With the continuous expansion of modern power systems and the increasing complexity of their structures and operational modes, real-time and accurate state estimation of power systems is crucial. To address this, a power system state estimation method based on dual attention convolutional bidirectional long and short-term memory neural networks (DA-CNN-BiLSTM) is proposed. This model introduces a channel attention mechanism to adaptively adjust the weights of feature channels in convolutional neural networks (CNN), and incorporates a feature attention mechanism to dynamically allocate weights for individual features before inputing them into the bidirectional long short-term memory neural network (BiLSTM). Important features are filtered from spatiotemporal characteristics based on acquired importance metrics and the correlation between measurements and state variables is dynamically explored. By constructing a measurement dataset from historical data, the DA-CNN-BiLSTM state estimation model is established. Real-time measurement data is then fed into this model to obtain real-time state estimation results. Case studies on IEEE standard systems demonstrate that compared to WLS, SE-CNN, and FA-BiLSTM state estimation methods, the proposed method achieves superior estimation accuracy, robustness, and computational efficiency.