  We consider a machine learning approach based on Gaussian process regression
(GP) to position users in a distributed massive multiple-input multiple-output
(MIMO) system with the uplink received signal strength (RSS) data. We focus on
the scenario where noise-free RSS is available for training, but only noisy RSS
is available for testing purposes. To estimate the test user locations and
their 2{\sigma} error-bars, we adopt two state-of-the-art GP methods, namely,
the conventional GP (CGP) and the numerical approximation GP (NaGP) methods. We
find that the CGP method, which treats the noisy test RSS vectors as
noise-free, provides unrealistically small 2{\sigma} error-bars on the
estimated locations. To alleviate this concern, we derive the true predictive
distribution for the test user locations and then employ the NaGP method to
numerically approximate it as a Gaussian with the same first and second order
moments. We also derive a Bayesian Cramer-Rao lower bound (BCRLB) on the
achievable root- mean-squared-error (RMSE) performance of the two GP methods.
Simulation studies reveal that: (i) the NaGP method indeed provides realistic
2{\sigma} error-bars on the estimated locations, (ii) operation in massive MIMO
regime improves the RMSE performance, and (iii) the achieved RMSE performances
are very close to the derived BCRLB.
