False positives in pedestrian detection remain a challenge that has yet to be effectively resolved. To address this issue, this paper proposes a Full-stage Refined Proposal (FRP) algorithm aimed at eliminating these false positives within a two-stage CNN-based pedestrian detection framework. The main innovation of this work lies in employing various pedestrian feature re-evaluation strategies to filter out low-quality pedestrian proposals during both the training and testing stages. Specifically, in the training phase, the Training mode FRP algorithm (TFRP) introduces a novel approach for validating pedestrian proposals to effectively guide the model training process, thereby constructing a model with strong capabilities for false positive suppression. During the inference phase, two innovative strategies are implemented: the Classifier-guided FRP (CFRP) algorithm integrates a pedestrian classifier into the proposal generation pipeline to yield high-quality proposals through pedestrian feature evaluation, and the Split-proposal FRP (SFRP) algorithm vertically divides all proposals, sending both the original and the sub-region proposals to the subsequent subnetwork to evaluate their confidence scores, filtering out those with lower sub-region pedestrian confidence scores. As a result, the proposed algorithm enhances the model's ability to suppress pedestrian false positives across all stages. Various experiments conducted on multiple benchmarks and the SY-Metro datasets demonstrate that the model, supported by different combinations of the FRP algorithm, can effectively eliminate false positives to varying extents. Furthermore, experiments conducted on embedded platforms underscore the algorithm's effectiveness in enhancing the comprehensive pedestrian detection capabilities of the small pedestrian detector in resource-constrained edge devices.