The question is not very clear to me. However, target tracking definitely needs "time" as one of its variables, hence, time stamp is an essential feature in that application.
Yuo can still estimate your parameters without time tags if you are simply doing a target tracking, e.g., using a tottal station. However, you need to have enough measurements record by record (at each tracking record) to determine your parameters (e.g., the target position etc.). A Kalman filter normally consists of a system model and a measurement model. However, the number of the measurements are not enough to estimate the state vector without the system model . The situaion where you do not have a system model and you have enough measurements to determine your target positions at each tracking, you can just simply run a Least -Squares adjustment.
It depdends on what your application is. The traditional target tracking using the total stations may only need to determine the target's path in position. why do you have to have timing tags?
The problems of delay and oosm are usually handled using time stamped measurements in papers. But sometimes timing tags of measurements aren't available so one can not determine delays of measurements. There aren't any method to solve this type of problems in multi target tracking literatures.
I still cannot thnik more without the real situation. Are you using the standard tracking mode with a total station? What is the accuracy requirement?
What I can recall was: as you may know, the positioning of the boat for underwater topographic mapping was done in this way long time ago in the past. We set up two theodolites on the (river) bank to track the target on the boat to determine its trajectory as the water depth was measured at the same time. There was no time involved.
Two factors should be the keys: slow motion and reasonable accuracy requirement.