arXiv subjects

Gustaf Hendeby

Publications and source records attributed to Gustaf Hendeby.

At least 19 recordsLinked to original sources

arXiv2026

A Computationally Efficient Likelihood Approximation for Target Tracking in Time-Varying Multipath Channels

Active sonar target tracking in shallow-water environments is challenging when weak target echoes are embedded in a time-varying background containing structured multipath components. Conventional detect-before-track methods rely on thresholded detections, which may discard weak target evidence or generate false tracks from multipath-induced detections. At low signal-to-noise ratios, track-before-detect filtering can improve tracking performance by exploiting weak target information directly from raw sensor measurements, but directly accounting for the time-varying background leads to a joint target--background inference problem, which is computationally demanding. To address this, this paper develops a physics-motivated and computationally efficient approximation of the raw sensor measurement likelihood for Bernoulli track-before-detect filtering. The multipath components in the background are modeled in the raw sensor measurement domain and recursively tracked using an extended Kalman filter. By neglecting the posterior dependence between the target and background state, the predicted background statistics are used to construct approximate target-present and target-absent likelihoods for the Bernoulli filter. Evaluations using measurements generated from the statistical model and BELLHOP show improved target-confirmation and localization performance over constant-false-alarm-rate-based tracking. These results indicate that explicitly accounting for the background through a computationally tractable approximate likelihood can exploit weak target information without requiring full joint target--background inference.

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arXiv2026

Bernoulli Filtering for Multi-Sensor Tracking with Thresholded Measurements

Target tracking is challenging when sensor detection thresholds cause state-dependent missed detections, particularly in multi-sensor scenarios with clutter and uncertain target existence. A recently developed missed detection framework models detection probability as a function of target state, sensor characteristics, and detection threshold, but it is limited to individual measurements and does not address the recursive tracking problem. This work extends the framework using a Bernoulli filter formulation to jointly handle recursive target tracking, clutter, and target existence uncertainty. A Bernoulli particle filter is evaluated in a simulated 2D multi-sensor tracking scenario with nonlinear measurements, clutter, and detection uncertainty. Incorporating accurate detection threshold knowledge reduces the generalized optimal subpattern assignment (GOSPA) metric by 62.4% compared to a conventional Bernoulli filter with fixed detection probability, while better balancing missed detections and false alarms.

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arXiv2026

Utilizing Missed Detections in Directional Sensitivity-Based DOA Estimation

This paper introduces a signal strength-based direction of arrival (DOA) estimation approach for directional sensors that explicitly accounts for missed detections. In traditional phase-based DOA estimation frameworks, negative information from expected emitters that fall below the detection threshold fall outside the scope of standard measurement models. Unlike phase-based DOA estimation methods, the proposed approach relies only on received signal strength measurements. As a result, missed detections arise naturally from the sensing and detection process and convey valuable information via the known detection thresholds. By incorporating both detected signals and missed detections into the likelihood function, we develop a probabilistic estimation method that fully leverages the underlying measurement and detection models. Simulation results show that the proposed method significantly improves DOA estimation accuracy compared to baseline techniques, particularly in challenging scenarios with high missed-detection rates. Real-world experiments using Bluetooth Low Energy (BLE) signals and directional antennas further validate the effectiveness of the approach, demonstrating substantial performance gains. These findings highlight the value of modeling missed detections in sensor array processing and open new avenues for enhancing localization performance in wireless communication systems.

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arXiv2026

Joint Magnetometer-IMU Calibration via Maximum A Posteriori Estimation

This paper presents a new method for jointly calibrating a magnetometer and inertial measurement unit (IMU), focusing on balancing calibration accuracy and computational efficiency. The proposed method is based on a maximum a posteriori estimation framework, treating both the calibration parameters and orientation trajectory of the sensors as unknowns. This method enables efficient optimization of the calibration parameters using analytically derived derivatives. The performance of the proposed method is compared against that of two state-of-the-art methods. Simulation results demonstrate that the proposed method achieves the lowest root mean square error in calibration parameters, increasing the calibration accuracy by 20-30%, while maintaining competitive computational efficiency. Further validation through real-world experiments confirms the practical benefits of the proposed method. The proposed method calibrated 30 magnetometer-IMU pairs in under two minutes on a consumer-grade laptop, which is one order of magnitude faster than the most accurate state-of-the-art algorithm as implemented in this work. Moreover, when calibrated using the proposed method, a magnetic-field-aided inertial navigation system achieved positioning performance comparable to when it is calibrated with the state-of-the-art method. These results demonstrate that the proposed method is a reliable and effective choice for jointly calibrating magnetometer-IMU pairs.

