There are three primary Jewush calendars
These are:
1. the Biblical Hebrew Calendar
2. the Talmudic Hebrew Calendar
3. the Post-Talmudic Hebrew Calendar
The Biblical Hebrew Calendar was based on visual observations of the "signs" (the moon and seasons).
The Talmudic Hebrew Calendar was developed to address issuss of beginning Nisan at the inappropriate time.
For example, under the patriarchate of Rabbi Judah I (163-193) the Samaritan set fires to disrupt the existing system and obscuring visibility the month was started at an inappropriate time. Weather, inaccurate reports from messengers, and errors in the Sanhedrin evaluation - like under the leadership of Gamaliel II (80 AD to 118 AD) - highlighted the need for a new system.
Under the leadership of Rabbi Judah III. (300-330) the testimony of the witnesses became secondary to mathametical calculations.
The issue, however, was that this calendar was still ad hoc with adjustments made for seasons.
The Post-Talmudic Hebrew Calender began under Hillel II's leadership (330-365 AD). While Hillel II is regarded as the creator of the modern Hebrew Calender, much of his work was making Judah III's methods known.
This shows the main Hebrew systems throughout history, but these began systematically throughout history (post-exile, for example, the Hebrew Calendar was influenced by the Bablyonian Calendar).