Position, Velocity, and Timing for Lunar Descent and Landing with Joint Doppler and Ranging

Lunar descent and landing requires accurate position, velocity, and timing (PVT) knowledge in real-time. This paper introduces the use of Joint Doppler and Ranging (JDR) fused with additional sensors to estimate PVT for a lunar lander. JDR is a radiometric navigation method that utilizes geometric constraints with a surface reference station to reduce Doppler measurement errors and improve PVT performance. Previous papers introduced PVT estimation for surface users and lunar orbiters utilizing JDR with a three-satellite constellation and a self-positioned reference station. A well-known reference station enables measurement corrections through single and double differencing. Double differencing with JDR (DD-JDR) provides highly accurate navigation under significant range and Doppler bias, drift, and noise. This analysis fuses DD-JDR with an altimeter and an inertial measurement unit to achieve high accuracy navigation during active descent and landing. During the simulated lunar descent, the lander performs an impulsive braking burn and begins a coast towards the lunar surface. Once passing 10 km in altitude, it beings powered descent and thrusts continuously until soft landing at the lunar south pole. During the entire 10 minute trajectory, the lander receives one-way range and Doppler from the navigation constellation and reference station. The navigation simulation generates high-fidelity Doppler shift measurements including instrumentation and propagation errors. Oscillator models generate frequency errors from local oscillators in the lander, orbiters, and reference station. An extended Kalman filter fuses the DD-JDR, inertial, and altimeter measurements and estimates the lander's PVT. A Monte Carlo analysis results in PVT performance of DD-JDR with a root sum-squared (RSS) accuracy of <10 m for position, 0.45 m/s for velocity, and 340 ns for timing errors at 3σ confidence. Using the same measurements, measurement errors, and navigation architecture, traditional double differencing (TDD) achieves 18 m, 3.1 m/s, and 340 ns of RSS PVT error. DD-JDR improves positioning and velocity performance by a factor of two and six, respectively, with no additional measurements or changes in navigation architecture. The fusion of radiometric methods such as DD-JDR with standard descent and landing sensors can improve PVT performance and navigation robustness for lunar landers.