Human motion analysis using a smartphone-embedded accelerometer sensor provided important context for the identification of static, dynamic, and complex sequence of activities. Research in smartphone-based motion analysis are implemented for tasks, such as health status monitoring, fall detection and prevention, energy expenditure estimation, and emotion detection. However, current methods, in this regard, assume that the device is tightly attached to a pre-determined position and orientation, which might cause performance degradation in accelerometer data due to changing orientation. Therefore, it is challenging to accurately and automatically identify activity details as a result of the complexity and orientation inconsistencies of the smartphone. Furthermore, the current activity identification methods utilize conventional machine learning algorithms that are application dependent. Moreover, it is difficult to model the hierarchical and temporal dynamic nature of the current, complex, activity identification process. This paper aims to propose a deep stacked autoencoder algorithm, and orientation invariant features, for complex human activity identification. The proposed approach is made up of various stages. First, we computed the magnitude norm vector and rotation feature (pitch and roll angles) to augment the three-axis dimensions (3-D) of the accelerometer sensor. Second, we propose a deep stacked autoencoder based deep learning algorithm to automatically extract compact feature representation from the motion sensor data. The results show that the proposed integration of the deep learning algorithm, and orientation invariant features, can accurately recognize complex activity details using only smartphone accelerometer data. The proposed deep stacked autoencoder method achieved 97.13% identification accuracy compared to the conventional machine learning methods and the deep belief network algorithm. The results suggest the impact of the proposed method to improve a smartphone-based complex human activity identification framework.