In 2027 the Large Hadron Collider (LHC) at CERN will enter a high luminosity phase, deliver- ing 3000 fb 1 over the course of ten years. The High Luminosity LHC (HL-LHC) will increase the instantaneous luminosity delivered by a factor of 5 compared to the current operation pe- riod. This will impose significant technical challenges on all aspects of the ATLAS detector but particularly the Inner Detector, trigger, and data acquisition systems. In addition, many of the components of the Inner Detector are reaching the end of their designed lifetime and will need to be exchanged. As such, the Inner Detector will be entirely replaced by an all silicon tracker, known as the Inner Tracker (ITk). The layout of the Pixel and strip detectors will be optimised for the upgrade and will extend their forward coverage. To reduce the per-pixel hit rate and explore novel techniques for deal- ing with the conditions in HL-LHC, an inter-experiment collaboration called RD53 has been formed. RD53 is tasked with producing a front-end readout chip to be used as part of hybrid Pixel detectors that can deal with the high multiplicity environment in the HL-LHC. A silicon sensor, which makes up the other half of the hybrid Pixel detector, must also be designed to cope with the high fluences in HL-LHC. Significant damage will be caused by non- ionising energy loss in the sensor over its lifetime. This damage must be incorporated into the detector simulation both to predict the detector performance at specific conditions and to understand the e↵ects of radiation damage on data taking. The implementation of radiation damage in the ATLAS simulation framework is discussed in this thesis. Collisions produced by the HL-LHC also presents a challenge for the current track reconstruc- tion software. High luminosity is obtained, in part, by increasing the number of interactions per bunch crossing, which in turn increases the time taken for track reconstruction. Various ap- proaches to circumvent the strain on projected resources are being explored, including porting existing algorithms to parallel architectures. A popular algorithm used in track reconstruction, the Kalman filter, has been implemented in a neuromorphic architecture: IBM’s TrueNorth. The limits of using such an architecture for tracking, as well as how its performance compares to a non-spiking Kalman filter implementation, are explored in this thesis.

Underwater navigation faces many problems with accurately estimating the absolute positionof an underwater vehicle. Neither Global Positioning system (GPS) nor Long Baseline (LBL) orShort Baseline (SBL) are possible to use for a military vehicle acting under stealth, since thesetechniques require the vehicle to be in the vicinity of a nearby ship or to surface and raise its antenna. It will therefore have to rely on sensors such as Doppler Velocity Log (DVL) and a compassto estimate its absolute position using dead reckoning or an Inertial Navigation System (INS). Thisthesis presents an alternative Multiple model Kalman Filter (KF) to the existing Multiple ModelAdaptive Estimator (MMAE) algorithm using n-Modular Redundancy (NMR), in order to gaina more accurate result than with a single KF. By analyzing how different amounts of filters andvoter types affect the accuracy and precision of the velocity and heading estimations, the potentialbenefits and drawbacks can be drawn for each solution. Such benefits and drawbacks were alsovisually evaluated in a Matlab script which was used to calculate the coordinates using the velocityand heading from the speed sensors and compass, without the need for running the filtered states onthe vehicle’s navigation system. The results present the potential of using a multiple model KF inthe form of an NMR, which was demonstrated by both the amount of reduced noise in the velocitystates and how the filters were used in a virtual navigation system created in Matlab.

Time series data is very common in our daily life. Since they are related to time, most of them show a periodicity. The existence of this periodic in uence leads to our research problem, seasonal adjustment. Seasonal adjustment is generally applied around us, especially in areas of economy and nance. Over the last few decades, scholars around the world made a lot of contributions in this area, and one of the latest methods is X-13ARIMA-SEATS, which is built on ARIMA models and linear lters. On the other hand, state space modelling (abbreviated to SSM) is also a popular method to solve this problem and researchers including J. Durbin, S.J. Koopman and and A. Harvery have contributed a lot of work to it. Unlike linear lters and ARIMA models, the study on SSM starts relatively late, thus it has not been studied and developed widely for the seasonal adjustment problem. And SSMs have a lot advantages over those ARIMA-based and lter-based methods such as exibility, the understandable structure and the potential to do partial pooling, but in practice, its default decomposition result behaves bad in some cases, such as excessively spiky trend series; on the contrary, X-13ARIMA-SEATS could output good decomposition result for us to analyze, but it can't be tweaked or combined as easily as generative models and behaves like a black-box. In this paper, we shall use Bayesian inference to combine both methods' characteristics together. Simultaneously, to show the advantage of using SSMs concretely, we shall give a simple application in partial pooling and talk about how to apply the Bayesian analysis to partial pooling.

