| 1. |
- Boström-Rost, Per, 1988-
(författare)
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On Informative Path Planning for Tracking and Surveillance
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis studies a class of sensor management problems called informative path planning (IPP). Sensor management refers to the problem of optimizing control inputs for sensor systems in dynamic environments in order to achieve operational objectives. The problems are commonly formulated as stochastic optimal control problems, where to objective is to maximize the information gained from future measurements. In IPP, the control inputs affect the movement of the sensor platforms, and the goal is to compute trajectories from where the sensors can obtain measurements that maximize the estimation performance. The core challenge lies in making decisions based on the predicted utility of future measurements.In linear Gaussian settings, the estimation performance is independent of the actual measurements. This means that IPP becomes a deterministic optimal control problem, for which standard numerical optimization techniques can be applied. This is exploited in the first part of this thesis. A surveillance application is considered, where a mobile sensor is gathering information about features of interest while avoiding being tracked by an adversarial observer. The problem is formulated as an optimization problem that allows for a trade-off between informativeness and stealth. We formulate a theorem that makes it possible to reformulate a class of nonconvex optimization problems with matrix-valued variables as convex optimization problems. This theorem is then used to prove that the seemingly intractable IPP problem can be solved to global optimality using off-the-shelf optimization tools.The second part of this thesis considers tracking of a maneuvering target using a mobile sensor with limited field of view. The problem is formulated as an IPP problem, where the goal is to generate a sensor trajectory that maximizes the expected tracking performance, captured by a measure of the covariance matrix of the target state estimate. When the measurements are nonlinear functions of the target state, the tracking performance depends on the actual measurements, which depend on the target’s trajectory. Since these are unavailable in the planning stage, the problem becomes a stochastic optimal control problem. An approximation of the problem based on deterministic sampling of the distribution of the predicted target trajectory is proposed. It is demonstrated in a simulation study that the proposed method significantly increases the tracking performance compared to a conventional approach that neglects the uncertainty in the future target trajectory.
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| 2. |
- Boström-Rost, Per, 1988-
(författare)
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Sensor Management for Target Tracking Applications
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Many practical applications, such as search and rescue operations and environmental monitoring, involve the use of mobile sensor platforms. The workload of the sensor operators is becoming overwhelming, as both the number of sensors and their complexity are increasing. This thesis addresses the problem of automating sensor systems to support the operators. This is often referred to as sensor management. By planning trajectories for the sensor platforms and exploiting sensor characteristics, the accuracy of the resulting state estimates can be improved. The considered sensor management problems are formulated in the framework of stochastic optimal control, where prior knowledge, sensor models, and environment models can be incorporated. The core challenge lies in making decisions based on the predicted utility of future measurements.In the special case of linear Gaussian measurement and motion models, the estimation performance is independent of the actual measurements. This reduces the problem of computing sensing trajectories to a deterministic optimal control problem, for which standard numerical optimization techniques can be applied. A theorem is formulated that makes it possible to reformulate a class of nonconvex optimization problems with matrix-valued variables as convex optimization problems. This theorem is then used to prove that globally optimal sensing trajectories can be computed using off-the-shelf optimization tools. As in many other fields, nonlinearities make sensor management problems more complicated. Two approaches are derived to handle the randomness inherent in the nonlinear problem of tracking a maneuvering target using a mobile range-bearing sensor with limited field of view. The first approach uses deterministic sampling to predict several candidates of future target trajectories that are taken into account when planning the sensing trajectory. This significantly increases the tracking performance compared to a conventional approach that neglects the uncertainty in the future target trajectory. The second approach is a method to find the optimal range between the sensor and the target. Given the size of the sensor's field of view and an assumption of the maximum acceleration of the target, the optimal range is determined as the one that minimizes the tracking error while satisfying a user-defined constraint on the probability of losing track of the target. While optimization for tracking of a single target may be difficult, planning for jointly maintaining track of discovered targets and searching for yet undetected targets is even more challenging. Conventional approaches are typically based on a traditional tracking method with separate handling of undetected targets. Here, it is shown that the Poisson multi-Bernoulli mixture (PMBM) filter provides a theoretical foundation for a unified search and track method, as it not only provides state estimates of discovered targets, but also maintains an explicit representation of where undetected targets may be located. Furthermore, in an effort to decrease the computational complexity, a version of the PMBM filter which uses a grid-based intensity to represent undetected targets is derived.
