The Siddhāntas were a series of early works used by the early Vedic astronomers.
They slowly replaced much of the Vedāṅga Jyotiṣa, but were later on amended, corrected, and replaced in usefulness by the works of the moder modern astronomers.
There were 18:
|Yavana or The Greek|
|Sūrya or Saura|
|Lomaśa or Romaka|
The Romaka and Pauliśa are described by Kuppanna Sastry as 'clearly western'. 
Later analysis and improvement
The Paitāmaha contains information similar to the Vedāṅga Jyotiṣa, and thus was seen as less accurate than the more modern works. Vāsiṣṭha was more up to date. It described the Zodiac, Nakṣatras, the five planets, the sidereal and solar year, &c. The Pauliśa was very good as well,  but the Sūrya was described as the best. 
Muñjāla, in his Laghumānasa complained that the inconsistency between the different Siddhānta's produced confusion regarding the correct timing of Vedic rituals. Thus, "worldly life gets disrupted. Alas! We have been preciptated into a big calamity."