Smurfjet,
there are some references available in the public domain.
Good introductory reading is this FAA booklet on TCAS II V7.0 :
http://www.smartcockpit.com/operations/TCAS.pdf . It has nice background knowledge but few mathematical details.
More details can be found in the PhD Thesis by Dr. Raoul R. Schild which is available online at
http://www.eos.tuwien.ac.at/Oeko/RSc...ules/index.htm . The appendix A1.4 (
http://www.eos.tuwien.ac.at/Oeko/RSc...ules/id235.htm) has some mathematical details. However, they have been copied over - apparently - from the PhD thesis of Dr. Harro von Viebahn at Darmstadt University. The presentation in v. Viebahn's thesis is much (!) better and more clear, being an excellent reference on the mathematics of TCAS.
v. Viebahns Thesis is - however - only available in paper but not online and written in German. The full reference is
as follows:
v. Viebahn H., "Konzeption und Untersuchung eines boardautonomen Systems zur Vermeidung von Kollisionen im Luftverkehr", PhD-thesis, Technical University Darmstadt, 1997
Last but not least you might want to look into Nancy G. Leveson's "Sample TCAS Intent Specification" (
http://www.safeware-eng.com/publications/TCASInt.pdf). This book however is *very* technical and hard to read. You'll have a hard time extracting useful information from it if you are not familiar with the topic.
Sure, all these references do not include any propietary material by Honeywell and information on the latest filters used for special cases used in the latest TCAS software versions.
If you can read German, get v. Viebahn's thesis which is a great reference on the basic mathematical models and their limitations with all the derivations from basic formulae.
EoD