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| 3. |
- Kullberg, Anton, 1993-
(författare)
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Dynamic rEvolution : Adaptive state estimation via Gaussian processes and iterative filtering
- 2024
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- For virtually every area of science and engineering, state estimation is ubiquitous. Accurate state estimation requires a moderately precise mathematical model of the system, typically based on domain expertise. These models exist for a plethora of applications and available state estimators can generally produce accurate estimates. However, the models usually ignore hard-to-model phenomena, either due to the cost or the difficulty of modeling these characteristics. Further, the most widely used state estimator for nonlinear systems is still the extended Kalman filter (EKF), which may suffer from divergence for complex models, which essentially restricts the complexity of the usable models. Generally speaking, this thesis investigates ways of improving state estimation. Firstly, existing state-space models (SSMs) for target tracking are augmented with a Gaussian process (GP) in order to learn hard-to-model system characteristics online. Secondly, improved linearization-based state estimators are proposed that exhibit favorable robustness properties to the parameters of the noise processes driving the SSM.The first part of the thesis explores joint state estimation and model learning in partially unknown SSMs, where some a priori domain expertise is available, but parts of the model need to be learned online. Paper A combines a linear, a priori identified, SSM with an approximate GP. An EKF is applied to this GP-augmented SSM in order to jointly estimate the state of the system and learn the, a priori, unknown dynamics. This empirically works well and substantially reduces the prediction error of the dynamical model as compared to a non-augmented SSM. Paper B explores ways of reducing the computational complexity of the method of Paper A. Crucially, it uses a compact kernel in the GP, which admits an equivalent basis function (BF) representation where only a few BFs are non-zero at any given system state. This enables a method that is essentially computationally invariant to the number of parameters, where the computational complexity can be tuned by hyperparameters of the BFs.The second part explores iterated filters as a means to increase robustness to improper noise parameter choices. As the nonlinearities in the model are mainly contained in the dynamics, standard iterated filters such as the iterated extended Kalman filter (IEKF) can not be used. Papers C and D develop dynamically iterated filters (DIFs), which is a unified framework for linearization-based iterated filters that deal with nonlinearities in both the dynamics as well as the measurement model. The DIFs are shown to be robust toward improper noise parameter tuning and improve the mean square error (MSE) as compared to their corresponding non-iterated baselines.The third and final part of the thesis considers an alternative bf representation of the GP model, the Hilbert-space Gaussian process (HGP), which is essentially a sinusoidal representation on a compact domain. Paper E identifies previously unutilized Hankel-Toeplitz structure in the HGP, which enables a time complexity for learning that is linear in the number of BFs, without further approximation. Lastly, Paper F improves the computational complexity of prediction in the HGP, by adaptively choosing the most important BFs for prediction in a certain region of the input.
