordingly. Both examples show that the proposed framework provides significantly better position accuracy than a standard zero-velocity aided inertial navigation system. More importantly, the examples show that the proposed framework provides a theoretically well-grounded approach for developing new motion-constrained inertial navigation systems that can learn different motion patterns.

eess.SP↗

arXiv2023

On the validity of using the delta method for calculating the uncertainty of the predictions from an overparameterized model

The uncertainty in the prediction calculated using the delta method for an overparameterized (parametric) black-box model is shown to be larger or equal to the uncertainty in the prediction of a canonical (minimal) model. Equality holds if the additional parameters of the overparameterized model do not add flexibility to the model. As a conclusion, for an overparameterized black-box model, the calculated uncertainty in the prediction by the delta method is not underestimated. The results are shown analytically and are validated in a simulation experiment where the relationship between the normalized traction force and the wheel slip of a car is modelled using e.g., a neural network

eess.SY↗

arXiv2023

Uncertainty quantification in neural network classifiers -- a local linear approach

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.

cs.LG↗

arXiv2022

Inertial Navigation Using an Inertial Sensor Array

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.

eess.SP↗

arXiv2021

Online Joint State Inference and Learning of Partially Unknown State-Space Models

A computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion representing unknown system dynamics and inherits properties from both physical and data-driven modeling. The method uses an extended Kalman filter approach to jointly estimate the state of the system and learn the unknown system dynamics, via the parameters of the basis function expansion. The key contribution is a computational complexity reduction compared to a similar approach with globally supported basis functions. By using compactly supported radial basis functions and an approximate Kalman gain, the computational complexity is considerably reduced and is essentially determined by the support of the basis functions. The approximation works well when the system dynamics exhibit limited correlation between points well separated in the state-space domain. The method is exemplified via two intelligent vehicle applications where it is shown to: (i) have competitive system dynamics estimation performance compared to the globally supported basis function method, and (ii) be real-time applicable to problems with a large-scale state-space.

eess.SY↗

arXiv2020

Fifteen Years of Progress at Zero Velocity: A Review

Fifteen years have passed since the publication of Foxlin's seminal paper "Pedestrian tracking with shoe-mounted inertial sensors". In addition to popularizing the zero-velocity update, Foxlin also hinted that the optimal parameter tuning of the zero-velocity detector is dependent on, for example, the user's gait speed. As demonstrated by the recent influx of related studies, the question of how to properly design a robust zero-velocity detector is still an open research question. In this review, we first recount the history of foot-mounted inertial navigation and characterize the main sources of error, thereby motivating the need for a robust solution. Following this, we systematically analyze current approaches to robust zero-velocity detection, while categorizing public code and data. The article concludes with a discussion on commercialization along with guidance for future research.

eess.SP↗

arXiv2020

Learning Driver Behaviors Using A Gaussian Process Augmented State-Space Model

An inference method for Gaussian process augmented state-space models are presented. This class of grey-box models enables domain knowledge to be incorporated in the inference process to guarantee a minimum of performance, still they are flexible enough to permit learning of partially unknown model dynamics and inputs. To facilitate online (recursive) inference of the model a sparse approximation of the Gaussian process based upon inducing points is presented. To illustrate the application of the model and the inference method, an example where it is used to track the position and learn the behavior of a set of cars passing through an intersection, is presented. Compared to the case when only the state-space model is used, the use of the augmented state-space model gives both a reduced estimation error and bias.

eess.SP↗

arXiv2019

Zero-Velocity Detection - A Bayesian Approach to Adaptive Thresholding

A Bayesian zero-velocity detector for foot-mounted inertial navigation systems is presented. The detector extends existing zero-velocity detectors based on the likelihood-ratio test, and allows, possibly time-dependent, prior information about the two hypotheses - the sensors being stationary or in motion - to be incorporated into the test. It is also possible to incorporate information about the cost of a missed detection or a false alarm. Specifically, we consider an hypothesis prior based on the velocity estimates provided by the navigation system and an exponential model for how the cost of a missed detection increases with the time since the last zero-velocity update. Thereby, we obtain a detection threshold that adapts to the motion characteristics of the user. Thus, the proposed detection framework efficiently solves one of the key challenges in current zero-velocity-aided inertial navigation systems: the tuning of the zero-velocity detection threshold. A performance evaluation on data with normal and fast gait demonstrates that the proposed detection framework outperforms any detector that chooses two separate fixed thresholds for the two gait speeds.

eess.SP↗

arXiv2016

Map-aided Dead-reckoning --- A Study on Locational Privacy in Insurance Telematics

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.

cs.CR↗

arXiv2016

The $β$-model for Random Graphs --- Regression, Cramér-Rao Bounds, and Hypothesis Testing

We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $β$-model for random graphs by replacing the constant model parameters with regression functions. Cramér-Rao bounds are derived for the undirected $β$-model, the directed $β$-model, and the generalized $β$-model. The corresponding maximum likelihood estimators are compared to the bounds by means of simulations. Moreover, examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance. Last, the applicability of the model is demonstrated using dynamic social network data describing communication among healthcare workers.

stat.ME↗

arXiv2016

Smartphone-based Vehicle Telematics - A Ten-Year Anniversary

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

cs.CY↗

arXiv2016

Inertial Sensor Arrays, Maximum Likelihood, and Cramér-Rao Bound

A maximum likelihood estimator for fusing the measurements in an inertial sensor array is presented. The maximum likelihood estimator is concentrated and an iterative solution method is presented for the resulting low-dimensional optimization problem. The Cramér-Rao bound for the corresponding measurement fusion problem is derived and used to assess the performance of the proposed method, as well as to analyze how the geometry of the array and sensor errors affect the accuracy of the measurement fusion. The angular velocity information gained from the accelerometers in the array is shown to be proportional to the square of the array dimension and to the square of the angular speed. In our simulations the proposed fusion method attains the Cramér-Rao bound and outperforms the current state-of-the-art method for measurement fusion in accelerometer arrays. Further, in contrast to the state-of-the-art method that requires a 3D array to work, the proposed method also works for 2D arrays. The theoretical findings are compared to results from real-world experiments with an in-house developed array that consists of 192 sensing elements.

stat.AP↗

arXiv2013

Cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging

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.

cs.RO↗

arXiv2012

Bayesian Estimation with Distance Bounds

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE) estimate of the state is given by the conditional mean. Since finding the conditional mean requires multidimensional integration, an approximate MMSE estimator is proposed. The performance of the proposed estimator is evaluated in a positioning problem. Finally, the application of the estimator in inequality constrained recursive filtering is illustrated by applying the estimator to a dead-reckoning problem. The MSE of the estimator is compared with two related posterior Cramér-Rao bounds.

math.ST↗