Optimal “Off-Aiming”: Stochastic path planning with one-dimensional features

This paper investigates a traditional navigational technique, known as "off-course navigation," "landfall intercept," "single line-of-position," and "aiming off," which has been extensively used by navigators on foot, ancient ships, pre GPS aircraft, and modern submarines. Using this technique, the navigator deliberately aims to one side of their objective with the intention of following a line feature (e.g., a road, coastline, celestial bearing, or radio beacon) that is known to intersect the objective. Despite its extensive use, the question of "How much should one aim off?" has never been rigorously addressed. The main difficulty in quantifying the benefit of aiming off is that it entails optimal search as a sub-problem; how does one proceed once the line feature is reached? Recent scholarship has provided a strong heuristic policy for search on the real line. Given this policy, which we use as a black box, we are able pose the problem of "aiming off" as a straightforward optimization problem. This problem is relevant not only to path planning, e.g., in a GPS-denied environment, but also to search problems such as target acquisition.