[Paper Reading] A Tutorial on Quantitative Trajectory Evaluation for Visual(-Inertial) Odometry
Quantitatively comparing the estimated trajectory with the groundtruth, however, is not an easy task. There are two major difficulties.
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First, the estimated trajectory and the groundtruth are usually expressed in different reference frames, and, therefore, cannot be compared directly.
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Second, a trajectory consists of the states at many different times and, therefore, is high-dimensional data.
Thus, how to summarize the information of the whole trajectory into concise accuracy metrics is not trivial.
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To address the first problem, the estimated trajectory requires to be properly transformed into the same reference frame as the groundtruth, which is often called trajectory alignment.
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To address the second problem, meaningful error metrics need to be used and their properties well understood.
Roughly speaking, we integrate the raw IMU measurements to get the relative rotation ∆ R̃ ik , velocity ∆ṽ ik and position ∆p̃ ik between two states x i and x k , and the integration is formulated to be independent of the states (except for the biases) so that re-integration is not needed when the states change (e.g., during optimization iterations). The corresponding measurement model is
(6) has infinite solutions that have the same minimum cost. The reason is that the predicted measurements f (X) are invariant to certain transformations g(·) of the parameter, namely $f (X) = f (X’ )$ with $X’ = g(X)$. Since the measure- ments z̃ are constant, the cost function (7) is also invariant to