19.5 The Generation of Synthetic Data

In order to evaluate the performance of the various tracking filter methods, we developed a synthetic rigid body and created synthetic trajectories indicative of the store release event. This gives us a synthetic “truth” trajectory that allows us to create synthetic observation sets as seen from synthetic cameras by adding Monte Carlo sets of pixel noise. The synthetic camera measurements can then be used to perform Monte Carlo RMS error analysis comparisons of the estimation (solver) methods.

19.5.1 Synthetic Rigid Body Feature Points

We first construct a rigid body with eight feature points out of a unit cube by constructing a 3 × 8 matrix S, where the i th column of S is the feature point img

(19.99) equation

Then we apply an affine transformation that makes the cube long and thin

(19.100) equation

where

(19.101) equation

19.5.2 Synthetic Trajectory

To build a synthetic trajectory we first generate a sequence of times t, where

(19.102) equation

Then we define a damped sinusoidal function ...

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