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Location service demands precise positioning, which can be obtained by applying maximum likelihood or least squares (LS) directly to measurements such as ranges and/or pseudoranges or to the computed quantities of measurements such as squared ranges and their differences. Nonlinearity and the stochastic models of computed quantities of measurements are not yet taken into account in precise location estimation. We propose a bias-corrected weighted LS method for precise location service, which consists of two basic elements. One is to automatically correct both the bias due to model nonlinearity and the induced biases in squared ranges/pseudoranges, and the other is to sequentially estimate unknown location parameters by treating equality constraints as a condition adjustment. As a result, the location estimation is theoretically almost unbiased. The method is applied to ranges, squared ranges and the differences of squared ranges. We also work out bias-corrected precise location estimation from pseudoranges, squared pseudoranges and the differences of pseudoranges. A large scale of simulations is carried out with range- and pseudorange-based models, respectively. The simulation results have clearly indicated: (i) the proposed bias-corrected weighted LS method can indeed result in almost unbiased estimates of location and further improve precise location estimation, depending on model nonlinearity and the ratio of signal to noise; (ii) the bias-corrected weighted LS method with the Gauss—Newton algorithm is shown to perform best in terms of the smallest bias and mean squared errors (MSE), if directly applied to ranges with a well-conditioned configuration, since it avoids the extra nonlinearity of squared ranges/pseudoranges and the induced bias of these computed quantities; (iii) the bias-corrected weighted LS and the weighted LS methods are of almost the same best performance in terms of MSE roots for each type of measurement models of ranges/pseudoranges, squared ranges/pseudoranges and the differences of squared ranges/pseudoranges. Nevertheless, the measurement models with the differences of squared ranges perform less accurate in the vertical component than those with ranges and squared ranges in the example, due to a weaker geometrical constraint; and (iv) the ordinary LS method clearly results in the most biased estimates of location and is of the worst accuracy for all the six measurement models of ranges/pseudoranges, squared ranges/pseudoranges and the differences of squared ranges/pseudoranges, indicating the importance of using correct stochastic models of measurements for location estimation. [ABSTRACT FROM AUTHOR]

The algebraic fitting of circles was first proposed by Delogne (1972) and Kasa (1976). We extend the work by Delogne (1972) and Kasa (1976) and propose fast and almost unbiased weighted least squares to best fit circles. The simulations have shown that two non-iterative versions of the bias-corrected weighted LS method are fast and almost unbiased and perform much better than the naive weighted LS method (without applying any bias correction), the ordinary LS-based methods and the gradient-based weighted LS method in terms of both biases and mean squared errors, no matter whether fitting of circles is strongly or weakly constrained geometrically. Nevertheless, a weak geometrical constraint results in a poor fitting of circles. We accordingly propose the regularized variants of the bias-corrected weighted LS method to fit circles from data with a weak geometrical constraint. The simulations have also shown that the two non-iterative regularized variants fit circles satisfactorily well and consistently perform the best among all the regularization methods under study for ill-conditioned problems of fitting circles. • Removing the bias of computed data to construct almost unbiased estimates for algebraic fitting. • Improving the standard algebraic fitting of circles by Delogne (1972) and Kasa (1976). • Proving that the gradient-based weighting is not statistically optimal. • Proposing the statistically rigorous weighted LS method to estimate the circular parameters. • Proposing a fast, bias-corrected regularization for algebraic fitting of circles. [ABSTRACT FROM AUTHOR]

Landslides, resulting from disturbances in slope equilibrium, pose a significant threat to landscapes, infrastructure, and human life. Triggered by factors such as intense precipitation, seismic activities, or volcanic eruptions, these events can cause extensive damage and endanger nearby communities. A comprehensive understanding of landslide characteristics, including spatio-temporal patterns, dimensions, and morphology, is vital for effective landslide disaster management. Existing remote sensing approaches mostly use either optical or synthetic aperture radar sensors. Integrating information from both these types of sensors promises greater accuracy for identifying and locating landslides. This study proposes a novel approach, the ML-LaDeCORsat (Machine Learning-based coseismic Landslide Detection using Combined Optical and Radar Satellite Imagery), that integrates freely available Sentinel-1, Palsar-2, and Sentinel-2 imagery data in Google Earth Engine (GEE). The approach also integrates relevant spectral indices and suitable bands used in a machine learning-based classification of coseismic landslides. The approach includes a robust and reproducible training and validation strategy and allows one to choose between five classifiers (CART, Random Forest, GTB, SVM, and Naive Bayes). Using landslides from four different earthquake case studies, we demonstrate the superiority of our approach over existing solutions in coseismic landslide identification and localization, providing a GTB-based detection accuracy of 87–92%. ML-LaDeCORsat can be adapted to other landslide events (GEE script is provided). Transfer learning experiments proved that our model can be applied to other coseismic landslide events without the need for additional training data. Our novel approach therefore facilitates quick and reliable identification of coseismic landslides, highlighting its potential to contribute towards more effective disaster management. [ABSTRACT FROM AUTHOR]