Fitting a smooth curve to 2D, a surface to 3D, and a manifold to 4D irregular point cloud data is becoming a common practice in many engineering and science applications. Piecewise-polynomial spline functions provide a powerful tool applicable to interpolation and approximation problems. This study presents the least squares B-spline approximation (LSBSA) theory, which is a generalized version of the spline interpolation and can be applied to any irregularly scattered point cloud data at knots specified by the user. The formulation allows to apply the well-established body of knowledge of least squares theory to the B-spline approximation. This for example has the benefit of embedding quality control measures such as hypothesis testing and proper error propagation to assess the quality of the approximation problem. The method is applicable to many 1D curve, 2D surface and 3D manifold fitting problems of which both simulated and real data are used to illustrate the efficacy of the proposed theory. In particular, its real-world applications to multi-beam echo-sounder bathymetric data, digital terrain modeling and Greenland ice sheet deformation monitoring will be highlighted. The performance of the method for linear, quadratic, cubic and quartic spline functions will be investigated. The primary application of LSBSA lies in its ability to perform 3D manifold fitting for deformation monitoring. This capability provides the possibility of monitoring changes in continuous spatial and temporal domains. The Python and Matlab source codes of LSBSA are freely accessible at https://github.com/tudelft4d/lsbsa.

The study of long-term GNSS time series provides valuable insights for researchers in the field of earth sciences. Understanding the trends in these time series is particularly important for geodynamic researchers focused on earth crust movements. Functional and stochastic models play a crucial role in estimating trend values within time series data. Various methods are available to estimate variance components in GNSS time series. The least squares variance component estimation (LS-VCE) method stands out as one of the most effective approaches for this purpose. We introduce an innovative method, which streamlines calculations and simplifies equations, and therefore significantly boosting the processing speed for diagonal(ized) cofactor matrices. The method can be applied to the GNSS time series of linear stochastic models consisting of white noise, flicker noise and random walk noise. Moreover, unlike the conventional approaches, our method experiences high computational efficiency even with an increase in the number of colored noise components in time series data. For GNSS time series, this variable transformation has been applied to both univariate and multivariate modes, preserving the optimal properties of LS-VCE. We conducted simulations on daily time series spanning 5, 10, 15, and 20 years, employing two general and fast modes with one and two colored noise components plus white noise. The computation time for estimating variance components was compared between the two modes, revealing a notable decrease in processing time with the fast mode.

The multibeam echosounder (MBES) has been widely used in seabed mapping, considering its ability to collect continuous and broad-scale seabed measurements efficiently. The presence of shellfish or dead shell material can alter the geophysical properties of the sediment and thus affect the MBES backscatter intensity, making acoustic surveys with the MBES a potential non-invasive solution for regularly monitoring the benthic habitats of shellfish aggregations. Although there exists an increasing interest in mapping marine benthos with MBES measurements recently, the use of multi-spectral backscatter data is still limited. Thus, this research aims to enhance the acoustic mapping of benthic habitats using multi-spectral MBES data, with a focus on a shell bed region in the Dutch North Sea. With backscatter measurements from three frequencies, 90, 300, and 450 kHz, we achieved seabed classification in two steps. First, a semi-supervised backscatter completion was conducted to generate full-coverage backscatter data for each incident angle, mitigating the limited overlap between adjacent survey lines. We then classified the multi-Angle backscatter data from each individual frequency using the Gaussian Mixture Model. Our results indicate an improved seabed classification performance compared to the classical Bayesian method. Comparisons of classification maps across frequencies also show their different abilities to distinguish the shell bed region from other coarse sediments, demonstrating the value of leveraging multi-spectral backscatter data in seabed habitat mapping.

For models that evaluate aircraft noise, thrust is an essential input. From aircraft flight recorder data or measured noise spectra, the engine's rotational speed can be estimated for which a conversion is then needed to obtain the engine's thrust. This research investigates three conversion methods. The first uses the expressions from the ANP database while the second method is based on the fuel flow. The third employs Gas Turbine Simulation Program (GSP) predictions. The thrust estimates are compared to airline performance calculations where significant variations up to 3 dBA in predicted noise were found. Methods one and three were found to be in good agreement with the performance data. An important finding of this paper is that combining methods one and three using least-squares is capable of providing the required conversion expressions, in line with those in the ANP database, but without being limited to a few aircraft types only.

