Nowadays many people use smartphones with built-in accelerometers which makes these smartphones capable of recognizing daily activities. However, mobile phones are carried along freely instead of a firm attachment to a body part. Since the output of any body-worn triaxial accelerometer varies for the same physical activity at different positions on a subject's body, the acceleration data thus could vary significantly for the same activity which could result in high within-class variance. Therefore, realization of activity-aware smartphones requires a recognition method that could function independent of phone's position along subjects' bodies. In this study, we present a method to address this problem. The proposed method is validated using five daily physical activities. Activity data is collected from five body positions using a smartphone with a built-in triaxial accelerometer. Features including autoregressive coefficients and signal magnitude area are calculated. Kernel Discriminant Analysis is then employed to extract the significant non-linear discriminating features which maximize the between-class variance and minimize the within-class variance. Final classification is performed by means of artificial neural nets. The average accuracy of about 96% illustrates the effectiveness of the proposed method.