Retrieval-augmented language model (RALM) relies on retrieved external knowledge to generate responses, resulting in vulnerability in the face of retrieval results with noisy documents. Previous works integrate additional filters or finetune Large Language Models (LLMs) to learn adaptive retrieval to reduce the performance damage of noisy documents. However, prior noise filtering may lead to the loss of crucial information, and these methods do not focus on distracting documents with high semantic relevance, which is the most challenging problem. In this study, we propose a training method for fact-centric preference alignment (FPA) to improve the ability of LLMs to directly extract useful information from noisy retrieval results without prior filtering. Our method performs positive document mining based on factual consistency and uses LLMs self-generated synthetic data as training data without manual annotation. We evaluate our FPA on four question answering benchmarks, and the experimental results demonstrate that our method achieves significant improvement with a small scale of training data.