Frequency Bias Mitigation for Surface User Navigation Using Double Differencing Joint Doppler and Ranging

Radiometric measurements from a lunar constellation can enable autonomous positioning and timing for lunar surface users. However, time-varying errors in range and range-rate measurements can significantly degrade navigation performance. This article introduces measurement differencing methods with joint Doppler and ranging (JDR), a relative Doppler and range-based positioning method that can localize a surface user with a minimal navigation infrastructure, to reduce the effects of Doppler frequency noise and biases. This article first discusses the accurate simulation and generation of Doppler-shift measurement errors including instrumentation and propagation errors for the orbiters, user, and reference station. This analysis implements a high-fidelity oscillator model that generates frequency noise from a given oscillator phase noise profile. Then, the article introduces measurement differencing methods with JDR and compares them against conventional measurement differencing methods. This analysis develops and compares three pairs of navigation methods: 1) traditional range and Doppler versus conventional JDR, traditional single differencing versus single measurement differencing with JDR, and traditional double differencing (DD) versus double measurement differencing with JDR (DD-JDR). An extended Kalman filter estimates a static user's relative position and timing with high fidelity simulated range and Doppler measurements. A Monte Carlo simulation creates a distribution of performance for each method. The DD methods improve on all other methods due to their ability to reduce the effects of Doppler frequency biases. Assuming a static lunar surface user, two LRS, a well-known reference station, and one-way measurements to the user with a space qualified chip-scale atomic clock, DD-JDR provides root sum-squared positioning errors around 11 m and timing errors of 250 ns at 95% confidence. This improves on traditional DD by almost a factor of two due to the ability of JDR to further reduce Doppler errors (Trad DD: 18 m @ 95%). Ultimately, DD-JDR is able to provide accurate positioning and timing to surface users with significant Doppler biases and noise within a minimal navigation infrastructure.