The Global Navigation Satellite System (GNSS) is a valuable tool for Earth and Atmospheric Science, as it not only provides position and attitude information for remote-sensing platforms, but its variety of radio signals may also be used to probe the atmosphere. This dissertation presents a set of projects that aim to improve several of these functions by employing model-based estimation techniques. The first algorithm addresses the issue of large uncertainties in the dynamic variations of signal observables due to refraction during Earth limbscanning. It pre-processes raw GNSS data with a Levenberg-Marquardt batch filter, and performs signal tracking with a Square-Root Extended Kalman Filter (SREKF) in a new type of combined phase-locked/delay-locked loop. This constitutes an alternate way for deducing meteorological conditions down to few metres from the terrestrial surface using GNSS signals. The second project estimates the attitude of a spinning sounding rocket carrying sensors for studying space weather. The GPS attitude determination problem for this rocket poses two major challenges that result from equipment limitations: Frequent signal data gaps due to telemetry bandwidth restrictions and only one antenna baseline vector with which to perform full, three-axis attitude determination. The first problem is circumvented by an adaptation of the algorithm from the first project, and the second by using another Levenberg-Marquardt batch filter that contains an Euler dynamics model. The last project combines refractive ray- tracing concepts and an SREKF, utilizing both ionosonde and GNSS signals, in order to solve for the parameters of a node-based profile of the ionosphere. In addition, a trust-region-reflective algorithm, a modern form of the LevenbergMarquardt algorithm, is used to extract electron content information from GNSS data to parameterize ionospheric irregularities resulting from an experiment that involves controlled heating of the ionosphere.