E.1 INTRODUCTION

This appendix develops exact and approximate relationships between parameters in target location and clutter doppler spread equations. The parameters are shown in Figure E.1, using the North-referenced coordinate System of Figure 3.1. Because exact relationships are required, the isorange contour must be an ellipse, rather than the tangent approximation (perpendicular to the bistatic angle bisector). Initially, this requirement would seem to be intimidating, but the results are surprisingly tractable when ellipse eccentricity, e, is used in the development.

Figure E.1: Geometry for target location and clutter doppler spread

The isorange contour of interest is defined by an ellipse as

where 2 a is the major axis of the ellipse. Eccentricity of the ellipse, e, is

In all expressions involving e, when the target lies on the baseline, e = 1 and the parameters become indeterminate.

E.2 TARGET LOCATION

When L, ( R _T + R _R), and ? _R are measured, R _R and R _T are calculated as follows. From the law of cosines:

and

Combining (E.2b) and (E.6) yields

Combining (E.2b) and (E.7) yields

When L, ( R _T + R _R), and ? _T are measured, R _R and R _T are calculated in a similar manner. From the law of cosines:

and

Combining (E.2b) and (E.1 1) yields

Combining (E.2b) and (E.12) yields

E.3 PARAMETER RATIOS

From the law of sines:

Thus,

and

Combining (E.8), (E.13), and...