A canonical definition of bistatic doppler, or doppler shift, f B, ignoring relativistic effects, is the time rate of change of the total path length of the scattered signal, normalized by the wavelength ? [1]. Because the total path length is the range sum, R T + R R,
Figure 6.1 defines the geometry and kinematics for bistatic doppler when the target, transmitter, and receiver are moving. The target's velocity vector projected onto the bistatic plane has magnitude V and aspect angle ? referenced to the bistatic bisector. The aspect angle is positive when measured clockwise from the bistatic bisector. The transmitter and receiver have projected velocity vectors of magnitude ? T and ? R and aspect angles ? T and ? R, respectively, per the North-referenced coordinate System of Figure 3.1.
When the transmitter and receiver are stationary ( V T = V R = 0) and the target is moving ( V ? 0), the target's bistatic doppler at the receiver site is developed as follows. The term d R T/d t is the projection of the target velocity vector onto the transmitter-to-target LOS:
where ? and ? are shown in Figure 6.1. Similarly, d R R/d t is the projection of the target velocity vector onto the receiver-to-target LOS:
Combining (6.1b), (6.2), and (6.3) yields
where f Tgt
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