Human activity recognition (HAR) is a crucial task in various applications, including healthcare, fitness, and the military. Deep learning models have revolutionized HAR, however, their computational complexity, particularly those involving BiLSTMs, poses significant challenges for deployment on resource-constrained devices like smartphones. While BiLSTMs effectively capture long-term dependencies by processing inputs bidirectionally, their high parameter count and computational demands hinder practical applications in real-time HAR. This study investigates the approximation of the computationally intensive BiLSTM component in a HAR model by using a combination of alternative model components and data flipping augmentation. The proposed modifications to an existing hybrid model architecture replace the BiLSTM with standard and residual LSTM, along with convolutional networks, supplemented by data flipping augmentation to replicate the context awareness typically provided by BiLSTM networks. The results demonstrate that the residual LSTM (ResLSTM) model achieves superior performance while maintaining a lower computational complexity compared to the traditional BiLSTM model. Specifically, on the UCI-HAR dataset, the ResLSTM model attains an accuracy of 96.34% with 576,702 parameters, outperforming the BiLSTM model's accuracy of 95.22% with 849,534 parameters. On the WISDM dataset, the ResLSTM achieves an accuracy of 97.20% with 192,238 parameters, compared to the BiLSTM's 97.23% accuracy with 283,182 parameters, demonstrating a more efficient architecture with minimal performance trade-off. For the KU-HAR dataset, the ResLSTM model achieves an accuracy of 97.05% with 386,038 parameters, showing comparable performance to the BiLSTM model's 98.63% accuracy with 569,462 parameters, but with significantly fewer parameters.