Smartphone-based activity recognition (SP-AR) recognizes users' activities using the embedded accelerometer sensor. Only a small number of previous works can be classified as online systems, i.e., the whole process (pre-processing, feature extraction, and classification) is performed on the device. Most of these online systems use either a high sampling rate (SR) or long data-window (DW) to achieve high accuracy, resulting in short battery life or delayed system response, respectively. This paper introduces a real-time/online SP-AR system that solves this problem. Exploratory data analysis was performed on acceleration signals of 6 activities, collected from 30 subjects, to show that these signals are generated by an autoregressive (AR) process, and an accurate AR-model in this case can be built using a low SR (20 Hz) and a small DW (3 s). The high within class variance resulting from placing the phone at different positions was reduced using kernel discriminant analysis to achieve position-independent recognition. Neural networks were used as classifiers. Unlike previous works, true subject-independent evaluation was performed, where 10 new subjects evaluated the system at their homes for 1 week. The results show that our features outperformed three commonly used features by 40% in terms of accuracy for the given SR and DW.