Autonomous driving is a rapidly growing sector that is attracting increasing attention from industry and academia. The rise of deep learning techniques has made it possible for autonomous vehicles to perceive the environment around them, including detecting objects of interest around the vehicle. The technology used to detect objects is quite dependent on sensors such as cameras, radars, and LiDARs, which are commonly used in autonomous vehicles for 3D object detection. Current state-of-the-art 3D object detection methods often use a fusion of LiDAR and camera features. As such, the perception abilities of autonomous vehicles are susceptible to sensor corruptions, whether the corruptions are caused by internal sensor faults or extreme environmental conditions. A particularly hazardous corruption occurs when a LiDAR does not record points in certain regions, which can be caused, among other reasons, by dirt accumulation on the LiDAR, a wet ground, and dark-colored objects, which can absorb LiDAR beams or reflect them away from the LiDAR. Corruptions to the LiDAR can be very dangerous as they contribute significantly to the ability of multi-modal 3D object detectors, and the robustness of multi-modal 3D object detection methods against such corruptions is understudied. In this thesis, I propose Ada-UniBEV, which detects missing laser beam returns for the LiDAR based on its geometric pattern of shooting beams, and determines a severity of corruption based on the number of missing beams. Camera features corresponding to the corrupted region of the LiDAR are weighed as more important, with the exact weight being determined as a function of the severity of corruption. The weights also vary spatially around the autonomous vehicle depending on the properties of each spatial location. Ada-UniBEV improves the 3D object detection performance over state-of-the-art UniBEV in moderate to high-severity LiDAR corruption scenarios involving missing points while maintaining the same performance on clean data.

Occupancy grid mapping represents the surrounding environment with a discretized grid, providing information about obstacles and the drivable region using sensors such as LiDAR or radar. For automotive driving applications, these maps are central to safe autonomous navigation. While both model-driven and deep learning-based approaches exist, this thesis develops a hybrid method to estimate the occupancy grid map from point cloud data. Specifically, the proposed method builds on the pattern-coupled sparse Bayesian learning (PC-SBL) algorithm, which is well suited to the block-sparse, spatially correlated structure of automotive grids. By replacing explicit parameter updates with a lightweight convolutional neural network, the spatial correlations and sparsity profile are learned directly from the data. Based on qualitative and quantitative evaluation on LiDAR point cloud data from the nuScenes dataset, we show that the proposed approach surpasses the strong PC-SBL baseline in both accuracy and runtime. Moreover, when applied without further training to LiDAR and radar point clouds from the RADIATE dataset, it marginally outperforms PC-SBL, indicating robust cross-dataset and cross-sensor generalization.

This thesis asks whether spiking neural networks (SNNs) and neuromorphic computing constitute a promising alternative to present-day artificial neural networks (ANNs) for autonomous space missions. Focusing on a resource- and power-constrained 1U CubeSat transiting the Van Allen radiation belts, TIENOS is a toolchain that injects radiation-inspired perturbations into trained models and records the layer-specific reactions.

The framework systematically emulates dominant soft-error mechanisms by applying (i) bit-flip faults representative of single-event upsets, (ii) additive Gaussian noise as a proxy for thermal/analog variability, and (iii) dropout-style masking to approximate transient loss or zeroing of activations. Using MNIST (frame-based) and N-MNIST (event-based) benchmarks, we compare LeNet-5–style convolutional neural networks and size-matched multilayer perceptrons with their spiking counterparts to establish an ideal software training baseline. The tool produces per-layer vulnerability profiles and robustness heatmaps across a broad range of perturbation rates, quantifies activity sparsity in SNNs, and can be used to evaluate noise-aware retraining to improve robustness without any overhead, with a path towards on-chip protections such as selective redundancy (such as triple-modular redundancy for neuron parameters), ECC and scrubbing.

Results show that fragility concentrates in a limited subset of layers depending on the fault mechanism, enabling targeted hardening with modest cost. It also indicates that noise-aware retraining improves tolerance without prohibitive accuracy loss and that SNN sparsity yields favourable energy–robustness trade-offs for bursty, event-driven sensing typical of small spacecraft. In this study, the noise-aware learned weights used for inference by the two-tinyODIN setup deliver a 15% higher accuracy for up to 2% of bit-flips in the system. Hybrid ANN–SNN pipelines could further enlarge this envelope by deploying spiking computation where sparsity is highest while retaining dense processing elsewhere, acknowledging that the scalability and baseline power of current neuromorphic platforms remain practical constraints. Overall, the methodology translates environmental assumptions for a 1U CubeSat in the Van Allen belts into actionable, layer-level design rules, providing a principled basis for space-grade, energy-efficient digital SNN accelerators and an open, extensible tool to localise and mitigate radiation-induced vulnerabilities.

