There are different variations within Tropical and Sidereal Astrology to determine what specific variation of calculations are used.
To break it down, Tropical and Sidereal are two different maths systems. Totally different. And then within them, you have mini slight variations based on its calculation. An Ayanamsa is the calculation of these slight variations within its chosen system.
This is to do with a mathematic variation on where it is believed the exact star points within the constellation are located. This is especially important if you have something within 29-1 degree in which the slight variation can change your sign! :D So I feel Krishnamurti is most accurate from my testings. I note this through some systems moving my Mercury which is at 1 degree and my Ketu moving in and out of Magha.
But of course Kapiel goes into a lot more of the Astrologers that he follows using KP.
Also I believe its closest to the Ayanamsa system provided by J K Goodwin.
In 1997 the ayanamsa mathematics calculation was:
Fagan-Bradley: 24° 49′
Lahiri: 23° 49′
K.S. Krishnamurti: 23° 43′
B. V. Raman: 22° 22′
The difference in the degrees of the systems are for an example for 1988:
Sun: 15.01, Moon: 4.12, Mercury: 0.57, Venus: 21.51, Mars: 25.35, Jupiter: 3.09, Saturn: 11.41, Rahu: 12.54 and Ketu: 12.54.
Sun: 14:08, Moon: 3.19, Mercury: 0.04, Venus: 20.58, Mars: 24.52, Jupiter: 2.16, Saturn: 10.48, Rahu: 12.01 and Ketu: 12.01.
Sun: 15:07, Moon: 04:18, Mercury: 1:03, Venus: 21:56, Mars: 25:41, Jupiter: 03:14, Saturn: 11:46, Rahu: 13:0 and Ketu: 13:0.
Ayanamsa Krishnamurti Degrees [Coming Soon]
(c) Watcher, S, 2014. Specific Maths System Used (Ayanamsa). www.freesiderealastrology.com [ONLINE]. http://www.freesiderealastrology.com/specific-maths-system-used-ayanamsa/.