Sensor data occasionally produces spikes that do not reflect the real environment. The Hampel filter flags these outliers live during a mission.

The implementation can be applied to any sensor data (salinity, temperature, pH, dissolved oxygen, etc.):

• Header: src/lib/utils/hampel_filter.h
• Tests: src/test/utils/test.cpp

The current implementation only reports whether a reading is an outlier and never alters the raw value. Wiring into individual sensors is handled separately.

Algorithm

The filter holds onto a sliding window of the most recent window_size raw readings. The window only uses past and current samples, so there is no waiting on future samples.

Once the window is established, the filter:

1. Computes the median of the window.
2. Computes the Median Absolute Deviation: MAD = median(|x_i − median|).
3. Scales it: scaled_mad = 1.4826 × MAD. The 1.4826 constant converts the MAD into an approximation of the standard deviation for normally distributed data.
4. Flags x as an outlier when |x − median| > num_mads × scaled_mad.

The median and MAD are used instead of the mean and standard deviation because they are robust. A single large spike barely moves them, so the spike can't unfoundedly shift the statistics used to judge it.

Configuration

• window_size (default 7): the number of recent readings used for the estimate. Larger windows are more resistant to noise but slower to adapt to real new data trends.
• num_mads (default 3.0): outlier threshold represented as a multiple of the scaled MAD. Lower means a stricter threshold that triggers more; higher means a looser threshold that triggers less.

Behavior notes

• All raw readings enter the window, including flagged outliers. Using a median-based filter keeps this accurate, allowing the filter to adapt to real sustained data shifts once enough new samples accumulate. Without this, a real change would be rejected repeatedly.
• Initial wait time: no value is flagged until the window is full (the first window_size − 1 readings).
• Edge case: if every value in the window is identical, scaled_mad is 0. A genuine data shift looks the same as an outlier, so the value is accepted.