By M. Schetzen
The e-book starts with a easy dialogue of the Doppler influence and its numerous purposes, and the way Doppler radar can be utilized for the stabilization and navigation of plane. A quasi-static approximation of the Doppler spectrum is gifted besides illustrations and discussions to assist the reader achieve an intuitive realizing of the approximation and its barriers. A precis of the mathematical strategies required for improvement of an actual concept is then offered utilizing the case of a slim beam antenna. this can be via the advance of the precise conception for the overall case, that's graphically illustrated and in comparison with the quasi-static approximation. normal stipulations for which the quasi-static approximation mistakes will be over the top – particularly as utilized to laser Doppler radars and low-flying airplane – are presented.
- facts and data showing during this e-book are for informational reasons simply. AIAA and the writer aren't liable for any damage or harm caused by use or reliance, nor do AIAA and the writer warrant that use or reliance could be loose from privately owned rights..
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Additional info for Airborne Doppler Radar
Unfortunately, even though the transmitted wave is a sinusoid, the echo will not be a sinusoid with a frequency that is the transmitted frequency v0 shifted by d. Rather, the echo will be a nonsinusoidal waveform. The reason is that the echo is the sum of the reﬂections from many terrain particles in the antenna beam. Observe that dr=dt varies as a particle travels through the antenna beam and it also differs from particle to particle. In addition, the return from a given particle is amplitude modulated by the antenna pattern and with the manner in which the backscattering from the particle varies with angle.
Clearly, if T is a period, then so is nT in which n ¼ 1, 2, 3, . . The smallest value of T ¼ T1 is called the fundamental period of p(t). If a waveform p(t) is periodic with a fundamental period T1, then, with certain mild conditions that are met by physical waveforms, it can be expressed as the linear combination of sinusoids with the harmonic frequencies vn ¼ nv1 in which v1 ¼ 2p=T1 as p(t) ¼ 1 X An cos (vn t) þ Bn sin (vn t) n¼0 This expression is called the Fourier series of the periodic waveform p(t).
Aircraft Navigation and Stabilization In order not to obscure our discussion of the manner by which an aircraft can be stabilized and navigated using an airborne Doppler radar, we shall simplify our discussion by considering the echo to be a sinusoid with a frequency that has been shifted from the transmitted frequency by the Doppler shift given by Eq. 8). In practical application, the actual spectrum width causes a small random error in the measurements that can be determined using the exact theory developed later in this text.