Using integro-differential operators on low cost underwater autonomous vehicles

When operating low cost autonomous vehicles, we are often faced with the need to apply integro-differential operators to numerical sequences. The need may arise in many different contexts, from vehicle navigation to data collection/estimation, and is strongly reinforced by constraints to the number of deployable sensors. Integration and, particularly, differentiation of discrete data sequences are, however, error prone operations. Even in the absence of noise, the traditional approaches introduce distortions and artifacts in the output data, mostly due to the mismatch between their underlying polynomial model and the spectral contents of the collected data. This article presents an alternative way to apply integro-differential operators to discrete data streams. The operators are applied in a strictly bandlimited way, in both time and frequency, and no extraneous artifacts are introduced in the data. No assumptions or models are used, other than assuming that the original data stream was correctly sampled. As such, the procedure can be safely applied to data streams sampled at rates close to Nyquist, without the usual performance degradation.