Recursive Filters: SMA, EMA, Low‑Pass, and a Tiny Kalman
2 days ago
- Recursive filters are ideal when compute and memory are limited, data streams in, and immediate response is needed.
- They require O(1) memory and O(1) compute per sample, making them suitable for microcontrollers and real-time systems.
- The EMA (Exponential Moving Average) is a simple leaky integrator with a smoothing factor alpha, where higher alpha means smoother output but more lag.
- SMA (Simple Moving Average) averages the last N samples, effectively reducing noise but introducing lag and requiring a buffer.
- A first-order low-pass filter is mathematically equivalent to an EMA, with the parameter alpha controlling the trade-off between noise suppression and responsiveness.
- A tiny 1D Kalman filter provides adaptive gain by balancing trust between prediction and measurement based on sensor and process noise.
- Parameter choices: SMA window N for smoothness versus lag, EMA alpha around 0.1–0.3, Kalman R for sensor noise and Q for process drift.
- SMA is robust, EMA is the default for streaming, and a 1D Kalman adds principled adaptivity when noise estimates are available.