By M. Schetzen
The e-book starts with a easy dialogue of the Doppler impression and its quite a few purposes, and the way Doppler radar can be utilized for the stabilization and navigation of airplane. 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 boundaries. A precis of the mathematical suggestions required for improvement of an actual idea is then provided utilizing the case of a slender beam antenna. this can be by way of the improvement of the precise conception for the final case, that's graphically illustrated and in comparison with the quasi-static approximation. common stipulations for which the quasi-static approximation mistakes will be over the top – in particular as utilized to laser Doppler radars and low-flying airplane – are presented.
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Extra info for Airborne Doppler Radar
QUASI-STATIC APPROXIMATION OF THE DOPPLER SPECTRUM 43 We’ll present illustrative graphs of dqs and sqs versus various antenna parameters for the case in which the terrain is a diffuse surface. A diffuse surface is one for which the backscatter follows the Lambert law, which is b sin b in which b is the angle between the incident wave and the plane of the terrain. A surface for which this is a good model is a smooth sandy ocean beach. In Fig. 1, b is the angle between the x –y plane and the line from the antenna to the point P.
3:4) AIRCRAFT DOPPLER STABILIZATION AND NAVIGATION 33 in which cr is the range angle and ca is the azimuth angle. Substituting this result in Eq. 3), we obtain dr ¼ Àv sin cr cos ca dt (3:5) The Doppler shift thus is d¼À 2v0 dr 2v0 ¼ v sin cr cos ca c dt c rad=s (3:6) Because, c ¼ lf0 , this expression also can be written in terms of the wavelength of the radiated wave l as d ¼ 2p 2v sin cr cos ca l rad=s (3:7) Because v ¼ 2pf in which f is in hertz, we also have d¼ 2v sin cr cos ca l hertz (3:8) The aircraft navigation and control will be obtained by determining the Doppler shift d at various range and elevation angles.
The Doppler shifts in hertz thus are: 1) For the fore antenna beam, df ¼ 2v sin (ue þ f p ) cos (fd ) l hertz (3:9a) 2) For the aft antenna beam, 2v sin (Àue þ f p ) cos (fd ) l 2v ¼ À sin (ue À f p ) cos (fd ) l da ¼ hertz (3:9b) 3) For the starboard antenna beam, p 2v sin (ua þ fr ) cos þ fd l 2 2v ¼ À sin (ua þ fr ) sin (fd ) hertz l dS ¼ (3:9c) 4) For the port antenna beam, p 2v sin (ua À fr ) cos À þ fd l 2 2v ¼ sin (ua À fr ) sin (fd ) hertz l dp ¼ (3:9d) Using standard trigonometric identities we then obtain 4v cos fd sin f p cos ue l 4v d f À da ¼ cos fd cos f p sin ue l 4v d p þ dS ¼ À sin fd sin fr cos ua l 4v d p À dS ¼ sin fd cos fr sin ua l d f þ da ¼ (3:10a) (3:10b) (3:10c) (3:10d) We then obtain by dividing one equation by another tan f p ¼ d f þ da tan ue d f À da (3:11a) 36 AIRBORNE DOPPLER RADAR tan fr ¼ À d p þ ds tan ua d p À ds (3:11b) tan fd ¼ À d p þ ds cos ue sin f p d f þ da cos ua sin fr (3:11c) We now can determine the pitch angle fp from Eq.