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Abstract

Multi-GNSS now routinely measures positions precisely at a high sampling rate, up to mm-level of precision within a few minutes or cm-level in the long term of hours and days. A high sampling rate becomes critical in GNSS determination of velocity and acceleration, since difference methods are always used to determine velocity and acceleration from GNSS precise positioning on the implicit assumption of a low sampling rate of GNSS measurements, because the random errors of GNSS-based velocity and acceleration are proportional to the sampling rate in the case of velocity or square-proportional to the sampling rate in the case of acceleration. There are a number of critical technological problems with GNSS accelerometry: (i) with the increase of sampling rate, measurement errors are significantly amplified such that computed velocity and acceleration are completely immersed into noise and of no physical significance. Thus, GNSS precise positioning with a sampling rate higher than a few Hz has to be first down-sampled to, say 1 or 2 Hz; (ii) down-sampling very high-rate GNSS precise positioning measurements directly results in a lower resolution of velocity and acceleration, a larger aliasing effect and signal distortion, the extent of which depend on that specific rate of sampling; and (iii) a low sampling rate also implies impossibility to provide instantaneous velocity and acceleration. We present a regularization method to compute velocity and acceleration and design its apparatus, which solves the mentioned critical technological problems and lead to the technological invention of accelerometers.