Range rate
Range rate defines a signed scalar value describing the time rate of change of the range between two locations.Derivation
Given a differentiable vector defining the instantaneous position of a target relative to an observer.
Let
with , the instantaneous velocity of the target with respect to the observer.
The magnitude of the position vector is defined as
The quantity range rate is the time derivative of the magnitude of, expressed as
Substituting into
Evaluating the derivative of the right-hand-side
using the expression becomes
Since
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.