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arXiv2026

B$^2$F-Map: Crowd-sourced Mapping with Bayesian B-spline Fusion

Crowd-sourced mapping offers a scalable alternative to creating maps using traditional survey vehicles. Yet, existing methods either rely on prior high-definition (HD) maps or neglect uncertainties in the map fusion. In this work, we present a complete pipeline for HD map generation using production vehicles equipped only with a monocular camera, consumer-grade GNSS, and IMU. Our approach includes on-cloud localization using lightweight standard-definition maps, on-vehicle mapping via an extended object trajectory (EOT) Poisson multi-Bernoulli (PMB) filter with Gibbs sampling, and on-cloud multi-drive optimization and Bayesian map fusion. We represent the lane lines using B-splines, where each B-spline is parameterized by a sequence of Gaussian distributed control points, and propose a novel Bayesian fusion framework for B-spline trajectories with differing density representation, enabling principled handling of uncertainties. We evaluate our proposed approach, B$^2$F-Map, on large-scale real-world datasets collected across diverse driving conditions and demonstrate that our method is able to produce geometrically consistent lane-level maps.

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arXiv2026

Tracking Time-Varying Multipath Channels forActive Sonar Applications

Reliable detection and tracking in active sonar require accurate and efficient learning of the acoustic multipath background environment. Conventionally, background learning is performed after transforming measurements into the range-Doppler domain, a step that is computationally expensive and can obscure phase-coherent structure useful for monitoring and tracking. This paper proposes a framework for learning and tracking the multipath background directly in the raw measurement domain. Starting from a wideband Doppler linearization of the impulse response of a time-varying multipath channel, a state-space model with a heteroscedastic measurement equation is derived. This model enables channel tracking using an extended Kalman filter (EKF), and unknown model parameters are learned from the marginalized likelihood. The statistical adequacy of the proposed models is assessed via a p-value significance test. Finally, this paper integrates the learned channel model into a sequential likelihood-ratio test for target detection. BELLHOP-based simulations show that the proposed model better captures channel dynamics induced by sea-surface fluctuations and transmitter and receiver drift, yielding more reliable detection in time-varying shallow-water environments

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arXiv2026

Magnetic-Field-Based Localization Using Spatial Field Variations: Signal Processing Principles, Models, and Challenges

Signal processing has played, and continues to play, a fundamental role in the evolution of modern localization technologies. Localization using spatial variations in the Earth's magnetic field is no exception. It relies on signal-processing methods for statistical state inference, magnetic-field modeling, and sensor calibration. Contemporary localization techniques based on spatial variations in the magnetic field can provide decimeter-level indoor localization accuracy and outdoor localization accuracy on par with strategic-grade inertial navigation systems. This article provides a broad, high-level overview of current signal-processing principles and open research challenges in localization using spatial variations in the Earth's magnetic field. The aim is to provide the reader with an understanding of the similarities and differences among existing key technologies from a statistical signal-processing perspective. To that end, existing key technologies will be presented within a common parametric signal-model framework compatible with well-established statistical inference methods.

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arXiv2025

MI-SLAM: Magnetic Inertial SLAM Systems

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, which may not be available under certain situations. To address this limitation, this work proposes two magnetic inertial SLAM (MI-SLAM) systems --- a loosely coupled version and a tightly coupled version --- that rely solely on low-cost sensors: an inertial measurement unit (IMU) and seven magnetometers. Both systems use a magnetic field aided inertial navigation system (MAINS) to obtain odometry. 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 proposed MI-SLAM systems outperform the state-of-the-art magnetic-inertial odometry system, MAINS, achieving a positioning RMSE below 1 meter on a trajectory lasting approximately 200 seconds. A potential application of the proposed systems is for the positioning of emergency response officers in mine or fire rescue operations, where one cannot rely on a GNSS or visual-based localization system.

