The filamentation dynamics of 15 GW femtosecond laser pulses at 800 and 400 nm wavelengths upon their tight focusing in air is studied experimentally. The spatial position and extent of plasma channel formed within the filamentation zone as a function of laser pulse power are investigated. The processing of the experimental data according to the Marburger formula by J. H. Marburger [Prog. Quantum. Electron. 4, 35 (1975)] and the dispersion relations for air cubic nonlinearity has allowed to estimate the effective value of the Kerr-driven air refractive index on 400 nm as 5.36 × 10−19 cm²/W with a 5% error.