Оценка матрицы пассажирских корреспонденций с использованием метода наименьших квадратов для калибровки гравитационной модели

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The matrix of passenger correspondence plays a key role in many issues of planning and forecasting the development of the transport system. Usually, a gravitational model is used to evaluate the correspondence matrix. The specification and calibration method of the gravity model depends on what data is known from observations. In particular, if the volumes of departures and arrivals for each point and the average cost (duration) of the trip are known, then a gravitational model with an exponential gravity function is used, and the Hyman method is used to calibrate it. If the correspondence matrix is partially known, then a piecewise constant function can be taken as the gravity function and the Poisson method can be used for calibration. In this paper, we investigate the possibility of using the least squares method to calibrate a gravitational model with an exponential gravity function based on the observed correspondence matrix obtained on the basis of automated data collection on the online service of announcements about joint trips (carpooling). For such an observed correspondence matrix, a model correspondence matrix is calculated using the Huffman method and the least squares method. As a result, it was found that both methods produce models that approximate the observed data equally well.