State Tracking and Fault Diagnosis for Dynamic Systems Using Labeled Uncertainty Graph

. 2015 Nov 5;15(11):28031–28051. doi: 10.3390/s151128031

Algorithm 2: Roll back process

1:  Input:    Label uncertainty graph LUG
2:  Output: A set of possible trajectories  $T r a j e c t o r y = {T_{1}, T_{2}, ..., T_{n}}$ 
3:  For each time-step t>0 do
4:         For each belief state  $B_{t}$  in proposition layer  $P_{t}$  do
5:               For each particle  $p_{j}, j = 1, ..., N$  in belief state  $B_{t}$  do
6:                     Extract the belief state  $B_{t - 1}$  in  $P_{t - 1}$  which also contains the same particle  $p_{j}$ 
7:                     Roll back to generate the trajectory  $T r a j_{j} = {B_{t - 1}, A_{t - 1}, B_{t}}$  from  $B_{t}$  to  $B_{t - 1}$ 
8:                     Construct a new trajectory tuple  $T_{j} = (T r a j_{j}, w_{j} = 1)$ 
9:                     Add  $T_{j}$  into obtained most likely trajectories  $T r a j e c t o r y$ 
10:                   Merge the same trajectory and update the weight 
11:               End For
12:      End For
13: End For