In single-frequency receivers, high noise in pseudorange measurements often leads to false alarms, missed detections, and poor sensitivity to small cycle slips. Most existing methods reduce the measurement noise by filtering. However, filtering attenuates inter-epoch variations, which degrades cycle-slip observability and prevents real-time correction. A two-stage cycle-slip detection and correction method was proposed. In the first stage, a pseudorange-carrier-phase combination with high real-time capability was used to coarsely detect large cycle slips. In the second stage, a Kalman-filter-based noise reduction algorithm was applied to finely detect the remaining small cycle slips. The detected cycle slips were then accumulated and used to correct the carrier phase in real time, thereby achieving high accuracy and real-time performance in cycle-slip detection and correction. To mitigate the loss of inter-epoch variation caused by filtering, a regional accumulation strategy was introduced to enhance the prominence of cycle-slip values. An adaptive threshold was further designed to suppress false and missed detections induced by pseudorange observation noise by dynamically adjusting to the noise characteristics. Experimental results on test data validate the effectiveness of the proposed method: under high pseudorange observation noise, the two-stage method maintains detection and correction accuracy at approximately ±0.5 cycles. Compared with conventional algorithms, such as the higher-order difference method and the polynomial fitting method, the proposed method improves the accuracy by 84.9% and 72.5%, respectively.