  This paper considers planning a path for a single underwater cooperative
navigation aid (CNA) vehicle to sequentially aid a set of N agents to minimize
average navigation uncertainty. Both the CNA and agents are modeled as
constant-velocity vehicles. The agents travel along known nominal trajectories
and the CNA plans a path to sequentially intercept them. Navigation aiding is
modeled by a scalar discrete time Kalman filter. During path planning, the CNA
considers surfacing to reduce its own navigation uncertainty. A greedy planning
algorithm is proposed that uses a heuristic to schedule agents to the CNA that
is based on the optimal time-to-aid, the overall navigation uncertainty
reduction, and the transit time. The approach is compared to an optimal
(exhaustive enumeration) algorithm through a Monte Carlo experiment with
randomized agent trajectories and initial navigation uncertainty.
