# Gustaf HendebyLinköping University | LiU · Department of Electrical Engineering (ISY)

Gustaf Hendeby

Docent, PhD, MSc

## About

143

Publications

45,272

Reads

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1,877

Citations

Citations since 2017

Introduction

The focus of Dr. Hendeby's research is statistical and model based sensor fusion; in particular with applications in target tracking, simultaneous localization and mapping (SLAM), positioning, and general nonlinear estimation problems. In doing so he has worked with different Kalman filter approximations (extended and unscented Kalman filter), as well as the particle filter. By understanding these methods better, it will be possible to make the algorithms more accessible by non-experts.

Additional affiliations

January 2016 - present

Education

May 2015 - May 2015

January 2003 - April 2008

August 1998 - December 2002

## Publications

Publications (143)

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The...

Nonlinear Kalman filters are algorithms that approximately solve the Bayesian filtering problem by employing the measurement update of the linear Kalman filter (KF). Numerous variants have been developed over the past decades, perhaps most importantly the popular sampling based sigma point Kalman filters.
In order to make the vast literature access...

A platform for sensor fusion consisting of a standard smartphone equipped with the specially developed Sensor Fusion app is presented. The platform enables real-time streaming of data over WiFi to a computer where signal processing algorithms, e.g., the Kalman filter, can be developed and executed in a Matlab framework. The platform is an excellent...

The particle filter (PF) has during the last decade been proposed for a wide range of localization and tracking applications. There is a general need in such embedded system to have a platform for efficient and scalable implementation of the PF. One such platform is the graphics processing unit (GPU), originally aimed to be used for fast rendering...

This paper investigates the usefulness of multi-frequency received signal strength (RSS) for indoor localization. A collected set of data from four sites containing 7 frequencies from dual receivers and a high accuracy reference positioning system is presented. The collected data is also made publicly available. The data is analyzed with respect to...

Network-centric multitarget tracking under communication constraints is considered, where dimension-reduced track estimates are exchanged. Earlier work on target tracking in a dimension-reduced configuration has focused on fusion aspects only and derived optimal ways of reducing dimensionality based on fusion performance. In this work we propose a...

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 i...

Decentralized state estimation in a communication constrained sensor network is considered. To reduce the communication load only dimension-reduced estimates are exchanged between the networking agents. The considered dimension-reduction is restricted to be a linear mapping from a higher-dimensional space to a lower-dimensional space. The optimal,...

The classical SIR model is a fundamental building block in most epidemiological models. Despite its widespread use, its properties in filtering and estimation applications are much less well explored. Independently of how the basic SIR model is integrated into more complex models, the fundamental question is whether the states and parameters can be...

A theoretically sound likelihood function for passive sonar surveillance using a hydrophone array is presented. The likelihood is derived from first order principles along with the assumption that the source signal can be approximated as white Gaussian noise within the considered frequency band. The resulting likelihood is a nonlinear function of t...

A signal-of-opportunity based method to automatically calibrate the orientations and shapes of a set of hydrophone arrays using the sound emitted from nearby ships, is presented. The calibration problem is formulated as a simultaneous lo-calization and mapping (SLAM) problem, where the locations, orientations, and shapes of the arrays are viewed as...

Long-term autonomy of robots requires localization in an inevitably changing environment, where the robots' knowledge about the surroundings are more or less uncertain. Inspired by methods in target tracking, this paper proposes a multi-hypothesis feature based map representation to provide robust localization under these conditions. It is derived...

A belief-space planning problem for GNSS-denied areas is studied, where knowledge about the landmark density is used as prior, instead of explicit landmark positions. To get accurate predictions of the future information gained from observations, the probability of detecting landmarks needs to be taken into account in addition to the probability of...

Data fusion in a communication constrained sensor network is considered. The problem is to reduce the dimensionality of the joint state estimate without significantly decreasing the estimation performance. A method based on scalar subspace projections is derived for this purpose. We consider the cases where the estimates to be fused are: (i) uncorr...

Linearized Direction of Arrival (LinDoA) is a method for sound source localization that is designed for use with wearable microphone arrays. The method uses a Taylor series expansion of the sound source signal in the time domain to beamform and estimate the direction of arrival. The original method is limited to spatial sampling, but is here genera...

A tightly integrated magnetic-field aided inertial navigation system is presented. The system uses a magnetometer sensor array to measure spatial variations in the local magnetic-field. The variations in the field are --- via a recursively updated polynomial magnetic-field model --- mapped into displacement and orientation changes of the array, whi...

Marginalization enables the particle filter to be applied to non-trivial problems by invoking the Kalman filter to estimate a larger part of the state vector. The marginalized (a.k.a. Rao-Blackwellization) particle filter (MPF) has found many use cases in tracking and navigation applications. These are characterized of having position and its deriv...

A tightly integrated magnetic-field odometry aided INS is presented. The system is based on an array of magnetometers that is used to take images of the filed. From the images the pose change of the system is estimated and used to aid the inertial navigation system. Practically this is done by modeling the variations in the local magnetic-field usi...

