To address the challenge of detecting weak target signals on the ocean surface under strong sea clutter backgrounds, this study investigates the theory of chaotic phase space reconstruction and the improved Newton-Raphson optimization algorithm. A novel method for weak signal detection in chaotic backgrounds is proposed, based on an optimized bidirectional long short-term memory network (BiLSTM). The reconstructed phase space signal is used as the input to the BiLSTM network, with the length of the training data determined by the embedding dimension and delay time. The parameters of the BiLSTM model are optimized using the improved Newton-Raphson optimization algorithm, and the model is trained with an adaptive weighted error (AWE) loss function. Both approaches work together to enhance prediction accuracy, improve runtime speed, and reduce the detection threshold. A single-step prediction is performed using the BiLSTM model, and weak target signals are detected from strong chaotic background noise by analyzing the prediction errors. Simulation experiments were conducted using the Lorenz chaotic system as the chaotic background to detect superimposed weak signals. The results demonstrate that the proposed method effectively detects weak signals. Further validation was carried out using the IPIX radar dataset and sea surface detection data from Yantai, confirming the method’s robustness and effectiveness.