Radar (Radio Detection and Ranging) sensors are cost-efficient and robust under adverse weather conditions, making them an attractive component in modern automated driving perception systems, but they provide significantly sparser information about the environment than camera or LiDAR sensors. Thus, to fully exploit radars in perception solutions, it is crucial to exploit not only local but also global contextual information of the scene. However, existing 4D radar models often struggle to fully exploit both types of information, resulting in suboptimal performance. This paper proposes DRIFT, a dual-representation model that effectively captures and fuses both local and global contexts through a dual-path architecture. The model incorporates a point path to aggregate fine-grained local features and a pillar path to encode coarse-grained global features. These two parallel paths are inter-fused via novel feature-sharing layers at multiple stages, enabling full utilization of both representations. DRIFT is evaluated on the widely used View-of-Delft (VoD) dataset and an internal dataset, demonstrating its state-of-the-art performance across multiple tasks, including object detection and free-road segmentation. Notably, DRIFT achieves a mean average precision (mAP) of 52.6% (compared to 45.4% from the CenterPoint baseline) on the VoD dataset, surpassing existing methods.

Cardiac cine MRI is a modality used to visualize the beating heart by acquiring a sequence of images within a short acquisition window. Even if data collection spans multiple heartbeats, the goal is to capture a single cardiac cycle, that is, one full heartbeat. Achieving this often requires undersampling of k-space, which leads to artifacts that degrade image quality, such as aliasing, blurring, and ghosting. This thesis investigates how deep learning can be used to reconstruct high-quality cardiac cine MR images, which are anatomically accurate and diagnostically useful. A deep learning-based reconstruction method is developed, with particular attention given to the role of training data, network architecture, and k-space sampling strategies. The models are trained using two types of datasets, each of which is transformed to mimic cardiac cine MRI acquisition characteristics and augmented to increase the data variability. The proposed model architecture consists of initial image formation, data consistency, and convolutional denoiser blocks. The denoiser block includes variations in the use and size of temporal kernels to evaluate their impact on reconstruction performance. Experiments are conducted across 4-shot and single-beat acquisition protocols, under different sampling conditions. The proposed models achieve improved reconstruction quality over the benchmark model in most scenarios. This improvement is primarily attributed to the temporal processing of the training data and the inclusion of temporal convolutions. The findings of this work show possible paths for future research in deep learning-based cardiac cine MRI reconstruction.

Magnetic Resonance Imaging (MRI) is a powerful tool for visualizing internal body structures and is widely used in clinical fields. However, MRI's long scanning times and high computational demands for post-processing pose challenges, especially in resource-limited environments. Recent advancements in machine learning, specifically model compression techniques, have offered solutions to accelerate MRI post-processing and make it more accessible.

This thesis systematically investigates the application of several model compression methods, such as low-rank factorization, knowledge distillation, and quantization, to enhance the efficiency of a baseline MR reconstruction neural network. By exploring multiple variations within each compression technique, this study evaluates their impact on key performance metrics such as inference speed, model size reduction, and reconstruction accuracy. Extensive tests show significant trade-offs between image fidelity and computational efficiency, providing insights into the practical feasibility of deploying compressed models in clinical workflows.

Among the techniques tested, low-rank factorization implemented via Tucker decomposition emerged as the most effective approach. This method achieved a threefold reduction in inference time while maintaining high reconstruction quality, highlighting its potential to improve MRI processing times in real-world applications significantly.

