Typical iterated filters, such as the iterated extended Kalman filter (IEKF), KF (IUKF), and , have been developed to improve the linearization point (or density) ofthe likelihood linearization in the well-known extended KF (EKF) and unscented KF (UKF). A shortcoming of typical iterated filters is thatthey do not treat the linearization of the transition model of the system. To remedy this shortcoming, we introduce dynamically iterated filters (DIFs), a unified framework for iterated linearization-based nonlinear filters that deals with nonlinearities in both the transition modeland the likelihood, thereby constituting a generalization of the afore mentioned iterated filters. We further establish a relationship between the general DIF and the approximate iterated Rauch–Tung–Striebel smoother. This relationship allows for a Gauss–Newton interpretation, which in turn enables explicit step-size correction, leading to dampedversions of the DIFs. The developed algorithms, both damped and non-damped, are numerically demonstrated in three examples, showing superior mean squared error as well as improved parameter tuning robustness as compared to the analogous standard iterated filters.

A method for obstacle detection using the sound that a drone naturally emits is proposed.  The sound emitted from a vehicle, ego-noise, is often considered a complicating factor for mission fulfilment, without purpose.  The idea in this paper is to utilise this ego-noise for obstacle detection, being the first to perform practical experiments of this.  Adding a few microphones to the vehicle, the ego-noise is utilised as the sound source for echolocation.  The method consists of auto-correlating the received signals to estimate echo delays, using the known array geometry and signal propagation speed to relate delays to distances, and then beamforming to position targets.  A proof-of-concept has been constructed, and promising results are presented for experiments in a controlled environment.

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.

The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. These properties result in a favorable data-independent O(M³) computational complexity during hyperparameter optimization but require a dominating one-time precomputation of the precision matrix costing O(NM²) operations. In this paper, we lower this dominating computational complexity to O(NM) with no additional approximations. We can do this because we realize that the precision matrix can be split into a sum of Hankel-Toeplitz matrices, each having O(M) unique entries. Based on this realization we propose computing only these unique entries at O(NM) costs. Further, we develop two theorems that prescribe sufficient conditions for the complexity reduction to hold generally for a wide range of other approximate GP models, such as the Variational Fourier Feature (VFF) approach. The two theorems do this with no assumptions on the data and no additional approximations of the GP models themselves. Thus, our contribution provides a pure speed-up of several existing, widely used, GP approximations, without further approximations.

This letter 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. 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.

This paper addresses the trade-off between time and energy-efficiency for the problem of loading and unloading a ship. Container height constraints and energy consumption and regeneration are dealt with. We build upon a previous work that introduced a coordinate system suitable to deal with container avoidance constraints and incorporate the energy related modeling. In addition to changing the coordinate system, standard epigraph reformulations result in an optimal control problem with improved numerical properties. The trade-of is dealt with through the use of weighting of the total time and energy consumption in the cost function. An illustrative example is provided, demonstrating that the energy consumption can be substantially reduced while retaining approximately the same loading time.

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.

This letter investigates relationships between iterated filtering algorithms based on statistical linearization, such as the iterated unscented Kalman filter (IUKF), and filtering algorithms based on quasi–Newton (QN) methods, such as the QN iterated extended Kalman filter (QN–IEKF). Firstly, it is shown that the IUKF and the iterated posterior linearization filter (IPLF) can be viewed as QN algorithms, by finding a Hessian correction in the QN –IEKF such that the IPLF iterate updates are identical to that of the QN–IEKF. Secondly, it is shown that the IPLF/ IUKF update can be rewritten such that it is approximately identical to the QN–IEKF, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.

A new approach to anomaly detection in maritime traffic based on Automatic Identification System (AIS) data is proposed. The method recursively learns a model of the nominal vessel routes from AIS data and simultaneously estimates the current state of the vessels. A distinction between anomalies and measurement outliers is made and a method to detect and distinguish between the two is proposed. The anomaly and outlier detection is based on statistical testing relative to the current motion model. The proposed method is evaluated on historical AIS data from a coastal area in Sweden and is shown to detect previously unseen motions.

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.