Performance Analysis of 1D Linear Kalman Filter in Modern Scientific Computing Environments
Keywords:
computational benchmarking, kalman filtering, linear state estimation, programming language performanceAbstract
We present a comprehensive performance analysis of 1D linear Kalman filter implementations across three modern scientific computing environments: Python, Julia, and R. Using a position tracking problem with hypothetical noisy sonar measurements, we evaluated both numerical accuracy and computational efficiency. All implementations produced numerically identical results within machine precision (maximum differences of m for position estimates), demonstrating the filter's ability to reduce measurement noise by 73.1% while accurately estimating unmeasured velocity states. Performance benchmarking revealed significant efficiency differences, with Python achieving a median execution time of 1.87 seconds, compared to 4.38 seconds for R and 34.82 seconds for Julia. Statistical analysis confirmed these differences were highly significant (Kruskal-Wallis ) with extremely large effect sizes (Cohen's d > 13 for all comparisons). Memory profiling revealed significant differences in resource utilization, with Python maintaining the most efficient footprint (97.67 MB), followed by Julia (132.45 MB) and R (168.21 MB), all with minimal variation. The unexpected underperformance of Julia relative to Python contradicts theoretical expectations and highlights the importance of empirical benchmarking for scientific computing applications. Our results provide practical guidance for implementing Kalman filters in time-critical or resource-constrained applications.
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