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Kalman Filter for Irregular Time Series with Optional Resampling

Source: R/filter_kalman.R
filter_kalman_irregular.Rd

Implements a Kalman filter for irregularly sampled time series data with optional resampling to regular intervals. Handles variable sampling rates, missing values, and automatically adjusts process variance based on time intervals.

Usage

filter_kalman_irregular(
  measurements,
  times,
  base_Q = NULL,
  R = NULL,
  initial_state = NULL,
  initial_P = NULL,
  resample = FALSE,
  resample_freq = NULL
)

Arguments

measurements

Numeric vector containing the measurements to be filtered.

times

Numeric vector of timestamps corresponding to measurements.

base_Q

Optional. Base process variance per second. If NULL, automatically calculated.

R

Optional. Measurement variance. If NULL, defaults to 0.1.

initial_state

Optional. Initial state estimate. If NULL, uses first non-NA measurement.

initial_P

Optional. Initial state uncertainty. If NULL, calculated from median sampling rate.

resample

Logical. Whether to return regularly resampled data (default: FALSE).

resample_freq

Numeric. Desired sampling frequency in Hz for resampling (required if resample=TRUE).

Value

If resample=FALSE: A numeric vector of filtered values corresponding to original timestamps If resample=TRUE: A list containing:

  • time: Vector of regular timestamps

  • values: Vector of filtered values at regular timestamps

  • original_time: Original irregular timestamps

  • original_values: Filtered values at original timestamps

Details

The function implements an adaptive Kalman filter that accounts for irregular sampling intervals. Process variance is scaled by the time difference between measurements, allowing proper uncertainty handling for variable sampling rates.

Key features:

  • Handles irregular sampling intervals

  • Scales process variance with time gaps

  • Optional resampling to regular intervals

  • Automatic parameter selection based on median sampling rate

  • Missing value (NA) handling

When resampling, the function uses linear interpolation and warns if the requested sampling frequency exceeds twice the median original sampling rate (Nyquist frequency).

Note

Resampling considerations:

  • Avoid resampling above twice the median original sampling rate

  • Consider the physical meaning of your data when choosing resample_freq

  • Be cautious of creating artifacts through high-frequency resampling

Parameter selection guidelines:

  • base_Q controls the expected rate of change per second

  • R should reflect your measurement noise level

  • For slow-changing signals, reduce base_Q

  • For noisy measurements, increase R

See also

filter_kalman for regularly sampled data

Examples

# Example with irregular sampling
measurements <- c(1, 1.1, NA, 0.9, 1.2, NA, 0.8, 1.1)
times <- c(0, 0.1, 0.3, 0.35, 0.5, 0.8, 0.81, 1.0)

# Basic filtering with irregular samples
filtered <- filter_kalman_irregular(measurements, times)

# Filtering with resampling to 50 Hz
filtered_resampled <- filter_kalman_irregular(measurements, times,
                                             resample = TRUE,
                                             resample_freq = 50)
#> Warning: Requested resampling frequency (50 Hz) exceeds twice the median sampling rate (6.66667 Hz).
#>             This may lead to poor interpolation.

# Plot results
plot(times, measurements, type="p", col="blue")
lines(filtered_resampled$time, filtered_resampled$values, col="red")