Range rate
Range rate defines a signed scalar value describing the time rate of change of the range (distance) between two locations.
Derivation
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.
See also
References
Sources
- Hoffman, Kenneth M.; Kunzel, Ray (1971), Linear Algebra (Second ed.), Prentice-Hall Inc., ISBN 0135367972
- Renze, John; Stover, Christopher; and Weisstein, Eric W. "Inner Product." From MathWorld—A Wolfram Web Resource.http://mathworld.wolfram.com/InnerProduct.html
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