As the Internet of Things (IoT) continues to expand across various industries, the demand for self-generating and sustainable power solutions is increasing more urgent. Piezoelectric energy harvesters offer a promising solution as they can generate electrical energy from ambient mechanical vibrations and operate independently even in locations that are difficult to reach. This thesis explores the modeling and measurements of a piezoelectric harvesting (PEH) system designed to power a low-power IoT circuit embedded in aircraft wings. Focusing on a piezoelectric cantilever beam implementation made from a PZT-5H transducer, the research evaluates three commercial models developed by 'Mide Technology': PPA-1021, PPA-2011 and PPA-4011. Every model is evaluated for their performance under mechanical vibrations in the 30-120 Hz range, characteristic for aircraft environments. The methodology includes electromechanical modeling and a structured series of laboratory experiments to validate key parameters such as resonance frequency tuning, impedance matching, power output, and behavior in noisy environments. Among the tested models, the PPA-2011 demonstrated the best overall performance achieving a peak power output of 1.61 mW at resonance of 58 Hz and was able to stably power an IoT circuit even in a noisy environment. The results validate the ability to use PEHs for the power generation of aircraft wireless sensor networks. Future work should explore long-term stability and extensive testing of real-world aircraft vibrations.

Automotive radar is an important sensor technology for self-driving cars and Advanced Driver-Assistance Systems (ADAS). Current automotive radars lack the ability to classify and categorize objects due to their limited angular resolution. A new generation of automotive radar systems, known as automotive imaging radars, proposes to overcome this limitation by using larger apertures with more antenna elements. During the radar operation, automotive imaging radar systems face challenges in the accurate estimation of the Direction-of-Arrival (DoA) due to phase incoherency in the spatially sampled information caused by hardware imperfections, temperature variations, and aging effects. This work proposes a method combining convex optimization and alternating updates to first jointly calibrate the phase incoherencies and estimate the DoAs, and then update them iteratively. It further derives the Cramér-Rao Bound (CRB) and investigates the impact of the phase incoherency on DoA estimation using the CRB. In the proposed approach, the MUltiple SIgnal Classification (MUSIC) algorithm is applied to estimate the DoAs after each calibration. Additionally, the eigenvalue decomposition process in MUSIC is replaced by the Projection Approximation Subspace Tracking (PAST) algorithm to reduce computational complexity while maintaining the accuracy of DoA estimation. Experimental results illustrate the effectiveness of these techniques, highlighting their potential in improving next-generation automotive radar systems.

The rapid development of Advanced Driver Assistance Systems (ADAS) necessitates enhanced performance in automotive radar systems, with Phase Modulated ContinuousWave (PMCW) radar emerging as a key technology due to its high resolution, interference resistance, and robust performance. Despite these advantages, PMCW radar faces challenges such as high computational complexity and Doppler-induced range sidelobes. This thesis addresses these challenges by proposing an adaptive block FFT correlation method to reduce computational complexity and enhance processing efficiency, ensuring reliable target detection. Additionally, we tackle Dopplerinduced range sidelobes by introducing code diversity and novel frame designs for MIMO systems, leveraging cyclic shifts and Hadamard matrices to balance sidelobe attenuation and sequence set size requirements. Through extensive analysis and simulations, the proposed methods demonstrate significant improvements in radar performance, especially in detecting weak targets behind strong reflectors. The findings contribute to developing more efficient, reliable, and scalable PMCW radar systems for advanced automotive applications.

This thesis investigates the application of multi-agent reinforcement learning (MARL) to the optimization of radar waveforms. Radar technology is crucial in fields such as aviation, maritime navigation, and defense, but faces challenges such as interference, clutter, and the need for high resolution and accuracy. Cognitive radar, which adapts to environmental changes in real-time, offers a promising solution. This research aims to explore the potential of MARL in optimizing radar waveforms and examines whether incorporating domain knowledge can enhance performance.

The radar waveform optimization problem is framed within the Decentralized Partially Observable Markov Decision Process (Dec-POMDP) framework, defining the radar environment, agents' observations and actions, and reward functions. The study experiments with different architectures, including decentralized actors with a centralized critic. The centralized critic, having access to global state information, helps stabilize the learning process and mitigate non-stationarity and credit assignment problems. The use of GNNs as a centralized critic is proposed to leverage graph data sparsity, enhancing scalability.

The proposed models are trained and tested in a radar-tracking scenario, evaluated in terms of Pareto optimality and optimization times. The results show that both Independent Actor-Critic (IAC) and Independent Actor with Centralized Critic (IACC) models outperform traditional methods in terms of probability of detection, waveform duration, and optimization speed. The findings highlight the effectiveness of MARL approaches in optimizing radar waveforms, emphasizing the benefits of centralized critics for robustness and coordination. However, the choice of architecture significantly impacts performance, and while GNNs offer potential scalability advantages, their integration of domain knowledge did not yield significant improvements in this study. This research lays a foundation for future exploration of MARL and GNNs in radar waveform optimization.

