Editing MISTRAM (section)

==Principles of operation==
[[Image:MISTRAM-layout.jpg|thumb|right|Five receiving stations on 10,000 ft and 100,000 ft baselines receive signals from missile, compute the velocity, position and trajectory.]]
MISTRAM is a sophisticated interferometer system consisting of a group of five receiving stations arranged in an L shape. Baselines are {{convert|10000|ft|m|abbr=on}}. and {{convert|100000|ft|m|abbr=on}}. The central stations contains a simple tracking antenna. The distance from the central station to the furthest remote station is approximately {{convert|100000|ft|m|abbr=on}}. Antennas at the central station and the four remote stations follow the flight of a missile and receive signals from its radio beacon.

In the MISTRAM system, the ground station transmits a carrier to the spacecraft and the spacecraft returns this carrier on another frequency. The ground station sweeps the uplink carrier and the phase shift of the downlink carrier is measured (counted) while it is being swept. The round trip delay time can be shown to be T=(delta-phi)/(delta-f); where delta-f is the frequency shift (~4000&nbsp;Hz for example) and delta-phi the measured phase shift in radians. Suppose T=2 sec (~lunar distance) then delta-phi=8000 radians, i.e. (8000*180)/Pi. Assume also that the phase can be measured with an accuracy of 1 deg, i.e. means that the range can be determined with a precision of (600000*1*Pi)/(2*8000*180)=0.33&nbsp;km. An additional carrier quite near the one described above that remained fixed in frequency and used as a phase reference. That carrier and the two frequencies (that the sweep changed between) were generated as multiples of the same basic oscillator frequency. In this way, all signals would have a fixed phase relationship, as was done in MISTRAM. A similar technique was used in the Soviet Luna 20 spacecraft at 183.54&nbsp;MHz to survey the Moon's surface.<ref>{{cite web|title=Reception of signals on 183.54 MHz from the Luna 20 return spacecraft in Stockholm|url=http://www.svengrahn.pp.se/trackind/luna20/LUNA20.htm|author=Sven Grahn|location=Sollentuna, Sweden}}</ref>

MISTRAM was a multistatic long baseline radar interferometer developed for precision measurements of missile trajectories at the US Air Force Eastern Test Range. Multistatic radar systems have a higher complexity with multiple transmitter and receiver subsystems employed in a coordinated manner at more than two sites. All of the geographically dispersed units contribute to the collective target acquisition, detection, position finding and resolution, with simultaneous reception at the receiver sites. In a simpler sense, multistatic radars are systems which have two or more receiving sites with a common spatial coverage area, and data from these coverage areas are combined and processed at a central location. These systems are considered to be multiple bistatic pairs. Multistatic radar systems have various uses, including prevention of jamming and anti-radar munitions.

Although this method of measurement is not new, either in theory or in practice, the unique manner in which the techniques were implemented in the MISTRAM system permit measurement of vehicle flight parameters with a degree of precision and accuracy not previously obtainable in other long baseline trajectory measurement systems. To a large extent, this was accomplished by a unique method of transferring intact the phase information in the signals from outlying stations to the central station. A two-way transmission path on each baseline was used to cancel out uncertainties due to variance in ground geometry and temperature.<ref name="astronautics">{{cite journal|author1=R.A. Heartz  |author2=T.H. Jones |name-list-style=amp |title=Mistram and rendezvous|journal=Astronautics|volume=7|date=July 1962|pages=47–50}}</ref>

[[Image:MISTRAM-diagram.jpg|thumb|right|MISTRAM block diagram shows ground-based components and airborne transponder.]]
The transmitter at the master or central station generates two CW X-band frequencies, nominally 8148&nbsp;MHz and 7884 to 7892&nbsp;MHz. The higher frequency (the range signal) is very stable, whereas the lower frequency (the calibrated signal) is swept periodically over the indicated range. The airborne transponder receives the signals, amplifies & frequency shifts them by 68&nbsp;MHz, and retransmits back to earth. The Doppler shift is used to determine velocity.<ref>{{cite journal|author=Jerome Hoffman|title=Relativistic and classical Doppler electronic tracking accuracies|journal=Journal of Spacecraft|volume=2|issue=1|date=Jan–Feb 1965|pages=55–61|doi=10.2514/3.28121|bibcode=1965JSpRo...2...55H|url=http://www.dtic.mil/get-tr-doc/pdf?AD=AD0409906|archive-url=https://web.archive.org/web/20170925112309/http://www.dtic.mil/get-tr-doc/pdf?AD=AD0409906|url-status=dead|archive-date=September 25, 2017}}</ref>

The Florida MISTRAM system had {{convert|100000|ft|m|abbr=on}} baselines (~18.9&nbsp;mi.) with design performance as follows:

{| class="wikitable"
|+ Range of Operation
|-
| Velocity|{{convert|0|to|50000|ft/s|m/s|abbr=on}}
|-
| Acceleration|{{convert|0|to|750|ft/s2|m/s2|abbr=on}}
|-
| Azimuth|360 deg
|-
| Elevation|5 to 85 deg
|-
| Range|20 to {{convert|1000|mi|km|abbr=on}}
|}

{| class="wikitable"
|+ Measurement Uncertainties (RMS)
|-
| Range|{{convert|0.4|ft|m|abbr=on}}
|-
| Range difference|{{convert|0.3|ft|mm|abbr=on}}
|-
| Range rate|{{convert|0.02|ft/s|mm/s|abbr=on}}<ref group=n name=note>one-half second of smoothing.</ref><ref name="astronautics"/>
|-
| Range rate difference|{{convert|0.002|ft/s|mm/s|abbr=on}}<ref group=n name=note/><ref name="astronautics"/>
|}
{{Reflist|group=n}}