This letter proposes to use a Gaussian process regression model to compensate for frequency dependent shadowing effects and multipath in received signal strength (RSS) observations. Parametric multi-channel RSS calibration models are introduced and characterized by the inter-channel bias and the scale factor terms. With the proposed calibration model, multi-channel RSS observations can be more effectively combined for localization over large space. Field tests with BLE 4.2 wireless radio broadcasting at channels 0, 12, and 39 have been conducted over a 9600 m ² outdoor area. Test results with sufficient and insufficient multi-channel RSS observations both confirm improved positioning performance by using the proposed model.