On the usage of derived quantities in tracking: Energy and other estimators

Survey of Maneuvering Target Tracking. Part II: Motion Models of Ballistic and Space Targets

“…It renders the 9-state general model as having only 7 free-state variables. This is consistent with the GT model (38) with (®,¯) replaced by (40), which has 7 states.…”

“…The uncertainty associated with the drag is a rather complex issue, analyzed in great detail in [81]. This uncertainty was coped with in [103] recently by using Additional references addressing modeling/ estimation issues include [20], [40], [1], [46].…”

“…The effect of the net (thrust minus drag) force is accounted for by (36)-(37) in this model. A similar model was given in [5, p. 138] as _ ® = ® 2 (t)=c (40) with an assumed known initial state ®(t 0 ) and known constant c, where the 7-dimensional state vector is x = [p 0 , v 0 , ®] 0 . The model (40) was also used in [54] within a state in spherical coordinates, along with two options to handle unknown c: includec (with _ c = 0) in the state vector as well as ®, or use multiple quantized values of c. It can be shown that for c = F(t 0 )=± = ®(t 0 )=¯(t 0 ), the only solution of (40) is given by (34) exactly; that is, both models describe the same net acceleration and are thus theoretically equivalent with this value of c. Equations (36)-(37) are preferable to (40) since the latter requires exact knowledge of the constant c while the former allow indirect estimation of it (at the expense of an extra state variable¯).…”

“…Similar to the 7-state GT model of (38) with (®,¯) replaced by (40), it presumes that the value of the exhaust velocity U is available [47,100]. Otherwise, a trivial solution is to include U as an extra state variable with the model _ U = 0.…”

“…Assuming negligible lift and coordinate accelerations, this 9-state general model with the GT constraint reduces to the 7-state GT model just mentioned with drag ignored (i.e., ® = ® T ). Indeed, with the GT constraint a T = ® T u v , (49) has the same form as (39), and (50) is equivalent to (40) without drag. This should come as no surprise.…”