How does MLAT work?

Mode S transponders transmit on 1030 Mhz. ADS-B receivers like the PIAware have only 1090Mhz receivers. How does MALT work when the receivers can not even receive the frequency that the transponders are transmitting on?

Mode S transponders don’t transmit on 1030 MHz, they transmit on 1090 MHz. 1030MHz is the uplink frequency used by ground stations to interrogate aircraft.

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The Air Traffic Control Radar Beacon System (ATCRBS) and the
Mode Select (Mode S) system have a ground-based and airborne component and operate
on the frequencies of 1030 MHz and 1090 MHz.

https://www.ntia.doc.gov/files/ntia/publications/compendium/0960.00-1164.00_01MAR14.pdf

The interrogation y ATC radar is done on 1030 MHz, the transponder then responds on 1090 MHz.

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MLAT is similar to how GNSS/GPS works.Both use trilateralisation
You have several known ground location. Each ground location gets timing information from specific ADS-B signals. The MLAT servers use this timing information to work out the location of aircraft that are not transmitting position information.
With MLAT the receiving locations are known. With GNSS/GPS the satellite locations are known. GNSS/GPS use much larger distances, however, the clocks are better.

Here are a couple of more detailed articles:-

https://www.e-education.psu.edu/natureofgeoinfo/c5_p12.html

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