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arXiv2025

Performance Analysis of Communication Signals for Localization in Underwater Sensor Networks

Efficient localization in underwater sensor networks faces challenges due to limited bandwidth, energy constraints, and hardware complexity. Traditional systems separate sensing and communication, often resulting in inefficient resource usage. To address this, integrated sensing and communication (ISAC) has emerged, leveraging shared waveforms for both functions. This paper investigates the feasibility of using communication-centric waveforms for underwater localization. Specifically, we evaluate the performance of super-permutated frequency shift keying and multiple frequency shift keying signals using a Cramer-Rao lower bound framework in a simplified bistatic scenario. Simulations incorporate temporally correlated autoregressive AR(1) noise and varying signal-to-noise ratio levels to assess localization accuracy. A comparative analysis with a traditional sonar waveform, linear frequency modulated signal, highlights the potential of communication signals for dual-purpose ISAC applications in bistatic sonar configurations in underwater environments.

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arXiv2025

Road Roughness Estimation via Fusion of Standard Onboard Automotive Sensors

Road roughness significantly affects vehicle vibrations and ride quality. We introduce a Kalman filter (KF)-based method for estimating road roughness in terms of the international roughness index (IRI) by fusing inertial and speed measurements, offering a cost-effective solution for pavement monitoring. The method involves system identification on a physical vehicle to estimate realistic model parameters, followed by KF-based reconstruction of the longitudinal road profile to compute IRI values. It explores IRI estimation using vertical and lateral vibrations, the latter more common in modern vehicles. Validation on 230 km of real-world data shows promising results, with IRI estimation errors ranging from 1% to 10% of the reference values. However, accuracy deteriorates significantly when using only lateral vibrations, highlighting their limitations. These findings demonstrate the potential of KF-based estimation for efficient road roughness monitoring.

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arXiv2025

Matrix-Valued Measures and Wishart Statistics for Target Tracking Applications

Ensuring sufficiently accurate models is crucial in target tracking systems. If the assumed models deviate too much from the truth, the tracking performance might be severely degraded. While the models are usually defined using multivariate conditions, the measures used to validate them are most often scalar-valued. In this paper, we propose matrix-valued measures for both offline and online assessment of target tracking systems. Recent results from Wishart statistics, and approximations thereof, are adapted and it is shown how these can be incorporated to infer statistical properties for the eigenvalues of the proposed measures. In addition, we relate these results to the statistics of the baseline measures. Finally, the applicability of the proposed measures are demonstrated using two important problems in target tracking: (i) distributed track fusion design; and (ii) filter model mismatch detection.

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arXiv2025

On the Connection Between Magnetic-Field Odometry Aided Inertial Navigation and Magnetic-Field SLAM

Magnetic-field simultaneous localization and mapping (SLAM) using consumer-grade inertial and magnetometer sensors offers a scalable, cost-effective solution for indoor localization. However, the rapid error accumulation in the inertial navigation process limits the feasible exploratory phases of these systems. Advances in magnetometer array processing have demonstrated that odometry information, i.e., displacement and rotation information, can be extracted from local magnetic field variations and used to create magnetic-field odometry-aided inertial navigation systems. The error growth rate of these systems is significantly lower than that of standalone inertial navigation systems. This study seeks an answer to whether a magnetic-field SLAM system fed with measurements from a magnetometer array can indirectly extract odometry information -- without requiring algorithmic modifications -- and thus sustain longer exploratory phases. The theoretical analysis and simulation results show that such a system can extract odometry information and indirectly create a magnetic field odometry-aided inertial navigation system during the exploration phases. However, practical challenges related to map resolution and computational complexity remain significant.

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arXiv2024

Broadband Passive Sonar Track-Before-Detect Using Raw Acoustic Data

This article concerns the challenge of reliable broadband passive sonar target detection and tracking in complex acoustic environments. Addressing this challenge is becoming increasingly crucial for safeguarding underwater infrastructure, monitoring marine life, and providing defense during seabed warfare. To that end, a solution is proposed based on a vector-autoregressive model for the ambient noise and a heavy-tailed statistical model for the distribution of the raw hydrophone data. These models are integrated into a Bernoulli track-before-detect (TkBD) filter that estimates the probability of target existence, target bearing, and signal-to-noise ratio (SNR). The proposed solution is evaluated on both simulated and real-world data, demonstrating the effectiveness of the proposed ambient noise modeling and the statistical model for the raw hydrophone data samples to obtain early target detection and robust target tracking. The simulations show that the SNR at which the target can be detected is reduced by 4 dB compared to when using the standard constant false alarm rate detector-based tracker. Further, the test with real-world data shows that the proposed solution increases the target detection distance from 250 m to 390 m. The presented results illustrate that the TkBD technology, in combination with data-driven ambient noise modeling and heavy-tailed statistical signal models, can enable reliable broadband passive sonar target detection and tracking in complex acoustic environments and lower the SNR required to detect and track targets.

