I am interested to know the basic principle of the "Delayed KF" when considering an underwater robot aiming to localize it self using a LBL system.
More practically, in order to calculate the distance to each anchor, the robot transmits a PING to and waits for the RESPONSE from the anchor. This is time consuming as the sound velocity is very low (1500m/s). Lets say it will take order of 5/10 seconds to complete such iteration (large distances).
If the robot is static (during this operation, or the anchors are very close), I can recover the two travel time, TWTT, and after that the distance (knowing the sound velocity, divide by two etc). In that case i can include the range to my EKF navigation filter.
Assuming that the robots moves (1 m/s) this assumption does not hold anymore as I can not divide the TWTT by a factor of 2.
Searching online i found talking about the delayed EKF in which (in my understanding) having a measurements timestamped (the real time and the time when i got it) i re-run the filter at the right time when the measurements was/or should have been done.
Does this hold also for this case and how can be integrated with the navigation filter of the robot?
Geometrically to find the right distance based on the TWTT and considering the movement done during that time seems hard to me to model. At least i have not found any paper in the literature.