In practical space debris laser ranging systems, the performance of operation depends on the accuracy of range predictions. However, widely used Two-Line-Element (TLE) predictions usually present too large range prediction deviation, which can not satisfy laser ranging demands, or requires a long time of so-called range searching. To improve the performance of space debris laser ranging operations, we further investigated the mechanism of range prediction deviation. With the help of orbital relative motion theory and ground to space observation geometry, we constructed a mathematical model for range prediction deviation of orbital objects on near-circular orbit. The predicted and actual positions on orbit were considered as adjacent objects. The orbital relative motion of adjacent objects was described by Clohessy-Wiltshire (C-W) equation, which models the relative motion, as well as their derivatives to time. Combining the relative motion vector with its time derivative made the six-dimensional state of relative motion (the state). Given the C-W equation as state transition, the state at any time was determined from the state at initial time, a.k.a. the initial state. On the other hand, the ground to space observation geometry provided linear mapping from the six-dimensional state of relative motion to two-dimensional observational angular offsets. In this manner, the Equation-of-Motion (EOM) and Equation-of-Observation (EOO) were formed for the initial state. We adopted a classical Kalman filter to solve for the initial state of relative motion from observations. Once estimated, the initial state was propagated to observation time and mapped into range prediction deviation. Thus, the optimal estimation of the current range prediction deviation was achieved in real-time. The testing scenario was setup to assess the real-time correction algorithm. The scenario contains nine Low-Earth-Orbit (LEO) satellites representing different orbit types. The simulated time span contains 20 days, from Dec. 1st to Dec. 20th in 2021. To simulate TLE-based space debris laser ranging, the nominal prediction trajectory data was generated with TLE, while the reference trajectory was generated by official Consolidated Prediction Format (CPF) data. Comparing prediction and reference trajectory formed real deviation data for each satellite pass. Simulated observational angular offset data was generated and fed to the correction algorithm as input, while the real deviation data was used as a reference, to assess the output. Each simulated pass started when elevation rises above 10 degrees in the scenario. The correction algorithm was iterated once per second, receiving angular offset data and outputting range correction data. Uncertainty of angular observation was assumed 2 or 5 arc-seconds in separate test cases. The correction algorithm began to run at the start of pass, and finished while the correction residue of range deviation was less than 100 m. The simulated passes were set to end with elevation below 10 degrees. Various criteria were adopted to assess the correction algorithm, including maximum range deviation, correction time, and percentage in the whole pass. The correction algorithm was found to be effective. For selected satellites, the max range deviations were about 500 m. In the test case with 2 arc-seconds observation uncertainty, the algorithm took less than 1.3 minutes in average to finish correction. In other words, the correction algorithm took no more than 15% of the whole pass time to make corrections, bringing down range prediction deviations from around 500 m to less than 100 m. The study demonstrates the correction algorithm's effectiveness in meeting laser-ranging demands. Further development and application in space debris operation is recommended.