The increase in flight volumes in the aviation industry has significant socioeconomic implications that affect different aspects of our communities and economies. Although it has great economic benefits, it also causes annoyance and disturbance to communities living near airports. The latter requires understanding and prediction of the varying noise levels generated by various aircraft types. Noise assessment on a fleet level is traditionally achieved by using prediction models such as the DOC29. Such models need to be validated using real measurements. For Amsterdam Schiphol Airport, the so-called NOMOS (Noise Monitoring System) with 39 measurement stations is used for this purpose. We analyze the time series of these stations, collecting annual data for the period from 2006 to 2023. The main objective is to determine how the aircraft-generated noise at these stations can be assigned to 13 different aircraft types, taking into account the different noise levels produced by each aircraft type. This is performed by time series analysis of individual stations and the averaged time series over all stations. The results from two least-squares methods, namely unconstrained least squares (LS) and a proposed bounded least squares subject to weighted constraints (BLS + WC), are compared. The constraints are based on certification data as prior information in the least squares method, which is expected to enhance the model's performance. Based on the above two least squares methods, predictions are performed for 2022 and 2023. The results clearly demonstrate the superiority of the BLS + WC over the LS method. We further extend our analysis to predict noise levels for a hypothetical future year with more newer aircraft models. The results indicate a substantial reduction in the noise level compared to 2023. These findings can thus underscore the effectiveness of the proposed method in outperforming the LS and highlight the model's capability to forecast the impact of fleet modernization on noise reduction.

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.

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.

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.

Permanent GNSS stations continuously monitor Earth's crust movements in horizontal and vertical directions. The recorded data include deterministic variations, including linear trends, periodic signals, and offsets, alongside stochastic variations represented by various noise models. Accurately detecting deterministic behaviors depends on a realistic estimation of the observation noise model. A new multivariate algorithm based on Monte Carlo singular spectrum analysis (MCSSA) is developed to analyze the multiple channels of time-series data simultaneously (e.g., different position components or data from multiple stations), considering noise correlations without being limited to a specific noise model. Testing on simulated GNSS data showed that, by increasing the number of channels, the algorithm could accurately identify dominant annual and semiannual components in the presence of colored noise. The results also indicated that unrealistic assumptions about the GNSS position time-series noise model can be misleading in the MCSSA hypothesis testing. Applying the algorithm to real Greenland GNSS data confirmed the significance of annual and semiannual harmonic patterns when white plus flicker noise (FLWN) combinations were considered as the stochastic behavior of data. In the univariate analysis of the vertical position time series contaminated with random walk noise, none of the annual and semiannual signals were interpreted to be significant. At the same time, the proposed multivariate algorithm successfully identified the annual signal but lacked sufficient channels (stations) to confirm the significance of the semiannual signal in the presence of random walk noise. The multivariate analysis has confirmed the significance of semiannual signal across 21 time series contaminated with FLWN, which univariate analysis missed due to a high level of colored noise.

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.

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.

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.

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.

Earth orientation parameters (EOP) are critical for applications in orbit determination, astronomy, space geodesy, and geophysics. Accurate predictions of EOP rely on the identification of both deterministic periodic patterns and noise characteristics. This study addresses these requirements by analyzing the Polar Motion (PM) and Length Of Day (LOD) time series to determine its stochastic model structure, estimated using least squares variance component estimation (LS-VCE). With this model, deterministic periodic patterns were extracted through least squares harmonic estimation (LS-HE) and validated against colored noise components to identify significant signals. Using the IERS 14 C04 data from January 1, 2000, to December 31, 2019, the study identified the noise as power-law with a spectral index of −1.5, suggesting non-stationary fractional Brownian characteristics. LS-HE detected dominant frequencies in PM–notably the Chandler and annual signals–and in LOD, with annual, semiannual, 14-day, and 9-day signals. Building on these findings, short-, mid-, and long-term prediction model were developed for the PM and LOD time series from September 2021 to December 2022. The predictive model combines the LS-HE-extracted signals and the noise model to generate forecasts. These predictions were compared with other models from the Second Earth Orientation Parameter Prediction Comparison Campaign, demonstrating competitive accuracy, particularly for the initial forecast days. The results validate that combining LS-HE with a realistic noise model provides an effective approach for short-term of the PM and LOD forecasting, meeting the accuracy goals of geodetic and geophysical applications.

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.

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.

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.

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.

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.

Over the last decade, the aerospace industry has experienced a remarkable growth in the use of Unmanned Aerial Vehicles (UAVs) due to their low manufacturing and operational costs, adaptability, and scalability. In the context of climate change and desired emissions targets, UAVs are realistic options to complement the current freight transportation methods, and in the future, as an viable option for human mobility. UAVs are also starting to gain a place in emergency response, both in urban and rural areas, where aid or surveillance capabilities are required in short notice and a fast response is crucial. However, an important obstacle towards their broader use is the expected noise annoyance caused by UAV operations. In this study, we combine extensive outdoor measurements of drone noise with statistical modelling to predict acoustic metrics relevant to determining acoustic annoyance. Array-based measurements combined with GPS positioning information of an eVTOL fixed-wing UAV are studied under realistic operational conditions in an open field. The linear least squares theory is used to establish an empirical model and identify a set of control parameters, including acceleration and velocity, that serve as effective predictors of noise output. The results pave the way for the establishing a model that predicts drone noise for different UAV types and for different operational conditions.

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.

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.

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.

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.