To deterministically validate Spotter motion sensing capabilities we use a purpose-built motion teststand, which provides extremely accurate positioning control. The control software can simulate any type of motions, limited only by the physical dimensions (6' by 6') and mechanical limitations (motor power, belt strength etc) of the stand. This motion-controlled validation stand provides a great platform for detailed testing of sensor capabilities. Note that although the results shown here are representative of our validation efforts, for any measurement device that relies in full or in part on GPS (such as Spotter), data results may vary depending on e.g. satellite constellation, multipath effects, view obstructions, and possibly atmospheric conditions.
Figure 1 shows time series of displacement for a periodic wave with 12s period and 1.2m wave height. A periodic - or sinusoidal - wave, is the most basic wave form we have. Although such a wave never actually occurs in the ocean, you could think of it as an archetype for a very narrow-band swell field traveling in from a remote storm. Due to its simplicity, the periodic wave is widely used as validation of wave sensors and it is certainly a good starting point. The agreement between the teststand and Spotter measurements for the periodic wave motion is excellent (see figure 1), both for the horizontal displacements (top panel) and vertical displacements (bottom panel). The correlation between the stand motion and Spotter data is 0.99 and 0.98 for the horizontal and vertical displacement time series respectively.
However, ocean waves are never purely periodic, and a more realistic simulation is that in which the wave energy has a wider distribution in frequency space. A well known and commonly occurring spectral shape in natural ocean wave fields is the so-called JONSWAP spectrum (see Hasselmann et al. 1973). A simulation with a realization that is randomly drawn from a JONSWAP frequency distribution is shown in figure 2. The random nature of the horizontal and vertical displacements are clearly visible, and the agreement between the motion stand and Spotter data is very good. Wave height estimates are within 4% of what was prescribed.
Since for random waves, the 'similarity' between two time series is less easily visually established (see figure 2), we can use a normalized cross-correlation function to help with that. In figure 3, the correlation functions between the teststand motion and Spotter data is shown for both the horizontal and vertical displacements. The correlation at zero time lag is a measure of 'similarity' of the two time series. In this case, the correlations are 0.96 and 0.9 for the horizontal and vertical motions respectively.
References
Hasselmann K., T.P. Barnett, E. Bouws, H. Carlson, D.E. Cartwright, K. Enke, J.A. Ewing, H. Gienapp, D.E. Hasselmann, P. Kruseman, A. Meerburg, P. Mller, D.J. Olbers, K. Richter, W. Sell, and H. Walden, 1973; "Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)" Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe, A(8) (Nr. 12).