Satellite-derived bathymetry (SDB) provides a cost-effective solution for coastal mapping, but challenges remain in model interpretability and uncertainty quantification. This study investigates the applicability of the least-squares-based deep learning (LSBDL) framework for SDB, leveraging its hybrid structure that integrates neural networks with the available least-squares theory to enhance model transparency. ICESat-2 photon-counting LiDAR was used to train depth estimation from Sentinel-2 multispectral imagery over an approximately 30 km × 30 km region of near-coastal bathymetry at Anegada, British Virgin Islands. ICESat-2 provided high-precision depth information, of which 80% were used for training and the remainder for validation. LBSDL depth estimation achieved a root-mean-square error (RMSE) of 2.74 m, representing around 10% of the maximum observed depth, with the best performance in the 2–15 m depth range. These findings demonstrate the potential of LSBDL for interpretable and reliable bathymetric mapping, highlighting ICESat-2 as a globally accessible training and validation source and advancing SDB capabilities for data-sparse coastal regions.

Identifying the correct stochastic model in GNSS time series is essential to study geophysical parameters such as site velocities, and hence enhancing their accuracy. The rate uncertainty is a critical aspect in GNSS time series analysis. The variance component estimation (VCE) methods commonly utilize unconstrained estimation principles. Simulating 1000-time series for 4 different noise combinations with 10 years’ time span, we have investigated the performance of non-negative least squares VCE (NNLS-VCE) method for identifying an appropriate noise model. Our results are provided for both univariate and multivariate analysis. As the noise model's complexity increases, the significance of employing multivariate analysis is prominent in contrast to univariate analysis. After thorough analysis, we have determined that treating the false-positive model as a stochastic model in time series yields significant insights. Specifically, if the accumulative spectral index is lower than the true value, it results in an underestimation of the rate uncertainty. Conversely, if the index is higher than the actual value, it leads to an overestimation. Additionally, we observed that as the noise model complexity increases, the number of false-positive models also increases. However, the implementation of multivariate analysis mitigates this increase, offering a more realistic and reliable approach. In case of four distinct noise models, the detection power percentages of 98.5%, 90.5%, 69.5%, 29.3% of univariate analysis increased to 99.5%, 99.8%, 88.4% and 83.7% for multivariate analysis.

Accurately predicting Earth’s rotation rate, as represented by Length of Day (LOD) variations, is essential for applications such as satellite navigation, climate studies, geophysical research, and disaster prevention. However, predicting LOD is challenging due to its sensitivity to various geophysical and meteorological factors. Current methods, including statistical approaches, often struggle with short-term forecasting accuracy. In this study, we use Monte Carlo Singular Spectrum Analysis (MCSSA) to distinguish between deterministic and non-deterministic components within the LOD time series. The deterministic components are extended using the SSA prediction algorithm. To enhance robustness, we refine Allen and Smith’s methodology (testing significance of eigenmodes against an autoregressive (AR) (1) noise null hypothesis) by integrating an autoregressive moving average (ARMA) model to account for noise, providing valuable insights into the non-deterministic behaviors present in the series. We comprehensively evaluate our methodology through a comparative analysis. For long-term prediction (365 days), we compare our method against the combined LS and autoregressive (AR) method. For short-term prediction (next 10 days), we compare it against the results of the second Earth Orientation Parameters Prediction Comparison Campaign (second EOP PCC). Using the IERS 20 C04 time series, our hybrid model demonstrates a superior long-term prediction accuracy with a mean absolute error (MAE) of 0.201 ms/day on the 365th day. Additionally, the short-term prediction performance is comparable to the second EOP PCC results. These results illustrate that the proposed method efficiently predicts LOD, showing significant improvement in long-term accuracy and robustness in short-term forecasting.

