Math Specifications

This section records the mathematical contracts used by LuPNT models. The goal is to make each model’s state conventions, units, time scales, optional corrections, and observable equations explicit enough that implementations can be tested against the same specification. Each page ties its algorithms to the implementing C++/Python code.

These same contracts are honored by pure-Python model subclasses: Applications, Agents, and Measurements can be authored in Python (pybind11 trampolines) and registered into a YAML-driven Simulation via pnt.register_application / pnt.register_agent, as demonstrated by Example 17.

Fundamentals

• Time Systems and Conversions
• Frame Conversions
• Dynamics Models
• Numerical Integration
• Automatic Differentiation

Estimation

• Estimation Filters

Measurements & Signals

• GNSS Measurement Model
• Link Budget and Visibility
• Ionosphere, Plasmasphere, and Ray Tracing
• Measurement Models

Navigation Message Design

• Ephemeris and LansAlmanac Design