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| 4. |
- Nordlöf, Jonas, 1987-
(författare)
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On Landmark Densities in Minimum-Uncertainty Motion Planning
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Accurate self-positioning of autonomous mobile platforms is important when performing tasks such as target tracking, reconnaissance and resupply missions. Without access to an existing positioning infrastructure, such as Global Navigation Satellite Systems (GNSS), the platform instead needs to rely on its own sensors to obtain an accurate position estimate. This can be achieved by detecting and tracking landmarks in the environment using techniques such as simultaneous localization and mapping (SLAM). However, landmark-based SLAM approaches do not perform well in areas without landmarks or when the landmarks do not provide enough information about the environment. It is therefore desirable to estimate and minimize the position uncertainty while planning how to perform the task. A complicating factor is that the landmarks used in SLAM are not known at the time of planning.In this thesis, it is shown that by integrating SLAM and path planning, paths can be computed that are favorable, from a localization point of view, during motion execution. In particular, it is investigated how prior knowledge of landmark distributions, or densities, can be used to predict the information gained from a region. This is done without explicit knowledge of landmark positions. This prediction is then integrated into the path-planning problem.The first contribution is the introduction of virtual landmarks which represent the expected information in unexplored regions during planning. Two approaches to construct the virtual landmarks that capture the expected information available, based on the beforehand known landmark density, are given. The first approach can be used with any sensor configuration while the second one uses properties of range-bearing sensors, such as LiDAR sensors, to improve the quality of the approximation.The second contribution is a methodology for generating landmark densities from prior data for a forest scenario. These densities were generated from publicly available aerial data used in the Swedish forest industry.The third contribution is an approach to compute the probability of detecting pole-based landmarks in LiDAR point clouds. The approach uses properties of the sensor, the landmark detector, and the probability of occlusion from other landmarks in order to model the detection probability. The model accuracy has been validated in simulations where a real landmark detector and simulated Li-DAR point clouds have been used in a forest scenario.The final contribution is a position-uncertainty aware path-planning approach. This approach utilizes virtual landmarks, the landmark densities, and the land-mark detection probabilities, to produce paths which are advantageous from a positioning point of view. The approach is shown to reduce the platform position uncertainty in several different simulated scenarios without prior knowledge of explicit landmark positions. The computed position uncertainty is shown to be relatively comparable to the uncertainty obtained when executing the path. Furthermore, the generated paths show characteristics that make sense from an application point of view.
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| 5. |
- Forsling, Robin, 1988-
(författare)
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Decentralized Estimation Using Conservative Information Extraction
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Sensor networks consist of sensors (e.g., radar and cameras) and processing units (e.g., estimators), where in the former information extraction occurs and in the latter estimates are formed. In decentralized estimation information extracted by sensors has been pre-processed at an intermediate processing unit prior to arriving at an estimator. Pre-processing of information allows for the complexity of large systems and systems-of-systems to be significantly reduced, and also makes the sensor network robust and flexible. One of the main disadvantages of pre-processing information is that information becomes correlated. These correlations, if not handled carefully, potentially lead to underestimated uncertainties about the calculated estimates. In conservative estimation the unknown correlations are handled by ensuring that the uncertainty about an estimate is not underestimated. If this is ensured the estimate is said to be conservative. Neglecting correlations means information is double counted which in worst case implies diverging estimates with fatal consequences. While ensuring conservative estimates is the main goal, it is desirable for a conservative estimator, as for any estimator, to provide an error covariance which is as small as possible. Application areas where conservative estimation is relevant are setups where multiple agents cooperate to accomplish a common objective, e.g., target tracking, surveillance and air policing. The first part of this thesis deals with theoretical matters where the conservative linear unbiased estimation problem is formalized. This part proposes an extension of classical linear estimation theory to the conservative estimation problem. The conservative linear unbiased estimator (CLUE) is suggested as a robust and practical alternative for estimation problems where the correlations are unknown. Optimality criteria for the CLUE are provided and further investigated. It is shown that finding an optimal CLUE is more complicated than finding an optimal linear unbiased estimator in the classical version of the problem. To simplify the problem, a CLUE that is optimal under certain restrictions will also be investigated. The latter is named restricted best CLUE. An important result is a theorem that gives a closed form solution to a restricted best CLUE. Furthermore, several conservative estimation methods are described followed by an analysis of their properties. The methods are shown to be conservative and optimal under different assumptions about the underlying correlations. The second part of the thesis focuses on practical aspects of the conservative approach to decentralized estimation in configurations where the communication channel is constrained. The diagonal covariance approximation is proposed as a data reduction technique that complies with the communication constraints and if handled correctly can be shown to preserve conservative estimates. Several information selection methods are derived that can reduce the amount of data being transmitted in the communication channel. Using the information selection methods it is possible to decide what information other actors of the sensor network find useful.