This thesis details the theoretical background and development process of a classification model for electroencephalogram-based (EEG) motor imagery (MI) signals, to be used in a brain-computer interface (BCI) system. This project was undertaken in order to demonstrate the possibility of distinguishing MI-EEG signals acquired using the g.tec Unicorn Hybrid Black EEG measurement cap. The classification model devised in this thesis is a hybrid deep neural network model, which combines a convolutional neural network (CNN) and long short-term memory (LSTM) recurrent neural network (RNN) in parallel, closing with a fully-connected (FC) layer. Much experimentation and research was needed to create this model, and this is extensively discussed within the thesis. The classification model produced for this thesis is one part of a complete end-to-end BCI system, which also entails a measurement and data processing procedure, and the development of a graphical user interface which provides visual feedback to the user.

On publicly available datasets, the classification model produced promising performance, achieving 55% on the BCI Competition IV-2a (4 class) dataset and 78% on the BCI IV-2a (2 class) dataset. The model has not yet been tested on self-collected data.

Radar technology has evolved into a versatile and robust tool for critical air traffic control, meteorology, surveillance, and defence applications. In surveillance radar, the need for continuous monitoring of large areas, often cluttered by ground or sea reflections, presents significant challenges for multitarget detection. This clutter can obscure true targets, complicating detection in environments where standard radar noise assumptions fall short.

This thesis introduces a novel implementation based on the relevance vector machine (RVM) to address the complexities of multitarget detection in cluttered environments. Unlike conventional approaches that assume white Gaussian noise, the proposed method jointly estimates a clutter covariance matrix, allowing it to adapt to the estimated clutter model over subsequent iterations. Performance evaluations using simulated data in one-dimensional (range or angle) and two-dimensional (range-angle) settings demonstrate that the framework achieves accurate AR parameter estimation. Results indicate a marked improvement in reducing false and missed detections compared to the white-noise-based model. Notably, the framework performs multitarget detection without prior knowledge of target locations and the need for guard cells, underscoring its adaptability to real-world scenarios.

In this study, we perform human identification using accumulated radar point clouds in an outdoor scene. We employ PointNet as classification network and explore the impact of adding radars' non-spatial features as input, namely doppler velocity and radar cross section (RCS). Furthermore, we encode time as an additional time identity dimension to each point within the accumulated point cloud. We examine the effects of normalizing the RCS values, canonicalizing the spatial dimensions of the point cloud, as well as normalizing the doppler velocity with respect to this canonicalization. We examine three different PointNet configurations to understand the impact of the TransformNet blocks (T-Net) within the PointNet architecture on our six-dimensional radar data input. We have created a realistic outdoor dataset for training and evaluation purposes. Our approach of using the unnormalized six-dimensional radar data on the PointNet architecture without the two T-Net blocks achieves the highest performance of 73.4 % on our test set.

Ambiguities are an often encountered nuisance in signal processing and are the source of some of the fundamental trade-offs encountered in radar systems. The goal of this thesis is to extract unambiguous information about targets by combining a limited amount of measurements on a video integration level. A novel framework is proposed to reach this goal. At the heart of the framework lives a relevance vector machine which is extended to process the ambiguities on a video integration level and to work off-grid. The relevance vector machine is then extended to become the ambiguity aware relevance vector machine. This extension is either performed by a frequentist test or by estimating a posterior distribution. The frequentist test is used to test whether we can statistically significantly discern the returned output from ambiguities. The posterior is estimated according to Bayes’ theorem and thus allows for the incorporation of prior information. In this thesis, the framework is specifically applied to Doppler processing of a pulse-Doppler radar system. Compared to existing methods for estimating unambiguous Doppler velocity in a multi-target environment, the framework provides a general increase in performance, allows for the incorporation of prior information, and is able to give a measure of confidence in the estimates. A simulation study is set up to show the performance increase. This simulation study also highlights the utility of incorporating prior information and the quantification of uncertainty.

