Many applications such as indoor navigation, search and rescue operations, and surveying, require accurate localization in challenging environments. In environments where absolute positioning (using for example GNSS receivers) fails due to dense obstruction of the required signals, positioning algorithms rely solely on dead reckoning, often using measurements from an Inertial Measurement Unit (IMU). This dead reckoning process suffers from integration drift due to the accumulation of errors in the sensor measurements. Pedestrian Dead-Reckoning (PDR) algorithms can reduce this integration drift in cases where the IMU is held by a walking person, by leveraging patterns from the periodic walking motion. This thesis investigates a state-of-the-art PDR algorithm from Liu et al. that combines an Extended Kalman Filter (EKF) with a velocity-predicting neural network that corrects the filter in the measurement update to mitigate integration drift. The focus is on finding if its performance can be improved by adapting the neural network in the algorithm. First, adaptations of the network’s parameters have been experimented with to investigate their effect on the algorithm’s accuracy and search for a bottleneck that limits it. This bottleneck was found to be a bias in the predicted velocity by the network, as this violates the EKF assumption that the error in the measurement update is distributed with zero mean. The second part investigates how using ideas from the Physics-Informed Neural Network (PINN) as an alternative to the data-driven neural network in the PDR algorithm affects its performance. Four network architectures have been trained using a loss function that includes a penalty for errors in the physics of the predicted velocities of the system. Training these PINN-inspired networks required a much longer training time. The results show that using this physics loss does not show significant improvements in the accuracy of the PDR algorithm, as the bias in the velocity prediction is not addressed by the physics loss. This thesis concludes that the main limitation of the neural network in the PDR algorithm by Liu et al. is a bias in the predicted velocity, and that a PINN is unable to provide significant improvements in the accuracy of the algorithm, whilst costing much more computational resources to train. It is therefore not recommended to use a PINN in this PDR algorithm, and the optimal configuration of the network was found to be a slightly adapted version of the network used by Liu et al., using IMU and device tilt data sampled at 50 Hz as network input. Future research could focus on understanding the origin of the bias in velocity predictions and to mitigate it once its source is known.

More insight has been gathered on the performance of the SPLITTER (Stationary spectrum Plus Low-rank Iterative TransmiTtance EstimatoR) algorithm as developed by Brackenhoff for denoising data gathered from observations of high-redshift galaxies. By using matrix decomposition to split the gathered data into a low-rank atmosphere matrix and a sparse matrix with the signal and photon noise, the algorithm avoids the subtraction of two noisy signals, and therefore the factor of √2 additional noise that comes with it. The algorithm was specifically developed for DESHIMA 2.0 (DEep Spectroscopic HIgh-redshift MApper), a wideband spectrometer that achieves a bandwidth from 220 to 440 GHz, using 347 spectral channels. Previous performance tests of the algorithm included the comparison of the weighted root mean square error between SPLITTER and the usual technique of Direct Subtraction on realistic data simulated using the TiEMPO (Time-dependent End-to-end Model for Post-process Optimization) software package. This resulted in a ~1.7 improvement factor for the whole spectrum and ~1.3 in the emission line area.

The performance of SPLITTER on two key components of the spectrum have been analyzed separately. First, the measurement of the continuum has been analyzed by using TiEMPO to create realistic simulations of the observation of custom spectra with a linear continuum. SPLITTER showed to be more precise as the noise level was lower, but less accurate, as there was a systematic offset in the estimated continuum. Using a modified black body model for the continuum and assuming the relative offset is independent of the strength of the continuum, the observed offsets and errors were propagated to offsets in estimations of dust temperature $T_{dust}$ and spectral emissivity of the dust $\beta$. Because of the offset, SPLITTER also showed a systematic offset in estimated $T_{dust}$, but as the algorithm is more precise, it performed better at estimating $\beta$, since $\beta$ determines the shape of the spectrum and has less influence on the strength. Second, to test the detection of emission lines, custom spectra have been created containing the same linear continuum and single spectral line at four different frequencies. Each line was set to have a known signal to noise ratio compared to the photon noise in its frequency bin. The retrieved signal to noise ratio as compared to noise of neighboring bins showed an improvement of ~1.9 for SPLITTER compared to Direct Subtraction for bright lines. Weak lines did not show any improvement in SNR. There seemed to be no correlation between continuum overestimation and emission line measurements.

Conclusion is that SPLITTER definitely shows improvement in noise reduction, but comes with an overestimation of the continuum. The consequences of this are that Direct Subtraction is still preferred for estimating dust temperature, but for estimations of spectral emissivity and detection of emission lines, SPLITTER is more robust.