Bathymetric data fusion: PCA based Interpolation and regularization, sea tests, and implementation

In this paper a recently introduced signal processing technique is exploited for the interpolation and regularization of multidimensional sampled signals with missing data, based on Principal Component Analysis (PCA). The non-iterative methodology proposed corresponds to the optimal solution to a regulated weighted least mean square minimization problem, based on estimates for the mean and covariance of signals corrupted by zero-mean noise. Additionally, is deduced an estimate for the mean square interpolation error, with upper and lower bounds also available. Some refinements are used to improve the solution proposed, namely: (i) mean substitution for covariance estimation, (ii) Tikhonov regularization and, (iii) dynamic principal components selection. The resulting method will be applied to bathymetric data, acquired at sea with the advanced robotic tools IRIS and the Infante AUV, in the passage between the islands of Faial and Pico, Azores. The results obtained pave the way to the use of the proposed framework in a number of sensor fusion problems, in the presence of missing data.