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)

Substituting (2) into (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 .

See also

References

  1. Hoffman, Kenneth M.; Kunzel, Ray (1971). Linear Algebra (Second ed.). Prentice-Hall Inc. p. 271. ISBN 0135367972.

Sources

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