  Constructing an occupancy representation of the environment is a fundamental
problem for robot autonomy. Many accurate and efficient methods exist that
address this problem but most assume that the occupancy states of different
elements in the map representation are statistically independent. The focus of
this paper is to provide a model that captures correlation of the occupancy of
map elements. Correlation is important not only for improved accuracy but also
for quantifying uncertainty in the map and for planning autonomous mapping
trajectories based on the correlation among known and unknown areas. Recent
work proposes Gaussian Process (GP) regression to capture covariance
information and enable resolution-free occupancy estimation. The drawback of
techniques based on GP regression (or classification) is that the computation
complexity scales cubically with the length of the measurement history. Our
main contribution is a new approach for occupancy mapping that models the
binary nature of occupancy measurements precisely, via a Bernoulli
distribution, and provides an efficient approximation of GP classification with
complexity that does not scale with time. We prove that the error between the
estimates provided by our method and those provided by GP classification is
negligible. The proposed method is evaluated using both simulated data and real
data collected using a Velodyne Puck 3-D range sensor.