Gaussian process regression (GPR), a potent non-parametric data modeling tool, has gained attention but is hindered by its high com- putational load. State-of-the-art low-rank approximations like struc- tured kernel interpolation (SKI)-based methods offer efficiency, yet lack a strategy for determining the number of grid points, a pivotal factor impacting accuracy and efficiency. In this thesis, we tackle this challenge.
We explore existing low-rank approximations that facilitates the computation, dissecting their strengths and limitations, particularly SKI-based methods. Subsequently, we introduce a novel approxima- tion framework, MKISSGP, which dynamically adjusts grid points us- ing a new hyperparameter of the model: density, according to changes in the kernel hyperparameters in each training iteration.
MKISSGP exhibited consistent error levels in the reconstruction of the kernel matrix, irrespective of changes in hyperparameters. This robust performance forms the bedrock for achieving accurate approx- imations of kernel matrix-related terms. When employing our rec- ommended density value (i.e., 2.7), MKISSGP achieved a comparable level of precision to that of precise GPR, while requiring only 52% of the time compared to the current state-of-the-art method.

Machine learning models offer promising potential in precipitation nowcasting. However, a common issue faced by many of these models is the tendency to produce blurry precipitation nowcasts, which are unrealistic. Previous research on the deep learning model - TrajGRU (Shi et al., 2017) indicated that data imbalance in radar images and the double-penalty effect of pixel-wise loss functions are underlying causes for this blurriness.
In this thesis, we continue to explore various approaches to improve the predictive performance of TrajGRU. Our research has first investigated spatially and temporally enhanced loss functions to address the two remaining issues: data imbalance and double penalty. The second part of our research focuses on manifold optimizations within the model network, such as incorporating additional model inputs or increasing batch size, to understand the model’s limitations.
Our results reveal that enhanced loss functions did not lead to predictive improvements and even resulted in undesired checkerboard patterns. Changes to the model network make a difference in the image sharpness and predictive rain evolution. Our visual analysis indicates that a larger batch size generates sharper rain field edges; predictions by using multiple parameter groups exhibit more rain dynamics. The incorporation with other transformed datasets introduces finer structures within rain fields. Although the blurriness has not been completely resolved, our study recommended future work can continue exploring the optimization in the TrajGRU network.

In recent years, neural networks (NNs) have seen a surge in popularity due to their ability to model complex patterns and relationships in data. One of the challenges of using NNs is the requirement for large amounts of labelled data to train the model effectively. In many real-world applications such as radar, labelled data may be scarce due to the high cost of acquiring measurements together with privacy and security concerns.

To overcome the lack of data, researchers have resorted to data augmentation (DA), a technique that aims to solve the problem at the root by generating new training samples by leveraging the available ones. In computer vision, image transformations and generative networks are used to perform DA. These techniques, however, may lead to the production of physically unfeasible samples that may hinder the generalization capabilities of classifiers in domains where the data has an underlying physical meaning.

Physics-informed machine learning aims to incorporate physical prior knowledge and governing equations of the target domain into the machine learning pipeline to improve the performance of NNs in fields with limited available data but with well-defined physical models. In this thesis, physics-informed DA in the radar domain is addressed to improve the task of classifying armed and unarmed walking individuals through micro-Doppler spectrograms.

To begin with, the usage of model-driven micro-Doppler radar simulations to improve the existing generative augmentations is investigated. After introducing several generative NN architectures, the quality and diversity of the produced synthetic spectrograms are evaluated together with their effect on the downstream classification task.


Next, the impact of visual transformations on micro-Doppler spectrograms is studied. Their effect on the underlying physics of the micro-Doppler spectrograms and their impact on feature extraction is assessed. Based on the results, a new DA technique is devised to improve the feature extraction process by informed segmentation of the input spectrogram, halving the size of the NN model and reducing the risk of overfitting.

This thesis presents a method for personnel activities observation, i.e., 3D human pose estimation and tracking, in a Catheterization Laboratory(Cath Lab). We mount five cameras from different angles in the Cath Lab, where surgeons and assistants are in similar clothes while doing surgery. Accurate 3D human pose estimation is the cornerstone of our method. Most previous 3D pose estimation methods train their models directly on a 3D pose dataset. However, these methods are not suitable for our task: 1) We do not have enough 3D pose data for training because of privacy issues and specificity 2) The model needs to be retrained in different operating rooms or the camera calibration changed. To solve these problems, we decompose the 3D human pose estimation task into two stages, avoiding the need for large amounts of 3D pose data and retraining. In the first stage, we apply YOLOX and HRNet for 2D human detection and 2D pose estimation. Simultaneously, the 2D object tracking network Bytetrack tracks person identities based on detection results. Then we use a matching algorithm to match the corresponding 2D poses from multiple views and reconstruct 3D poses. Given 3D poses and tracking identities, we at last introduce a hybrid method tracking algorithm. By feeding 2D tracking results into the matching and tracking algorithm, we increase the accuracy of the result in a scene where people are wearing similar clothes. We fine-tune and test our method with an operating room dataset. Finally, we validate the method on data from the Cath Lab.

