Method in [5] | Algorithm 1 | |
Max Error | 1.1849 | 0.25321 |
Mean Error | 0.51549 | 0.025642 |
The goal of motion tomography is to recover a description of a vector flow field using measurements along the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from trajectory data with the use of occupation kernels developed by Rosenfeld et al. [
Citation: |
Figure 3. A comparison of Algorithm 1 and the method of [5] for estimation of the vector field in (14)
Figure 4. To demonstrate universality of the occupation kernel basis, Algorithm 1 is used to estimate three different flow fields. The flow field in (14) (Flow field 1), a linear flow field (Flow field 2), and a constant flow field (Flow field 3). The plot shows the average estimation error, as defined in 16, plotted against the number of iterates of Algorithm 1 for the three flow fields
Figure 5. Simultaneous plots for estimation of the unknown flow field in the Gliderpalooza experiment using Algorithm 1 (green arrows) and the method of [5] (blue arrows)
Table 1. Algorithm 1, along with the technique in [5] are used to estimate the vector field in (14). The table shows the maximum and the average estimation error, as defined in (15) and (16), respectively, for the two methods
Method in [5] | Algorithm 1 | |
Max Error | 1.1849 | 0.25321 |
Mean Error | 0.51549 | 0.025642 |
Table 2. Norm difference statistics between estimates of the Gliderpalooza flow field, approximated using Algorithm 1 and the method in [5]
max norm difference | 0.14877 |
mean norm difference | 0.0088628 |
variance | 0.0001869 |
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Algorithm 1, used for estimation of the vector field in (14). The true trajectories are calculated via RK4 over the time frame
Calculated initial trajectories and output of Algorithm 1 for 5, 10, and 20 iterations on Gliderpalooza data
A comparison of Algorithm 1 and the method of [5] for estimation of the vector field in (14)
To demonstrate universality of the occupation kernel basis, Algorithm 1 is used to estimate three different flow fields. The flow field in (14) (Flow field 1), a linear flow field (Flow field 2), and a constant flow field (Flow field 3). The plot shows the average estimation error, as defined in 16, plotted against the number of iterates of Algorithm 1 for the three flow fields
Simultaneous plots for estimation of the unknown flow field in the Gliderpalooza experiment using Algorithm 1 (green arrows) and the method of [5] (blue arrows)