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| 6. |
- Kullberg, Anton, 1993-
(författare)
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On Joint State Estimation and Model Learning using Gaussian Process Approximations
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Techniques for state estimation is a cornerstone of essentially every sector of science and engineering, ranging from aeronautics and automotive engineering to economics and medical science. Common to state estimation methods, is the specification of a mathematical model of the underlying system in question. Typically, this is done a priori, i.e., the mathematical model is derived based on known physical relationships and any unknown parameters of the model are estimated from experimental data, before the process of state estimation is even started.Another approach is to jointly estimate any unknown model parameters together with the states, i.e., while estimating the state of the system, the parameters of the model are also estimated (learned). This can be done either offline or it can be done online, i.e., the parameters are learned after the state estimation procedure is “deployed” in practice. A challenge with online parameter estimation, is that it complicates the estimation procedures and typically increases the computational burden, which limits the applicability of such methods to models with only a handful of parameters.This thesis aims to investigate how online joint state estimation and parameter learning can be done using a class of models that is physically interpretable, yet flexible enough to be able to model complex dynamics. Particularly, it is of interest to construct an estimation procedure that is applicable to problems of a large scale, which is challenging due to a high computational burden because the models typically need to contain many parameters. Further, the ability to detect sudden deviations in the behavior of the observed system with respect to the learned model is investigated.The studied model class consists of an a priori specified part providing a coarse description of the dynamics of the considered system and a generic model part that describes any dynamics that is unknown a priori and is to be learnt from data online. In particular, a subclass of these models, in which it is assumed that the spatial correlation of the underlying process is limited, is studied. A computationally efficient method to perform joint state estimation and parameter learning using this model class is proposed. In fact, the proposed method turns out to be nearly computationally invariant to the number of model parameters, enabling online inference in models with a large number of parameters, in the order of tens of thousands or more, while retaining the interpretability. Lastly, the method is applied to the problem of learning motion patterns in ship traffic in a harbor area. The method is shown to accurately capture vessel behavior going in and out of port. Further, a method to detect whether the vessels are behaving as expected, or anomalously, is developed. After initially learning the vessel behaviors from historical data, the anomaly detection method is shown to be able to detect artificially injected anomalies.
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| 7. |
- Nielsen, Kristin, 1986-
(författare)
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Robust LIDAR-Based Localization in Underground Mines
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The mining industry is currently facing a transition from manually operated vehicles to remote or semi-automated vehicles. The vision is fully autonomous vehicles being part of a larger fleet, with humans only setting high-level goals for the autonomous fleet to execute in an optimal way. An enabler for this vision is the presence of robust, reliable and highly accurate localization. This is a requirement for having areas in a mine with mixed autonomous vehicles, manually operated vehicles, and unprotected personnel. The robustness of the system is important from a safety as well as a productivity perspective. When every vehicle in the fleet is connected, an uncertain position of one vehicle can result in the whole fleet begin halted for safety reasons.Providing reliable positions is not trivial in underground mine environments, where access to global satellite based navigation systems is denied. Due to the harsh and dynamically changing environment, onboard positioning solutions are preferred over systems utilizing external infrastructure. The focus of this thesis is localization systems relying only on sensors mounted on the vehicle, e.g., odometers, inertial measurement units, and 2D LIDAR sensors. The localization methods are based on the Bayesian filtering framework and estimate the distribution of the position in the reference frame of a predefined map covering the operation area. This thesis presents research where the properties of 2D LIDAR data, and specifically characteristics when obtained in an underground mine, are considered to produce position estimates that are robust, reliable, and accurate.First, guidelines are provided for how to tune the design parameters associated with the unscented Kalman filter (UKF). The UKF is an algorithm designed for nonlinear dynamical systems, applicable to this particular