A partitionenhanced leastsquares collocation approach (PELSC)
DOI: https://doi.org/10.1007/s00190021015406
Persistent URL: http://resolver.sub.unigoettingen.de/purl?gldocs11858/10790
Persistent URL: http://resolver.sub.unigoettingen.de/purl?gldocs11858/10790
Zingerle, P.; Pail, R.; Willberg, M.; Scheinert, M., 2021: A partitionenhanced leastsquares collocation approach (PELSC). In: Journal of Geodesy, Band 95, 8, DOI: 10.1007/s00190021015406.

View/

We present a partitionenhanced leastsquares collocation (PELSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into subregions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a timeconsuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we precalculate the covariance function on a twodimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multivariate chain rule, also crosscovariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PELSC method. The new PELSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PELSC yields a speedup of computation time by a factor of about 55 (i.e., the computation needs only hours instead of weeks) in comparison with the classical unpartitioned LSC. Likewise, the memory requirement is reduced by a factor of about 360 (i.e., allocating memory in the order of GB instead of TB).