Residual-Guided Boosted-LLL Refinement with Reliability-Time Analysis for GNSS Integer Ambiguity Resolution

Integer least-squares estimation for Global Navigation Satellite System ambiguity resolution requires balancing solution quality and computational cost. We propose residual-guided Boosted-LLL refinement, which selects coordinates with large conditional rounding residuals and evaluates a bounded neighborhood using the complete objective. Nested candidate sets guarantee non-increasing objective values. Accuracy-Time Conversion Loss and its normalized form assess whether acceptance-probability gains offset additional runtime. Controlled simulation experiments cover 70 settings with dimensions from 16 to 40. Nine-candidate refinement increases the mean probability of satisfying a 1\% objective-gap criterion by approximately four and five percentage points at two matched difficulty levels, while exact-fix gains are smaller. Residual guidance produces more frequent objective improvements than random coordinate selection under the same budget. With a target probability of 0.95 and 60 preprocessing reuses, refinement lowers the conversion-cost point estimate in half of the settings.