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New shipping routes are emerging as a result of iceberg melting in polar regions, allowing for more efficient transport of people and goods. Opening of the Northwest Passage, the maritime route connecting Pacific Ocean with Atlantic Ocean through Arctic region, is considered such a development. The increasing transport exploitation of the Northwest Passage requires the quality assessment of maritime navigation aids for compliance with the established requirements. Here we contribute to the subject with addressing the polar commercial-grade GPS positioning performance in the Northwest Passage in the extreme positioning environment conditions during the massive 2003 space weather storm, a space weather event similar to the Carrington Storm of 1859, the largest space weather event recorded. The GPS positioning environment in the Northwest Passage during the Carrington-like storm in 2003 was reconstructed through the GNSS SDR receiver-post processing of the experimental GPS observations. The raw GPS dual-frequency pseudoranges and navigation messages were collected at the International GNSS Service (IGS) reference station at Ulukhaktok, Victoria Island, Canada. Pseudorange processing and GPS position estimation were performed in three scenarios of pre-mitigation of the ionospheric effects, known as the single major contributor GPS positioning error: (i) no corrections applied, (ii) Klobuchar-based corrected GPS positioning, and (iii) dual-frequency corrected GPS positioning. Resulting GPS positioning error vectors were derived as positioning error residuals from the known reference station position. Statistical properties of the northing, easting, and vertical components of the GPS positioning error vector were analyzed with a software developed in the R environment for statistical computing to select suitable methods for the GPS positioning error prediction model development. The analysis also identified the most suitable theoretical fit for experimental statistical distributions to assist the model development. Finally, two competitive GPS positioning error prediction models were developed, based on the exponential smoothing (reference) and the generalized regression neural networks (GRNN) (alternative) methods. Their properties were assessed to recommend their use as mitigation methods for adverse massive space weather effects in polar regions. [ABSTRACT FROM AUTHOR]