positioning problem. There exists no general guidelines for how to choose the parameter values, and using the standard values suggested in the literature result in unreliable estimates in the considered application. Results show that a proper parameter setup substantially improves the performance of this algorithm.Next, strategies are developed to use only a subset of available measurements without losing quality in the position estimates. LIDAR sensors typically produce large amounts of data, and demanding real-time positioning information limits how much data the system can process. By analyzing the information contribution from each individual laser ray in a complete LIDAR scan, a subset is selected by maximizing the information content. It is shown how 80% of available LIDAR measurements can be dropped without significant loss of accuracy.Last, the problem of robustness in non-static environments is addressed. By extracting features from the LIDAR data, a computationally tractable localization method, resilient to errors in the map, is obtained. Moving objects, and tunnels being extended or closed, result in a map not corresponding to the LIDAR observations. State-of-the-art feature extraction methods for 2D LIDAR data are identified, and a localization algorithm is defined where features found in LIDAR data are matched to features extracted from the map. Experiments show that regions of the map containing errors are automatically ignored since no matching features are found in the LIDAR data, resulting in more robust position estimates.
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| 8. |
- Boström-Rost, Per, 1988-, et al.
(författare)
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PMBM Filter With Partially Grid-Based Birth Model With Applications in Sensor Management
- 2022
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Ingår i: IEEE Transactions on Aerospace and Electronic Systems. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9251 .- 1557-9603 .- 2371-9877. ; 58:1, s. 530-540
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Tidskriftsartikel (refereegranskat)abstract
- This article 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 approximation can efficiently represents intensities with abrupt changes with relatively few grid points compared to the number of Gaussian components needed in conventional PMBM implementations. This is beneficial in scenarios where the sensors field of view is limited. The proposed method is illustrated in a sensor management setting, where trajectories of sensors with limited fields of view are controlled to search for and track the targets in a region of interest.
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| 9. |
- Jonas, Nordlöf, 1987-, et al.
(författare)
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LiDAR-Landmark Modeling for Belief-Space Planning using Aerial Forest Data
- 2022
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Ingår i: Proceedings of the 25th International Conference on Information Fusion (FUSION). - : IEEE. - 9781737749721 - 9781665489416
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Konferensbidrag (refereegranskat)abstract
- 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 the existence of landmarks. Furthermore, these probabilities need to be calculated from prior data without knowledge of explicit landmarks. It is shown in this paper how the landmark detection probabilities can be generated for a ground-to-ground LiDAR sensor and integrated in the path-planning problem. Moreover, it is also shown how prior information can be generated for a forest scenario. Lastly, the approach is evaluated in a simulated environment using a real landmark detector applied to a simulated point cloud. Compared to previous approaches, an informative path planner, integrating the proposed approximation, is able to reduce the platform pose uncertainty. This is achieved using only prior aerial data of the environment.
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| 10. |
- Nordlöf, Jonas, 1987-, et al.
(författare)
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Improved Virtual Landmark Approximation for Belief-Space Planning
- 2021
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Ingår i: Proceedings of 2021 IEEE 24th International Conference on Information Fusion (FUSION). - : IEEE. - 9781737749714 - 9781665414272 ; , s. 813-820
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Konferensbidrag (refereegranskat)abstract
- A belief-space planning problem for GNSS-denied areas is studied where the location and number of landmarks available are unknown when performing the planning. To be able to plan an informative path in this situation, an algorithm using virtual landmarks to position the platform during the planning phase is studied. The virtual landmarks are selected to capture the expected information available in different regions of the map, based on the beforehand known landmark density. The main contribution of this work is a better approximation of the obtained information from the virtual landmarks and a theoretical study of the properties of the approximation. Furthermore, the proposed approximation, in itself and its use in a path planner, is investigated with successful results.
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