This thesis presents our efforts to build an operational ensemble forecasting system for the Red Sea, based on the Data Research Testbed (DART) package for ensemble data assimilation and the Massachusetts Institute of Technology general circulation ocean model (MITgcm) for forecasting. The Red Sea DART-MITgcm system efficiently integrates all the ensemble members in parallel, while accommodating different ensemble assimilation schemes. The promising ensemble adjustment Kalman filter (EAKF), designed to avoid manipulating the gigantic covariance matrices involved in the ensemble assimilation process, possesses relevant features required for an operational setting. The need for more efficient filtering schemes to implement a high resolution assimilation system for the Red Sea and to handle large ensembles for proper description of the assimilation statistics prompted the design and implementation of new filtering approaches. Making the most of our world-class supercomputer, Shaheen, we first pushed the system limits by designing a fault-tolerant scheduler extension that allowed us to test for the first time a fully realistic and high resolution 1000 ensemble members ocean ensemble assimilation system. In an operational setting, however, timely forecasts are of essence, and running large ensembles, albeit preferable and desirable, is not sustainable. New schemes aiming at lowering the computational burden while preserving reliable assimilation results, were developed. The ensemble Optimal Interpolation (EnOI) algorithm requires only a single model integration in the forecast step, using a static ensemble of preselected members for assimilation, and is therefore computationally significantly cheaper than the EAKF. To account for the strong seasonal variability of the Red Sea circulation, an EnOI with seasonally-varying ensembles (SEnOI) was first implemented. To better handle intra-seasonal variabilities and enhance the developed seasonal EnOI system, an automatic procedure to adaptively select the ensemble members through the assimilation cycles was then introduced. Finally, an efficient Hybrid scheme combining the dynamical flow-dependent covariance of the EAKF and a static covariance of the EnOI was proposed and successfully tested in the Red Sea. The developed Hybrid ensemble data assimilation system will form the basis of the first operational Red Sea forecasting system that is currently being implemented to support Saudi Aramco operations in this basin.

Tradition spacecraft proximity operations require large and expensive on-board sensors and significant ground support. Relative angle measurements can be obtained from small, simple, and inexpensive on-board sensors, but have not traditionally been used for proximity operation because of difficulty generating rang information. In this thesis it is shown that useful relative range data can be generated provided that the spacecraft is experiencing a small continuous thrust such as would be provided by a low-thrust propulsion system.

Angles-only navigation is simple, robust, and well proven in many applications. However, it is sometimes ill-conditioned for orbital rendezvous and proximity operations because, without a direct range measurement, the distance to approaching satellites must be estimated by firing thrusters and observing the change in the target's bearing. Nevertheless, the simplicity of angles-only navigation gives it great appeal. The viability of this technique for relative navigation is examined by building a high-fidelity simulation and evaluating the sensitivity of the system to sensor errors. The relative performances of square-root filtering methods, including Potter, Carlson, and UD factorization filters, are compared to the conventional and Joseph formulations. Filter performance is evaluated during closed-loop "station keeping" operations in simulation.

In this master thesis, image processing methods and methods for statistical modeling of motion are presented. First, description methods of image processing, such as background subtraction method used for object detection, are presented. Next, description of morphological operations, such as dilatation and erosion, is done. Finally, methods for statistical modeling, such as Kalman filter and particle filters, are shown.

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This thesis considers the problem of using signals of opportunity (SOO) with known direction of arrival (DOA) for aircraft positioning. SOO is a collective name for a wide range of signals not intended for navigation but which can be intercepted by the radar warning system on an aircraft. These signals can for example aid an unassisted inertial navigation system (INS) in areas where the global navigation satellite system (GNSS) is inaccessible. Challenges arise as the signals are transmitted from non-controllable sources without any guarantee of quality and availability. Hence, it is important that any estimation method utilising SOO is robust and statistically consistent in case of time-varying signals of different quality, missed detections and unreliable signals such as outliers. The problem is studied using SOO sources with either known or unknown locations. An extended Kalman filter (EKF) based solution is proposed for the first case which is shown to significantly improve the localisation performance compared to an unassisted INS in common scenarios. Yet, a number of factors affect this performance, including the measurement noise variance, the signal rate and the availability of known source locations. An outlier rejection mechanism is developed which is shown to increase the robustness of the suggested method. A numerical evaluation indicates that statistical consistency can be maintained in many situations even with the above-mentioned challenges. An EKF based simultaneous localisation and mapping (SLAM) solution is proposed for the case with unknown SOO source locations. The flight trajectory and initialisation process of new SOO sources are critical in this case. A method based on nonlinear least squares is proposed for the initialisation process, where new SOO sources are only allowed to be initialised in the filter once a set of requirements are fulfilled. This method has shown to increase the robustness during initialisation, when the outlier rejection is not applicable. When combining known and unknown SOO source locations, a more stable localisation solution is obtained compared to when all locations are unknown. Applicability of the proposed solution is verified by a numerical evaluation. The computational time increases cubically with the number of sources in the state and quadratically with the number of measurements. The time is substantially increased during landmark initialisation.