Summary

Jason Sachs explains Welford's online algorithm for computing mean and variance in a numerically stable way, and surveys related streaming-statistics techniques suited to resource-constrained systems. The article includes implementation notes, numerical/overflow considerations (floating- and fixed-point), and practical uses such as sensor calibration, anomaly detection, and merging partial statistics in embedded/IoT firmware.

Key Takeaways

• Implement Welford's online algorithm to compute running mean and variance with numerical stability.
• Avoid precision loss and overflow by using stable update formulas and pairwise combining of statistics.
• Adapt algorithms for constrained devices by applying fixed-point techniques and low-memory implementation patterns.
• Merge partial statistics from multiple threads or nodes using pairwise/aggregate formulas for distributed systems.
• Apply the methods to real embedded use cases such as sensor calibration, anomaly detection, and summary telemetry.

Who Should Read This

Intermediate embedded/IoT firmware engineers and developers who process streaming sensor data on microcontrollers and need reliable, low-overhead statistical summaries for calibration, diagnostics, or telemetry.

TimelessIntermediate

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