A key problem for an adaptive filter is to establish a suitable adaptive factor for balancing the contributions of the measurements and the predicted state information from some kinematic models. The reasonable adaptive factor needs a reliable learning statistics to judge the state kinematic model errors. After analyzing the existing two kinds of learning statistics based on the state discrepancy and variance component ratio, a new learning statistic based on predicted residuals is set up, which is different from the exiting learning statistics. The new learning statistic does not need to estimate the kinemetic state parameters before the filtering process, Of course, it does not need necessary measurements to estimate state parameters for all observation epochs. The new learning statistic can be applied together with the learning factor constructed by the state discrepancy. The advantages and shortcomings of the new learning factor are analyzed, and an example is given. A key problem for an adaptive filter is to establish a suitable adaptive factor for balancing the contributions of the measurements and the predicted state information from some kinematic models. The reasonable adaptive factor needs a reliable learning statistics to judge the state kinematic model errors. the existing two kinds of learning statistics based on the state discrepancy and variance component ratio, a new learning statistic based on predicted residuals is set up, which is different from the exiting learning statistics. The new learning statistic does not need to estimate the kinemetic state parameters before the filtering process, Of course, it does not need necessary measurements to estimate state parameters for all observation epochs. The new learning statistic can be applied together with the learning factor constructed by the state discrepancy. The advantages and shortcomings of the new learning factor are analyzed, and an example is given.