Advancements in smartphone sensor technologies have significantly enriched the field of human activity recognition, facilitating a wide array of applications from health monitoring to personal navigation. This study utilized such advancements to explore human locomotion and localization recognition using data from accelerometers, microphones, gyroscopes, magnetometers, and GPS, applying Deep Polynomial Neural Networks (DPNN) and Multilayer Perceptron (MLP) across three datasets: the Continuous In-The-Wild Smart Watch Activity Dataset, the Huawei Locomotion Dataset, and the Extra Sensory Dataset. We employ two distinct approaches for activity recognition: Deep Polynomial Neural Networks (DPNN) for deep learning-based feature extraction and Multilayer Perceptron (MLP) with manual feature extraction techniques, including Linear Predictive Coding Cepstral Coefficients (LPCC), step length, signal magnitude area, spectral, and sound features. Through rigorous experimentation, we achieved remarkable accuracy in recognizing both locomotion and localization activities, with DPNN consistently outperforming MLP in terms of accuracy. Specifically, for the Continuous In-The-Wild Dataset, DPNN achieved a 93% accuracy rate for localization activities and 95% for locomotion activities, while MLP recorded 86% and 91% in the respective categories. Similarly, on the Huawei Locomotion Dataset, DPNN attained 95% accuracy for localization and 97% for locomotion, with MLP achieving 88% and 91%, respectively. Furthermore, the application of these models to the Extra Sensory Dataset yielded 92% accuracy for both localization and locomotion activities with DPNN, and 90% and 89% with MLP. In our study, we observed that in terms of accuracy, DPNN emerges as the clear winner; however, it is computationally expensive. Conversely, MLP, while being less accurate, stands out for its computational efficiency. This study not only highlights the effectiveness of incorporating advanced machine learning techniques in interpreting sensor data but also emphasizes the trade-offs between computational demands and accuracy in the domain of human activity recognition. Through our comprehensive analysis, we contribute valuable insights into the potential of smartphone sensors in enhancing activity recognition systems, paving the way for future innovations in mobile sensing technology.