The Crazy Lune - Location Algorithm

			The Crazy Lune

Location Algorithm

In order to apply the Kalman Filter we use following model of our system:

where (xi ,yi , zi) denotes the position of tag i and (vx, vy, vz) denotes the velocity of the astronaut and w is a zero mean gaussian error with the covariance matrix.

We do not measure the velocity of the astronaut, but we know, that it has to be within a certain range, as the walking speed of the astronaut will be less than < 1.5m/s. Therefore, we assume the velocity to be zero and take the error into account with the process noise w. This gives us the ability, to easily implement velocity measurements of additional sensors in a later stage, if needed.

Following measurement model is used:

where di is the distance of tag i from the astronaut and r again is a zero-mean gaussian with error covariance

This is the measurement error we derived in the astronaut to RFID link section.

As you can see, not only the x,y and z coordinate of the astronaut, but also each coordinate of of the dropped tag is used in the algorithm. Each time we drop a tag, the state vector grows, so in order to save computation time at each step, only the tags that are 'active'(in reach) are considered and updated. This gives us the advantage, that after dropping a tag, the location estimate of the tag is not fixed and constantly improves as long as the tag is in reach.

Now the equations for the Extended Kalman Filter look like the following:

P is the error covariance matrix of the state vector that gets updated at each step in the Kalman filter.
This gives us at each time-step, the estimate of the state vector x and hence our position and the position of the tags.

Tuesday, December 8, 2009