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The current approach includes an assumption that the sigma points that represent the distribution of states are valid sigma points on the time axis (i.e., the time when the state sigma points cross the threshold form the sigma points of the new EOL distribution). This is based on the strong assumption that the EOL distribution is similar to a gaussian distribution and is consistent to the state distribution.
This may be true for simple state transition or for a simple threshold shape, but may not be true for complex arbitrary threshold functions and state transition equations
@matteocorbetta had an idea for addressing this. Since we know the state to be gaussian, can we at each tilmestep, estimate the portion of the state distribution that is beyond the threshold, recording those numbers instead of just the sigma points.
@teubert suggested that we use @kjjarvis sample gain/shed approach to strategically add extra samples around the sigma points closest to the threshold in order to better define the shape of the distribution as it passes the threshold. The samples would be shed as they pass the threshold, being replaced by others further away.
The text was updated successfully, but these errors were encountered:
The current approach includes an assumption that the sigma points that represent the distribution of states are valid sigma points on the time axis (i.e., the time when the state sigma points cross the threshold form the sigma points of the new EOL distribution). This is based on the strong assumption that the EOL distribution is similar to a gaussian distribution and is consistent to the state distribution.
This may be true for simple state transition or for a simple threshold shape, but may not be true for complex arbitrary threshold functions and state transition equations
@matteocorbetta had an idea for addressing this. Since we know the state to be gaussian, can we at each tilmestep, estimate the portion of the state distribution that is beyond the threshold, recording those numbers instead of just the sigma points.
@teubert suggested that we use @kjjarvis sample gain/shed approach to strategically add extra samples around the sigma points closest to the threshold in order to better define the shape of the distribution as it passes the threshold. The samples would be shed as they pass the threshold, being replaced by others further away.
The text was updated successfully, but these errors were encountered: