Centuries ago, navigators used compasses to traverse oceans, and compasses remain part of modern Inertial Navigation Systems (INS). Although Global Navigation Satellite Systems (GNSS) are widely used today, they are not always available, for example underground, indoors, in tunnels, or in conflict zones where GNSS can be jammed or spoofed. This motivates research into GNSS-independent navigation methods. Magnetic field-based navigation is a promising alternative, as the Earth’s magnetic field is globally present, relatively stable, and only weakly affected by environmental conditions or human activity at large scales.

Magnetic maps are also used in applications such as resource exploration, archaeology, and geophysical studies. The Earth’s magnetic field consists of contributions from both core and crustal sources. Global magnetic maps are commonly represented using spherical harmonics, which model large-scale fields originating from the Earth’s core. However, at regional scales these models become insufficient due to crustal and near-surface variations. In theory, infinite spherical harmonic expansion could represent the field, but this is not feasible in practice.

To address regional mapping, local extensions of global models are used. Techniques include interpolation methods, dipole approximations, and Equivalent Layer methods. Equivalent Layer formulates a linear inverse problem in which magnetic dipoles below the surface are fitted to measurements. While effective, it requires a priori assumptions on dipole placement. Upward continuation is another key technique, allowing estimation of the magnetic field at higher altitudes using measurements at a lower altitude by exploiting harmonic properties of the field.

This thesis advances magnetic map-making by providing a complete overview of the pipeline, from theory to applications. It reviews magnetic models, their limitations, and spatial resolution effects. It derives the Equivalent Layer formulation from first principles, extending from single dipole cases to multiple measurements. A novel method based on Anderson functions is introduced, enabling magnetic field reconstruction without prior knowledge of source locations and allowing dipole depth estimation. An orthonormalized wavelet extension is also developed.

A Python framework, MagMap, is developed to benchmark mapping techniques on simulated magnetic fields, comparing interpolation and extrapolation performance. The methods are further validated on real-world data, highlighting practical challenges such as noise and measurement distortions from ferromagnetic platforms.

The research is structured around understanding magnetic maps, improving reconstruction techniques, and evaluating their performance under realistic conditions. Key research questions address magnetic map definitions, existing methodologies, dipole depth estimation, interpolation accuracy, noise effects, and applications in navigation and exploration. The work demonstrates that magnetic maps are a viable candidate for regional-scale GNSS-independent navigation, particularly for aeromagnetic applications.

The transcription of voice using neural networks is a technique that deserves attention, as speech assistants are becoming increasingly popular. Neural networks have often difficulty with determining the differences between a talking person and noise. Humans have a much better understanding of this and could possibly apply their knowledge of the structure of the signals to improve the understanding of the neural network. A problem that is extremely difficult for a neural network is understanding and transcribing the lyrics of a song.

This thesis analyzes signal-processing techniques that can be applied to a song to improve the understanding of a speech-recognition algorithm. It is mainly focused on filtering the fore- ground lyrics from the accompaniment. Some basic filtering methods are described including a low-amplitude filter and a band-pass filter. But also two more complicated filters which make use of the periodicity of the background music will be treated.
The first filter is a method of voice separation using the two-dimensional Fourier transform. This method, proposed by Prem Seetharaman, Fatemeh Pishdadian, Bryan Pardo in 2017 [15], combines techniques of signal-processing and image-processing by finding periodic repetitions in a signal by identifying peaks in the two-dimensional Fourier transform of the spectrogram of the signal.
The second filter is a newly proposed method that can be used for the separation of foreground from background music. The algorithm compares columns in the spectrogram and classifies columns as overlapping if there are multiple occurrences of columns similar to the selected col- umn (repetitions). The frequency components, the different frequencies obtained from a discrete short-time Fourier transform, of overlapping columns are afterward compared with components of the same frequency in other columns. Under certain circumstances, overlapping frequency components are subtracted from components in other columns of the spectrogram. This removes repetitions of that frequency throughout the song. The components of the spectrogram that re- main after several iterations of this method are most likely to correspond to the least repetitive parts of the song.

The decisions that are made while constructing the method of comparing spectrogram columns are discussed and are compared with steps performed in the method that uses the two-dimensional Fourier transform. An implementation and demonstration are also attached. From the research it is expected that the two-dimensional Fourier transform perform better on strict periodic accompaniment, while the method that compares spectrogram columns is more likely to perform better on songs with a less tight rhythm.