Error estimation of the synthesized two-dimensional horizontal velocity in a bistatic Doppler radar system

This paper estimates the error of the magnitude of a synthesized two-dimensional horizontal velocity vector in a bistatic radar system that is composed of a single transmitter/receiver and a receiver. Two sources of error are identified in the synthesized velocity vector. One results from finite resolution in measuring the Doppler velocity at the transmitter/receiver and the receiver. The other is caused by finite resolution in detecting an azimuth angle at the transmitter/receiver and range at the receiver, resulting in errors in determining the scattering angle and the directions of the two Doppler velocities. The mean-square error of the synthesized Doppler velocity due to the former type of error is a minimum on an arc connecting the transmitter/receiver and the receiver, on which the scattering angle is approximately 100 degrees if the mean-square errors of the Doppler velocities at both the transmitter/receiver and receiver are equal. Within a crescent-shaped domain bounded by two arcs on which the scattering angle takes values of approximately 52 degrees and 142 degrees, respectively, this mean-square error is at most twice the minimum value. This domain naturally includes the arc of the minimum error mentioned above. This domain is called domain 1. The second type of error becomes very large near an infinite line that passes the transmitter/receiver and the bistatic receiver. The magnitudes of the mean-square errors of both types are compared for quickly rotating antennas and it is shown that the second type of error contributes more than 10% of the first one within a domain that contains the baseline (domain 2); thus, it cannot be neglected there. Outside domain 2, however, the contribution of the second type of error can be neglected. Then the optimal domain for measurement by this system is domain 1 with a domain in which domain 1 and domain 2 overlap being subtracted from it.