MATLAB Implementation for Computing Allan Variance

Before computing the Allan variance, we first need to calculate the Random Walk Coefficient (RWC). The RWC serves as a crucial metric for describing system stability, reflecting how stability characteristics evolve across different time intervals. In MATLAB implementation, this typically involves processing time-series data using functions like cumsum() for integration and std() for standard deviation calculations. Allan variance measurements are taken across varying time intervals, making the preliminary RWC calculation essential for proper normalization. The core algorithm involves segmenting the input data into clusters of different lengths and computing variances for each cluster size. Following the RWC computation, we proceed to calculate the Allan variance itself, which can be implemented using overlapping or non-overlapping sample methods with vectorized operations for efficiency. It's important to note that Allan variance maintains a strong correlation with system stability, necessitating the computation of related coefficients such as the bias instability coefficient, rate random walk coefficient, and quantization noise coefficient. These coefficients, often extracted through log-log plot fitting using polyfit() functions, provide enhanced assessment capabilities for system stability and precision evaluation. The complete implementation typically includes data preprocessing, tau array generation, variance computation, and logarithmic curve fitting for parameter extraction.