Although Light Detection and Ranging (LiDAR) technology is currently one of the most efficient methods for acquiring high-density point cloud, there are still challenges in terms of data reliability. In particular, the accuracy assessment of LiDAR data, especially in the height component, is one of the main issues in this context. This study introduces a rapid and cost-effective platform to improve the accuracy and precision of LiDAR data by integrating high-density GNSS-Ranging measurements with LiDAR data. The platform offers the capability to rapidly collect a significant number of network real time kinematic (NRTK) points with centimetric precision. A continuous correction surface is proposed to integrate the platform and LiDAR data, resulting in improved accuracy for all ground-class LiDAR data. Evaluation using GNSS benchmarks and NRTK checkpoints showed a significant reduction in LiDAR height errors after applying the correction surface. The root mean squares error (RMSE) decreased from 18.5 cm to 8.2 cm when compared to GNSS benchmarks and from 17.4 cm to 5.3 cm for approximately 1000 NRTK control points. The results indicate that collecting a large number of high-density GNSS ground targets and applying a correction surface to LiDAR height data significantly enhance the accuracy and precision of the LiDAR extracted products.

To regulate aircraft noise impact on communities surrounding airports, best-practice models are used to predict aircraft noise levels. In this research the Noise-Power-Distance (NPD) tables in the European Doc.29 noise model are evaluated with measurements around Amsterdam Airport Schiphol. Even with accurate input parameters (thrust and distance to the observer), differences in modelled and measured noise levels are found, which are assumed to be due to the errors in the NPD table. To further investigate this, thrust-noise relations are derived from measurements. These relations are found to differ from the original NPD tables. Using the measured thrust-noise relations, the modelled and measured mean noise levels are in agreement and the standard deviation of the differences is reduced by 25% for departure operations. This finding is consequently verified with independent measurements around Oslo Airport Gardermoen. Next to an improvement in best-practice noise modelling, the methods described in this research give insight into the creation and validation of NPD tables.

The growth shown by the aviation industry has given significant economic benefits, but also causes disturbance to communities living near airports, including annoyance and potential health problems due to the high aviation-induced noise levels. Therefore, regulations are implemented by imposing limits on the yearly cumulative noise levels at specific locations around airports. This requires understanding and prediction of the varying aircraft noise levels. This is traditionally achieved by using so-called best-practice or regulatory models, such as the Dutch aircraft noise model, which require low computational costs and limited model inputs. This way of noise monitoring comes with significant model approximations and hence potential deviations of the model predictions from the actual noise levels. The limitations of this current approach has given rise to distrust in communities near airports. Hence, the models need to be validated against real measurements, for which use is made of the stations from the Noise Monitoring System (NOMOS) around Schiphol Airport. In this contribution, we analyzed the time series of the yearly averaged L_den measured at 35 NOMOS stations for the period from 2006 to 2022. A distinction is made between noise from aircraft and that due to other noise sources. We observe a decreasing trend of 0.52 ± 0.04 dB(A)/year in L_den for the investigated time period. One of the objectives is to determine how the measured L_den can be assigned to the various aircraft types in the fleet at Schiphol. This is performed by an L_den time series analysis of the averaged time series over all stations, combined with changes in the fleet composition. The results from the unconstrained least squares (LS) and non-negative least squares (NNLS) methods are presented and compared. Based on the obtained model for 2006-2020, predictions are performed for 2021 and 2022.

