If a katyusha is a primitive rocket, it can't help but follow a ballistic path.
If you get 3 paintings, you can redraw the parabola. If you get more than 3, you can use a more complex trajectory that would compensate for spin.
Baseball players, if they are good batters, try to pick up the ball off the pitchers hand, then sample 2 or 3 more locations. If they can get 3 more, for a total of 4, they can compensate for the ball's spin. If they only get 2 more, for a total of 3, they swing as for a fastball.
Modern radars get hundreds of paintings, but for ballistic targets, they use them to correct error and ambiguity, rather than to get a more complex model.
My concern would be that physical asymmetries in missile shape, weight distribution, fuel burn pattern and the like would distort a simple ballistic trajectory, and cause a backward trace based on a few path points to indicate an erroneous launch point.
Maybe I'm wrong.