Trajectory Representation
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To track the n most likely trajectories
For each new time step until the end of time
Create full copy of the model for the new time step
Assign command and observation variables
Until n consistent trajectories found
Enumerate the next best t-length trajectory
Throw it out if inconsistent
Report the t-length trajectories

An Algorithm with Only Two Problems!
Space  - Representation grows linearly with time
Time   - Search space grows exponentially with time                          - Checks an exponential number of obviously wrong candidates

The assignments to t capture every possible trajectory
Trajectories can be enumerated in prior probability order
P(trajectory) = S P(t assignment)
Each trajectory can be checked for agreement with observations





Avoid committing to a small number of trajectories
Build a structure that compactly represents all evolutions
Generate additional trajectories in order as needed