This appendix includes expressions for partial derivatives of TOA and FOA measurements due to position, heading, and velocity in the notation used in the MathCad software tool. The subscripts i and k denote indices for a cross and downrange x-y emitter position, respectively.

Partial Derivative of TOA with Respect to Aircraft Position

Partial Derivative of FOA with Respect to Aircraft Position

Partial Derivative of FOA with Respect to Aircraft Heading

Partial Derivative of FOA with Respect to Aircraft Velocity

The following are the expressions for partial derivatives of emitter x-y location coordinates due to position and AOA measurements. The AOA measurement is computed as

Partial Derivative of Emitter x-y Location with Respect to Aircraft Position

Partial Derivative of Emitter x-y Location with Respect to AOA