Comparable Bathymetry Uncertainty Estimators with Kalman Filters or Linear Smoothers

We examine and contrast different estimation methods for creating gridded data products from bathymetry measurements, specifically 1) the Kalman filter that is used for processing data from modern, high-density, multibeam echo sounders and 2) the class of linear smoothers that have been used historically for gridding all forms of irregularly spaced geophysical measurements. Simulations are used to compare the performance of the simplest estimator, nearest neighbor, Kalman estimator and Loess from the class of linear smoothers. The issue of how to obtain comparable uncertainty estimates for the gridded data using the different estimation approaches is addressed. Achieving comparable estimation is accomplished by applying the propagated uncertainty concept that has been previously proposed in the literature and a numerical realization of Tobler’s first law to the measurement data prior to the computation of the estimate, no matter which form of estimator is used.