A tightly integrated magnetic-field aided inertial navigation system is presented. The system uses a magnetometer sensor array to measure spatial variations in the local magnetic-field. The variations in the field are-via a recursively updated polynomial magnetic-field model-mapped into displacement and orientation changes of the array, which in tu...

The increase in perception capabilities of connected mobile sensor platforms (e.g., self-driving vehicles, drones, and robots) leads to an extensive surge of sensed features at various temporal and spatial scales. Beyond their traditional use for safe operation, available observations could enable to see how and where people move on sidewalks and c...

This paper presents and experimentally evaluates an algorithm named Multiple Generalized Likelihood Ratio (MGLR) for detecting and estimating multiple consecutive measurement biases appearing frequently, in the case of non-redundant sensors, typically the case for a small Unmanned Aerial Vehicle (UAV). The algorithm itself is based on the Generaliz...

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 com...

GNSS receivers are vulnerable to spoofing attacks in which false satellite signals deceive receivers to compute false position and/or time estimates. This work derives and evaluates algorithms that perform spoofing mitigation by utilizing double differences of pseudorange or carrier phase measurements from multiple receivers. The algorithms identif...

Robust and highly accurate position estimation in underground mines is investigated by considering a vehicle equipped with 2D laser scanners. A survey of available methods to process data from such sensors is performed with focus on feature extraction methods. Pros and cons of the usage of different methods for the positioning application with 2D l...

Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the...

A static world assumption is often used when considering the
simultaneous localization and mapping
(SLAM) problem. In reality, especially when long-term autonomy is the objective, this is not valid. This paper studies a scenario where uniquely identifiable landmarks can attend multiple discrete positions, not known
a priori
. Based on a feature...

The increase in perception capabilities of connected mobile sensor platforms (e.g., self-driving vehicles, drones, and robots) leads to an extensive surge of sensed features at various temporal and spatial scales. Beyond their traditional use for safe operation, available observations could enable to see how and where people move on sidewalks and c...

This paper introduces a Poisson multi-Bernoulli mixture (PMBM) filter in which the intensities of target birth and undetected targets are grid-based. A simplified version of the Rao-Blackwellized point mass filter is used to predict the intensity of undetected targets and to initialize tracks of targets detected for the first time. The grid approxi...

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 meth...

This paper introduces a Poisson multi-Bernoulli mixture (PMBM) filter in which the intensities of target birth and undetected targets are grid-based. A simplified version of the Rao-Blackwellized point mass filter is used to predict the intensity of undetected targets, and the density of targets detected for the first time are approximated as Gauss...

A sensor management method for joint multitarget search and track problems is proposed, where a single user-defined parameter allows for a tradeoff between the two objectives. The multitarget density is propagated using the Poisson multi-Bernoulli mixture filter, which eliminates the need for a separate handling of undiscovered targets and provides...

A computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known state-space model with a radial basis function expansion representing unknown system dynamics. Thus, the model is inherently adaptive and can learn unknown and changing system dynamics on-the-...

A novel method for accurate speed estimation of a vehicle using a deep learning convolutional neural network (CNN), with accelerometer and gyroscope measurements as input, is presented. It does not suffer from the fundamental drift problem present in all dead reckoning methods, and yet yields about 2 m/s in accuracy. Efficient drift-free vehicle sp...

The problem of joint classification of gait and device mode from inertial measurement units (IMU) measurements is considered. For this, an approach for computing unique gait signature using measurements collected from body-worn inertial measurement units (IMUs) is proposed.The gait signature represents one full cycle of the human gait, and is suita...

Modern maritime navigation is heavily dependent on satellite systems. Availability of an accurate position is critical for safe operations, but satellite-based navigation systems are vulnerable to interference, jamming, and spoofing. In this work, we propose a method for maritime navigation independent of GNSS, able to provide absolute positioning...

An approach for belief space planning is presented, where knowledge about the landmark density is used as prior, instead of explicit landmark positions. Having detailed maps of landmark positions in a previously unvisited environment is considered unlikely in practice. Instead, it is argued that landmark densities should be used, as they could be e...

We consider a decentralized sensor network of multiple nodes with limited communication capability where the cross-correlations between local estimates are unknown. To reduce the bandwidth the individual nodes determine which subset of local information is the most valuable from a global perspective. Three information selection methods (ISM) are de...

Lidar-based positioning in a 2D map is analyzed as a method to provide a robust, high accuracy, and infrastructure-free positioning system required by the automation development in underground mining. Expressions are derived that highlight separate information contributions to the obtained position accuracy. This is used to develop two new methods...

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 (recursi...

An Informed Path Planning algorithm for multiple agents is presented. It can be used to efficiently utilize available agents when surveying large areas, when total coverage is unattainable. Internally the algorithm has a Probability Hypothesis Density (PHD) representation, inspired by modern multi-target tracking methods, to represent unseen object...

Estimation of the mean of a stochastic variable observed in noise with positive support is considered. It is well known from the literature that order statistics gives one order of magnitude lower estimation variance compared to the best linear unbiased estimator (BLUE). We provide a systematic survey of some common distributions with positive supp...

