Apply the One Euro filter

An adaptive low-pass filter that trades jitter against lag according to how fast the signal is moving: heavy smoothing while the subject is nearly still, light smoothing while it moves quickly.

Usage

filter_one_euro(
  x,
  sampling_rate,
  min_cutoff = 1,
  beta = 0,
  d_cutoff = 1,
  na_action = c("linear", "spline", "stine", "locf", "value", "error"),
  keep_na = TRUE,
  ...
)

Arguments

x: Numeric vector to filter.
sampling_rate: Sampling rate of the signal in Hz.
min_cutoff: Minimum cutoff frequency in Hz, the cutoff used when the signal is not moving. Lower means smoother but laggier. Default 1.
beta: Speed coefficient. 0 gives a plain low-pass filter at min_cutoff; larger values raise the cutoff more sharply as the signal speeds up, cutting lag. Default 0.
d_cutoff: Cutoff frequency in Hz for the derivative estimate, which keeps noise in the derivative from driving the adaptation. Default 1.
na_action: Method used to fill NA values before filtering, so the filter sees a complete series. One of "linear" (default), "spline", "stine", "locf", "value", or "error" to abort when NAs are present. Filling is internal: whether the filled values reach the output is controlled by keep_na.
keep_na: Logical. If TRUE (default), positions that were NA in the input are NA in the output — gaps stay gaps. If FALSE, the values used to fill those gaps are kept, so the output has fewer NAs than the input and genuinely-missing stretches come back as interpolated estimates.
...: Additional arguments passed to replace_na_with().

Value

Filtered numeric vector, same length as x.

Details

A fixed low-pass filter forces one compromise on the whole recording. Set the cutoff low and slow passages come out clean but fast ones lag behind; set it high and fast passages track well but slow ones jitter. The One Euro filter (Casiez, Roussel & Vogel, 2012) removes the compromise by making the cutoff a function of the estimated speed:

$$f_c = f_{c_{min}} + \beta |\dot{x}|$$

where $\dot{x}$ is itself low-pass filtered, at d_cutoff, so that noise in the derivative does not drive the cutoff around.

Tuning, following the authors' advice, is two-stage:

Set beta = 0 and lower min_cutoff until jitter is acceptable while the subject is still.
Raise beta until lag is acceptable while it moves quickly.

min_cutoff therefore governs the slow-movement end and beta the fast-movement end, and the two can be tuned almost independently.

The filter is recursive, so it needs a complete series: NAs are filled by na_action before filtering. With keep_na = TRUE (the default) they are restored afterwards, so the gaps are not silently invented.

References

Casiez, G., Roussel, N., & Vogel, D. (2012). 1 € Filter: A Simple Speed-based Low-pass Filter for Noisy Input in Interactive Systems. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI '12), 2527–2530. doi:10.1145/2207676.2208639

Examples