Design and evaluation of LNAV/VNAV guidance algorithms for time-of-arrival error characterization

This paper develops 3D-path tracking algorithms to simulate the Lateral Navigation (LNAV) and Vertical Navigation (VNAV) capabilities found in current day aircraft flight management systems. The LNAV/VNAV capability is realized using two modules: (i) Reference Trajectory Synthesis Module, and (ii) LNAV/VNAV Guidance Module. A separate paper deals with the Reference Trajectory Synthesis Module. The focus of the current paper is the design and evaluation of LNAV/VNAV Guidance Module. The guidance module is formulated as a reference-trajectory tracking controller. The control laws are based on single-input single-output linear feedback control principles. The outputs from the guidance module are: (i) bank-angle command, (ii) coefficient-of-lift command, (iii) thrust command, and (iv) spoiler drag command. The guidance module is evaluated on a simulation that models aircraft point-mass dynamics, bank-angle auto-pilot dynamics, pitch-axis auto-pilot dynamics, engine lag dynamics, atmospheric forecast model, and a realistic forecast uncertainty model. Test scenarios include A320 and MD82 aircraft flying along different arrival routes into San Francisco and Los Angeles International airports. Monte-Carlo simulation framework is used to estimate the time-of-arrival uncertainty associated with a A320 LNAV/VNAV flight.