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The paper deals with the uncertainty of differential measurements, obtained from the subtraction of a pair of absolute measurements. It is shown that if the same sensor is used to perform both measurements, a model of the sensor will reveal a correlation component between the uncertainty of each absolute measurement, reducing the uncertainty on its subtraction. The procedure followed is based on the Gauss-Markov estimation method, showing that differential measurement uncertainty vanishes when the gradient to be measured is zero. If the two absolute measurements are to be performed using different sensors, a calibration by comparison between them will result in a similar uncertainty reduction. Finally, a simulated example based on commercially available thermistor data is included.

The ESA Lunar Lander mission is tasked with landing safely on the lunar surface near the lunar South Pole. The mission aims to demonstrate the capability of performing soft precision landings and autonomous hazard detection and avoidance (HDA) during the descent and landing phase. The final portion of the descent and landing phase is the approach phase, during which time the spacecraft is steered to the final landing site via the GNC, while providing a vehicle attitude for sensor observations of the landing site and surrounding terrain. An HDA subsystem is active during this phase and uses data from a camera and a Lidar to assess the safeness of the terrain around the landing site and select a safe landing site for GNC targeting. The GNC drives autonomously the vehicle to perform a soft landing at the landing site, performing trajectory diverts when new landing sites are selected by HDA. This paper describes the GNC concept and architecture for the approach phase of the descent and landing portion of the Lunar Lander mission, with emphasis on the details on the guidance and control (G&C) algorithms and the achieved G&C performances. The performance of the G&C subsystem is demonstrated through Monte Carlo simulation campaigns on a functional engineering simulator, with both the GNC and HDA algorithms active. Nomenclature= reference propulsive acceleration, computed by the guidance. = reference and navigated position and position error, respectively. = reference and navigated velocity and velocity error, respectively. = rotation matrix from frame to frame . = parameter of a z-transform. = reference and navigated attitude and attitude error, respectively. = reference and navigated angular rate and angular rate error, respectively. = torque commanded by the attitude control.

This paper presents a solution of the translational control for a biconic atmospheric entry capsule using the bank angle as a command. The control algorithm is separated into path planning and reference-path tracking. The path-planning algorithm computes the entry trajectory from the navigated state at the Entry Interface Point until the desired Parachute Deployment Point. The algorithm aims to recover the landing site uncertainty caused by Entry Interface Point dispersions. Atmospheric and aerodynamic dispersions are compensated in real-time following the Embedded Model Control methodology in which parametric uncertainty is estimated and rejected as an external disturbance. A hierarchical control structure is designed for facilitating non-linear dynamic inversion of the altitude/density relation and tuning of noise estimators and control laws. Both path planning and reference-path tracking exploit longitudinal and lateral decomposition of the translational dynamics, as well as state equation linearization around a reference trajectory. The main concepts and solutions of the algorithms are presented without formal proofs of convergence, performance and stability. The results of a Monte Carlo simulation campaign conducted on a high fidelity simulator are provided and discussed.