The recent advances in wireless communication, micro-fabrication, and integration have led to the rise of multi-agent networks such as wireless sensor networks, drone swarms, and satellite arrays. These multi-agent networks comprise multiple agents, which cooperate to solve a problem collectively, beyond the individual knowledge of a single agent. Multi-agent networks are also known for improving overall system performance, especially in terms of scalability, robustness, and flexibility.

Multi-agent networks are tasked with a variety of tasks e.g., target tracking, surveillance, traffic control, and environmental monitoring. Traditionally these tasks are solved using distributed state-space filtering methods, however under the assumptions of linear models with underlying Gaussian noise. However, in general, the models could be Non-linear, and the underlying stochastic noise is not necessarily Gaussian in nature. To address this limitation, Distributed particle filters (DPF) have been investigated in recent years. Depending on the quantities exchanged in the network, DPFs can be categorized as weight-based, likelihood-based, or posterior-based.

One of the key challenges for effective implementation of the DPF is the need for approximation strategies to reduce the burden on communication and computation resources to suit engineering applications. To this end, we review two state-of-the-art DPF, (a) one based on applying the Graph Laplacian (GL) approximation to weights, and (b) the other using the Gaussian mixture model (GMM) to represent the local posteriors. These two algorithms significantly reduce the communication burden; however, the main limitation is the synchronization and heavy computational burden, which places high demands on hardware and software implementation of agents.

To improve on these existing methods, we propose the use of Gaussian process (GP) enhanced resampling algorithm, which reduces the particle set size, while ensuring an acceptable filter performance. Based on this GP-enhanced resampling scheme, we propose a novel Distributed particle filtering algorithm. Secondly, based on the proposed GP-enhanced sampling, we propose several metaheuristic optimization algorithms (i.e., genetic algorithm and firefly algorithm) to fuse the information across the whole network to improve the estimation performance (i.e., to seek the global optimal particle set as we can treat particles as “parents” or “fireflies”).

We compare our proposed algorithms and study their performance against the state-of-the-art DPFs in terms of time, space, and communication complexity, for a target tracking application. We use time-averaged root mean square error (ARMSE), which is used to quantify the performance of each DPF. Our numerical results demonstrate the superiority of our proposed algorithms under the condition of limited communication and computational resources, and still maintaining the optimality of particle filter.

For example, to achieve a certain ARMSE for a target tracking application, the traffic for existing GL and GMM based DPFs, is 12000 scalars/second/agent and 600 scalars/second/agent respectively, while our proposed GP-enhanced resampling and firefly algorithm uses only 900scalars/second/agent. In terms of the computation runtime, the GL and GMM based approaches take 40 and 300 seconds (about 5 minutes) respectively, while our proposed algorithm takes just 1.5 seconds, and thus shows significant improvement. Finally, we propose research directions to further improve our proposed algorithms in the future.

Accurate short term rain predictions are important for flood early warning systems, emergency services, energy management and other services that that make weather dependent decisions. Recently introduced machine learning models suffer from blurry and unrealistic predictions at longer lead times, causing poor performance on the rarer heavy rainfall events. The objective of this research was to explore how the loss function in a recurrent, convolutional neural network (TrajGRU, X. Shi et al. (2017)) can be modified, to get sharper and more realistic predictions, without worsening its performance. Six perceptive loss functions, which should better represent how an image is perceived, are thoroughly analysed to understand the reasons behind their functioning in the context of precipitation nowcasting. It was shown that these perceptive losses can lead to an improvement in sharpness for the first lead time, but that the blurriness for longer lead times arises due to the imbalance in the dataset and the uncertainty of the model with respect to the location of the rain. This thesis gets concluded with recommendations on how to deal with these two problems.