Hyperspectral unmixing (HU), an essential procedure for various environmental applications, has garnered significant attention within remote sensing communities. Among different groups of HU methods, nonnegative matrix factorization (NMF)-based ones have gained widespread popularity due to their high capability of simultaneously extracting endmembers and their corresponding abundances. However, converting a 3-D hyperspectral data cube into a 2-D matrix format leads to the loss of spatial and potential correlation information. Consequently, in recent years, nonnegative tensor factorization (NTF) methods, which preserve the 3-D nature of hyperspectral data cube, have been extensively embraced by numerous researchers. Nevertheless, incorporating prior information into NTF-based problems faces limitations owing to the inconsistency of such information, particularly concerning \ell {1} norm sparsity and the abundance sum-to-one constraint (ASC). To address this limitation, our study introduces a novel general regularization term. This term leverages sparsity and ASC simultaneously, integrating it into a matrix-tensor factorization framework. Our proposed method, named a matrix-tensor-based HU method with general \ell {q} norm regularization (MTUHL{q}), is established on the block term decomposition (BTD) paradigm, which ensures physical interpretability and simple implementation. To investigate the performance of the proposed MTUHL{q}, a series of experiments on both synthetic and real hyperspectral datasets were conducted. The results of the implemented experiments indicated that the proposed method outperformed other state-of-the-art HU methods.

High diversity seabed habitats, such as shellfish aggregations, play a significant role in marine ecosystem sustainability but are susceptible to bottom disturbance induced by anthropogenic activities. Regular monitoring of these habitats with effective mapping methods is therefore essential. Multibeam echosounder (MBES) has been widely used in recent decades for seabed characterization due to its non-destructive manner and extensive spatial coverage compared to traditional methods like bottom sampling. Nevertheless, bottom sampling remains essential to link ground truth with acoustic seabed classification. Using seabed samples and MBES measurements, machine learning techniques are commonly employed to model their relationships and generate classification maps of an extended seabed. However, limited ground truth data, resulting from constraints in regulations, budget, or time, may impede the development of robust machine learning models. To address this challenge, we applied a semi-supervised machine learning method to classify seabed sediments of a blue mussel (Mytilus edulis) cultivation area in the Oosterschelde, the Netherlands. We utilized nine boxcore samples to generate pseudo-labels on MBES data. These pseudo-labels enlarged the training data size, facilitated the training of three comprehensive machine learning algorithms (Gradient Boosting, Random Forest, and Support Vector Machine), and helped to classify the study site into mussel and non-mussel areas. We found the geomorphological and backscatter-related features to be complementary for mussel culture detection. Our classification results were demonstrated effective through expert knowledge of this cultivation area and brought insights for future research on natural mussel habitats.

This manuscript summarizes the main recent research efforts at Delft University of Technology in the field of drone and urban air mobility (UAM) vehicle noise. Illustrative examples are showcased, specifically in terms of acoustic measurements (both in-field and in wind-tunnel facilities), noise modelling (both data-driven and physics-based), and human perception of these sounds. In particular, the measurements feature microphone arrays and acoustic imaging to detect, localize, and isolate drone noise emissions. Regarding drone noise modelling, the proposed approaches cover noise generation, propagation, and acoustic footprint calculation. The evaluation of the human perception of drone noise and the perceived annoyance is another crucial aspect. To this end, psychoacoustic listening experiments are conducted in laboratory conditions and the results are analyzed using perception-based sound metrics. Data from aeroacoustic measurements and synthetic sound auralizations are considered. Combining these three main approaches holistically, the perception-driven design and assessment can be performed by targeting the minimization of the perceived noise annoyance, rather than merely reducing sound pressure levels.

Since 2020, all commercial aircraft have been mandated to be equipped with ADS-B Out
transponders. Despite the many advantages of locating an aircraft with openly available and
accessible data, it also has some limitations. Firstly, not all aircraft, such as general aviation, are required to transmit their locations; secondly, due to obstacles such as buildings,
a location is not always transmitted at lower altitudes (75-130 m); thirdly, it is vulnerable to cyberattacks. Therefore, while it is convenient to have ADS-B Out data, creating a
computationally efficient alternative methodology for determining the aircraft location is
advisable. This paper investigates the accuracy, efficiency, and computational cost of two
methods of source localization using data taken by an array of microphones: a global optimization (GO) method called the differential evolution (DE) and the conventional beam-
forming approach (CBF). The real-world data required as input for both methods is obtained
with a 64-microphone phased array placed at a distance of 1.14 km from Rotterdam The
Hague Airport (RTHA). The 2-dimensional flight trajectories, i.e., azimuth, and elevation
relative to the array, obtained from the GO and CBF methods, are compared with the ADS-
B Out data for approaching and departing flyovers. Furthermore, the smallest size of an
array required for satisfactory localization accuracy is investigated.

