Noise Removal from Duplicate Paleoceanographic Time-Series: The Use of Adaptive Filtering Techniques

This study demonstrates that adaptive filters can be used successfully to remove noise from duplicate paleoceanographic time-series. Conventional methods for noise canceling such as fixed filters cannot be applied to paleoceanographic time-series if optimal filtering is to be achieved, because the signal-to-noise ratio is unknown and varies with time. In contrast, an adaptive filter automatically extracts information without any prior initialization of the filter parameters. Two basic adaptive filtering methods, the gradient-based stochastic least-mean-squares (LMS) algorithm and the recursive least-squares (RLS) algorithm have been modified for paleoceanographic applications. The RLS algorithm can be used for noise removal from duplicate records corrupted by stationary noise, for example, carbonate measurements, species counts, or density data. The RLS filter performance is characterized by high accuracy and fast rate of convergence. The modified LMS algorithm out-performs the RLS procedure in a nonstationary environment (e.g., stable isotope records) but at the price of a slower rate of convergence and a reduced accuracy in the final estimate. The application of both algorithms is demonstrated by means of carbonate and stable isotope data.