Circuit : Overview : Calculation of LMST
The clock displays LMST - Local Mean Sidereal Time to within a second. There are a number of factors affecting the accuracy, some being:
The most significant source of error is the difference between UT1 and UTC, and for observational purposes the difference between LMST and LAST. The remaining sources of error contribute less than a tenth of a second. If display of UTC is selected, the display is updated about one millisecond after the 1ppS pulse.
LMST should be calculated from UT1, a time standard based on the earth's rotation. UT1 is determined by observatories to within a few milliseconds. The time provided by the GPS module is UTC (Coordinated Universal Time), an atomic timescale that approximates UT1 but can differ by up to 0.9 seconds. The difference between UTC and UT1, known as DUT or DUT1 is published by the United States Naval Observatory, a current link being http://maia.usno.navy.mil/ser7/ser7.dat. The accuracy of the UTC time from the GPS is determined by the 1ppS signal and has negligable error.
LMST does not include some data that is used to calculate LAST - Local Apparent Sidereal Time. The United States Naval Observatory also provides a page where the difference between Mean and Apparent times can be calculated. See http://aa.usno.navy.mil/data/docs/siderealtime.php.
The microprocessor relies on the GPS module 1ppS (one pulse per second) (1) to compensate for deviation of the microprocessor clock from a nominal 4MHz (2) to provide an accurate time base for calculations. According to the NEO-6 data sheet the pulse is within 60nS of accurate for 99% of the pulses. This is not significant.
According to the NEO-6 data sheet, horizontal accuracy is within 2.5 meters. This introduces a time uncertainty of about 5mS
A sidereal second pulse is available on pin RB3 of the processor, and is controlled by hardware. It is produced within a few microseconds of the calculated time. The update of the display is controlled by software and takes about 1mS.
The simple formula used does not include square and cube terms. In 2015 this introduces an error of about 2mS, which will increase to 10mS by 2100. The calculations use fixed point arithmetic, keeping time values in seconds with 24 bits of fraction. Summing all terms of the equation gives a maximum error of less than a microsecond, which is negligable.