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Range rate defines a signed scalar value describing the time rate of change of the range (distance) between two locations.
Given a differentiable vector defining the instantaneous position of a target relative to an observer.
Let
| (1) |
with , the instantaneous velocity of the target with respect to the observer.
The magnitude of the position vector is defined as
| (2) |
The quantity range rate is the time derivative of the magnitude (norm) of , expressed as
| (3) |
Evaluating the derivative of the right-hand-side
using ( 1 ) the expression becomes
Since [1]
With
The range rate is simply defined as
the projection of the observer to target velocity vector onto the unit vector.
A singularity exists for coincident observer target, i.e. . In this case, range rate does not exist as .
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