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arXiv2024

An Observability-Constrained Magnetic Field-Aided Inertial Navigation System -- Extended Version

Maintaining consistent uncertainty estimates in localization systems is crucial as the perceived uncertainty commonly affects high-level system components, such as control or decision processes. A method for constructing an observability-constrained magnetic field-aided inertial navigation system is proposed to address the issue of erroneous yaw observability, which leads to inconsistent estimates of yaw uncertainty. The proposed method builds upon the previously proposed observability-constrained extended Kalman filter and extends it to work with a magnetic field-based odometry-aided inertial navigation system. The proposed method is evaluated using simulation and real-world data, showing that (i) the system observability properties are preserved, (ii) the estimation accuracy increases, and (iii) the perceived uncertainty calculated by the EKF is more consistent with the true uncertainty of the filter estimates.

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arXiv2024

Adaptive Basis Function Selection for Computationally Efficient Predictions

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.

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arXiv2024

Joint State and Parameter Estimation Using the Partial Errors-in-Variables Principle

This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least squares, where the uncertainty in the parameter prior is explicitly considered. Based thereon, the PEIV regression can be solved iteratively through the Kalman smoothing and the regularized least squares for estimating the state and the parameter, respectively. The simulations demonstrate improved accuracy of the proposed method compared to existing approaches, including the joint maximum a posterior-maximum likelihood, the expectation maximisation, and the augmented state extended Kalman smoother.

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arXiv2024

Bayesian Simultaneous Localization and Multi-Lane Tracking Using Onboard Sensors and a SD Map

High-definition map with accurate lane-level information is crucial for autonomous driving, but the creation of these maps is a resource-intensive process. To this end, we present a cost-effective solution to create lane-level roadmaps using only the global navigation satellite system (GNSS) and a camera on customer vehicles. Our proposed solution utilizes a prior standard-definition (SD) map, GNSS measurements, visual odometry, and lane marking edge detection points, to simultaneously estimate the vehicle's 6D pose, its position within a SD map, and also the 3D geometry of traffic lines. This is achieved using a Bayesian simultaneous localization and multi-object tracking filter, where the estimation of traffic lines is formulated as a multiple extended object tracking problem, solved using a trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. In TPMBM filtering, traffic lines are modeled using B-spline trajectories, and each trajectory is parameterized by a sequence of control points. The proposed solution has been evaluated using experimental data collected by a test vehicle driving on highway. Preliminary results show that the traffic line estimates, overlaid on the satellite image, generally align with the lane markings up to some lateral offsets.

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arXiv2024

MAINS: A Magnetic Field Aided Inertial Navigation System for Indoor Positioning

A Magnetic field Aided Inertial Navigation System (MAINS) for indoor navigation is proposed in this paper. MAINS leverages an array of magnetometers to measure spatial variations in the magnetic field, which are then used to estimate the displacement and orientation changes of the system, thereby aiding the inertial navigation system (INS). Experiments show that MAINS significantly outperforms the stand-alone INS, demonstrating a remarkable two orders of magnitude reduction in position error. Furthermore, when compared to the state-of-the-art magnetic-field-aided navigation approach, the proposed method exhibits slightly improved horizontal position accuracy. On the other hand, it has noticeably larger vertical error on datasets with large magnetic field variations. However, one of the main advantages of MAINS compared to the state-of-the-art is that it enables flexible sensor configurations. The experimental results show that the position error after 2 minutes of navigation in most cases is less than 3 meters when using an array of 30 magnetometers. Thus, the proposed navigation solution has the potential to solve one of the key challenges faced with current magnetic-field simultaneous localization and mapping (SLAM) solutions: the very limited allowable length of the exploration phase during which unvisited areas are mapped.

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