The angular wheel speed of a vehicle is estimated by tracking the frequency of chassis vibrations measured with an accelerometer. A Bayesian filtering framework is proposed, allowing for straightforward incorporation of supporting information. The framework is evaluated on a large number of experimental test drives, showing comparable performance t...

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 (recursi...

We study the fundamental problem of fusing one round trip time (RTT) observation associated with a serving base station with one time-difference of arrival (TDOA) observation associated to the serving base station and a neighbor base station to localize a 2-D mobile station (MS). This situation can arise in 3GPP Long Term Evolution (LTE) when the n...

This paper addresses the problem of change detection for a quadcopter in the presence of wind disturbances. Different aspects of the quadcopter dynamics and various flight conditions have been investigated. First, the wind is modeled using the Dryden wind model as a sum of a low-frequent and a turbulent part. Since the closed-loop control can compe...

Novel features for joint classification of gait and device modes are proposed and multiple machine learning methods are adopted to jointly classify the modes. The classification accuracy as well as the F1 score of two standard classification algorithms, K-nearest neighbor (KNN) and Gaussian process (GP), are evaluated and compared against a propose...

Posterior Cramer-Rao bounds (CRBs) are derived for the estimation performance of three Gaussian process based state-space models. The parametric CRB is derived for the case with a parametric state transition and a Gaussian process based measurement model. We illustrate the theory with a target tracking example and derive both parametric and posteri...

Tracked targets often exhibit common behaviours due to influences from the surrounding environment, such as wind or obstacles, which usually are modelled as noise. Here these influences are modelled using sparse Gaussian processes that are learned online together with the state inference using an extended Kalman filter. The method can also be appli...

Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a mixture of normal and uniform distribution. This is a problem of great interest specially in cellular positioni...

This paper considers the problem of gathering information about features of interest in adversarial environments using mobile robots equipped with sensors. The problem is formulated as an informative path planning problem where the objective is to maximize the gathered information while minimizing the tracking performance of the adversarial observe...

This paper addresses the problem of retrieving consistent estimates in a distributed network where the communication between the nodes is constrained such that only the diagonal elements of the covariance matrix are allowed to be exchanged. Several methods are developed for preserving and/or recovering consistency under the constraints imposed by t...

An approach for computing unique gait signature using measurements collected from body-worn inertial measurement units (IMUs) is proposed. The gait signature represents one full cycle of the human gait, and is suitable for off-line or on-line classification of the gait mode. The signature can also be used to jointly classify the gait mode and the d...

The unscented Kalman filter (UKF) is a very popular solution for estimation of the state in nonlinear systems. Similar to the extended Kalman filter (EKF) and contrary to the Kalman filter (KF) for linear systems, the UKF provides no guarantees that the filter updates will improve the filtered state estimate. In the past, the iterated EKF (IEKF) ha...

We consider a linear state estimation problem where, in addition to the usual timestamped measurements, observations with uncertain timestamps are available. Such observations could, e.g., come from traces left by a target in a tracking scenario or from witnesses of an event, and have the potential to improve the estimation accuracy significantly....

This paper proposes a method to generate informative trajectories for a mobile sensor that tracks agile targets. The goal is to generate a sensor trajectory that maximizes the tracking performance, captured by a measure of the covariance matrix of the target state estimate. The considered problem is a combination of estimation and control, and is o...

The number of sensors used in tracking scenarios is constantly increasing, this puts high demands on the tracking methods to handle these data streams. Central processing (ideally optimal) puts high demands on the central node, is sensitive to inaccurate sensor parameters, and suffers from the single point of failure problem. Decentralizing the tra...

A model-based method to perform odometry using an array of magnetometers that sense variations in a local magnetic field is presented. The method requires no prior knowledge of the magnetic field, nor does it compile any map of it. Assuming that the local variations in the magnetic field can be described by a curl and divergence free polynomial mod...

The problem of path planning for mobile sensors with the task of target monitoring is considered. A receding horizon optimal control approach based on the information filter is presented, where the limited field of view of the sensor can be modeled by introducing binary variables. The resulting nonlinear mixed integer problem to be solved in each s...

Narrowband Internet of Things (NB-IoT) is an emerging cellular technology designed to target low-cost devices, high coverage, long device battery life (more than ten years), and massive capacity. We investigate opportunities for device tracking in NB-IoT systems using Observed Time Difference of Arrival (OTDOA) measurements. Reference Signal Time D...

Many positioning systems rely on accurate time of arrival measurements. In this paper, we address not only the accuracy but also the relevance of Time of Arrival (TOA) measurement error modeling. We discuss how better knowledge of these errors can improve relative distance estimation, and compare the impact of differently detailed measurement error...

In this work, we estimate a model of the vertical dynamics of a quadcopter and explain how this model can be used for mass estimation and diagnosis of system changes. First, a standard thrust model describing the relation between the calculated control signals of the rotors and the thrust that is commonly used in literature is estimated. The estima...

In polar region operations, drift sea ice positioning and tracking is useful for both scientific and safety reasons. Modeling ice movements has proven difficult, not least due to the lack of information of currents and winds of high enough resolution. Thus, observations of drift ice is essential to an up-to- date ice-tracking estimate. Recent years...