Millimeter-wave with ultra-wide bandwidth available and ability to pack massive number of antennas in a small area is considered the key enabler for the future generation communication systems. Accurate understanding and modeling of the ultra-wideband propagation channel with large-scale array configuration is essential. In this contribution, a realistic spherical-propagation signal model considering the spatial non-stationarity of path gain across the array elements is proposed. A novel Trajectory-Aided Maximum-likelihood (TAMax) algorithm is proposed to extract propagation parameters from the measured data, since the existing high-resolution propagation parameter estimation algorithms are not applicable due to either prohibitively high computation loads or assumption violations. In the proposed TAMax algorithm, the high-dimensional Maximum-Likelihood (ML) estimation problem is firstly decomposed into a sub-problem where delays and amplitudes of MultiPath Components (MPCs) are estimated at individual array elements. A novel transform is then proposed to identify multiple MPC trajectories in the delay-element domain. With interference cancellation and fast initialization obtained in the proposed transform, spherical propagation parameters are finally acquired via joint ML estimation with significantly decreased searching spaces. Moreover, a measurement campaign conducted at the frequency band of 27-29 GHz using a virtual uniform circular array is introduced, where the proposed TAMax algorithm is applied and validated.