Inspired by the attractive features of least-squares theory in many practical applications, this contribution introduces least-squares-based deep learning (LSBDL). Least-squares theory connects explanatory variables to predicted variables, called observations, through a linear(ized) model in which the unknown parameters of this relation are estimated using the principle of least-squares. Conversely, deep learning (DL) methods establish nonlinear relationships for applications where predicted variables are unknown (nonlinear) functions of explanatory variables. This contribution presents the DL formulation based on least-squares theory in linear models. As a data-driven method, a network is trained to construct an appropriate design matrix of which its entries are estimated using two descent optimization methods: steepest descent and Gauss–Newton. In conjunction with interpretable and explainable artificial intelligence, LSBDL leverages the well-established least-squares theory for DL applications through the following three-fold objectives: (i) Quality control measures such as covariance matrix of predicted outcome can directly be determined. (ii) Available least-squares reliability theory and hypothesis testing can be established to identify mis-specification and outlying observations. (iii) Observations’ covariance matrix can be exploited to train a network with inconsistent, heterogeneous and statistically correlated data. Three examples are presented to demonstrate the theory. The first example uses LSBDL to train coordinate basis functions for a surface fitting problem. The second example applies LSBDL to time series forecasting. The third example showcases a real-world application of LSBDL to downscale groundwater storage anomaly data. LSBDL offers opportunities in many fields of geoscience, aviation, time series analysis, data assimilation and data fusion of multiple sensors.

Gravity recovery and climate experiment (GRACE) and GRACE Follow-On (GRACE-FO) are Earth's gravity satellite missions with hydrological monitoring applications. However, caused by measuring instrumental problems, there are several temporal missing values in the dataset of the two missions where a long gap between the mission dataset also exists. Recent studies utilized different gap-filling methodologies to fill those data gaps. In this article, we employ a variety of singular spectrum analysis (SSA) algorithms as well as the least squares-harmonic estimation (LS-HE) approach for the data gap-filling. These methods are implemented on six hydrological basins, where the performance of the algorithms is validated for different artificial gap scenarios. Our results indicate that each hydrological basin has its special behaviour. LS-HE outperforms the other algorithms in half of the basins, whereas in the other half, SSA provides a better performance. This highlights the importance of different factors affecting the deterministic signals and stochastic characteristics of climatological time series. To fill the missing values of such time series, it is therefore required to investigate the time series behaviour on their time-invariant and time-varying characteristics before processing the series.

Acoustic classification using single-beam and multi-beam echosounders has been widely applied in characterizing seabed sediments. Although previous studies have shown a better discrimination of fine and coarse sediments using multi-spectral echosounder data, analysis regarding comprehensive seabed sediment properties is still needed. In this study, we used single-beam data of 24 kHz, as well as multi-beam data of 90 and 300 kHz to investigate the benefits of multi-spectral backscatter data in describing sediment properties including median grain size; weight percentages of gravel, sand, and mud; volume percentages of stones, shell fragments, and living bivalves; as well as density of acoustically hard animals (molluscs and the tube-building worm Lanice conchilega). We classified data of each frequency in an unsupervised manner, using K-means clustering for the single-beam echo time series and Bayesian classification for the multi-beam backscatter. Compared with the top-layer sediment properties, we found classification of 90 and 300 kHz consistent with variations of median grain size and L. conchilega density, whereas classification of 24 kHz can also be related to the percentages of shell fragments and stones. In addition, one acoustic class of 24 kHz might indicate a higher gravel content in the subsurface of the study area. Although quantitative relationships between backscatter and sediment properties are still difficult to achieve given a limited number of samples, using multi-spectral backscatter data is a potential approach to characterize seabed sediments from various perspectives.

Before geodetically derived strain and rotation rates can be robustly compared to geological or seismological observations, we need reliable strain rate uncertainties. Various methods exist to compute strain rates from GNSS-derived interseismic velocities, but a realistic representation of interpolation uncertainties has remained a challenge. The main problem is that commonly used deterministic interpolation methods do not account for uncertainty resulting from the absence of information in between observation sites. We apply stochastic interpolation by means of ordinary kriging to propagate errors both from discontinuous data coverage as well as from observation uncertainties to our strain rate estimates. However, interseismic horizontal surface velocities in tectonically active regions are spatially highly non-stationary, with high spatial variability around active faults and lower velocity variability in tectonically more stable regions. This requires an extension of traditional ordinary kriging approaches. For interpolation uncertainties that reflect the local variability and spatial correlation of the observed surface velocities, we apply a novel method that incorporates the spatially variable statistics of the underlying data. We estimate realistic uncertainties and covariances of the interpolated velocity field. For regions with a high spatial velocity variability, we find a large increase in uncertainty with increasing distance from observation sites, while in areas with little spatial variability, we estimate a small increase in uncertainty with distance. Subsequently, we propagate interpolated velocity covariance to strain rate uncertainties, such that we can assess the statistical significance of the interpolated strain rate field. Applied to a number of actively deforming regions, including the Pacific coast of North America and Japan, we show to what degree we can robustly determine strain rates based on available GNSS-derived velocities. Realistic uncertainties assist the community to better discriminate continuous or localized deformation on active faults from the available geodetic data.

This study aims to investigate how changes in meteorological indicators affect groundwater resources, and hence to predict groundwater levels using these indicators, particularly in regions experiencing drought and subsidence. Precipitation, temperature, evapotranspiration and precipitable water vapor (PWV) are important meteorological parameters to predict groundwater levels. Two subsidence areas with different weather conditions were selected to conduct a comprehensive study on the effect of temperature and precipitation on groundwater level changes. The correct locations of the two subsidence areas were determined by analyzing Interferometric Synthetic Aperture Radar (InSAR) images of Sentinel-1A using the small baseline subset algorithm. The interferograms were processed to correct tropospheric effects using the advanced integration method. Specifying the exact locations of the two areas, the meteorological parameters were downscaled using the Statistical DownScaling Model (SDSM), synoptic observations, meteorological data, and the General Circulation Model (GCM). An Artificial Neural Network (ANN) was then employed to predict the groundwater level changes as a function of meteorological data, including Global Positioning System (GPS)-based PWV and the evapotranspiration index. The trained ANN, along with the downscaled meteorological indicators, was used to predict groundwater level changes over two time periods. In the first period, the prediction was performed over the current years to investigate the performance of the method using the available data, whereas in the second period, the prediction was performed for the coming years, up until 2030. The results confirmed the high performance of the prediction algorithm, and the importance of including PWV and evapotranspiration in groundwater level predictions. The Pearson correlation coefficient was used to check the relationship between groundwater level changes and meteorological variables. The statistical significance of these coefficients was tested at the significance level α=0.05. In more than 80% of the cases, the correlation coefficients were statistically significant, reaching more than 0.70 in some of the months. It is also observed that an increase in the depth of groundwater level has an obvious relationship with an increase in temperature and a decrease in rainfall.

The weighted total least squares (WTLS) has been widely used in many geodetic problems to solve the error-in-variable (EIV) models in which both the observation vector and the design matrix contain random errors. This method is widely applied in its univariate form, where the observations and unknown coefficients appear in vector forms. However, in some geodetic problems, data sets appear in more than one dimension, and the vector representation of the univariate model may not be suitable to efficiently solve the problem. The observation and unknown parameter vectors can then be replaced with their counterparts in matrix representations in a multivariate model. In this paper, we propose a simple, fast, and flexible procedure for solving the multivariate WTLS (MWTLS) problem using the standard least squares theory. The method has the capability of applying to large-size and high-dimensional data sets. Our numerical experiments on both simulated and real datasets demonstrate the high performance of the proposed method for solving multivariate WTLS problems. In terms of computational complexity, our method outperforms the existing state-of-the-art methods, both numerically and analytically.