Interpolating and thinning trajectories

Real tracks are sampled irregularly, and some downstream analyses assume either regular sampling or a specific geometry. This vignette covers:

Interpolation — producing additional locations at a desired cadence or along a target line. Handled by move2::mt_interpolate().
Time-thinning — downsampling a dense track to a target cadence. Two complementary helpers: move2::mt_filter_per_interval() for the bucketed case, and move2utils::mt_thin_time() for tolerance-constrained downsampling.
Distance-thinning — downsampling based on cumulative travel distance. Provided by move2utils::mt_thin_distance().

Setting the scene

library(move2)
library(dplyr)
library(sf)
library(move2utils)  # loaded here so that future helpers are visible

fishers <- mt_read(mt_example())
fishers <- fishers[!st_is_empty(fishers), ]

leroy <- filter_track_data(fishers, .track_id = "M1")
leroy <- slice(leroy,1:300)

summary(mt_time_lags(leroy, units = "min"))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.     NAs 
#>   13.38   14.73   15.02   26.64   15.40  779.53       1

Interpolation

mt_interpolate() supports three use patterns.

A. Regular time cadence via an interval string

## one fix per five minutes, refusing to bridge gaps longer than 1 h
leroy_5min <- mt_interpolate(
  leroy,
  time         = "5 mins",
  max_time_lag = as.difftime(1, units = "hours")
)
nrow(leroy); nrow(leroy_5min)
#> [1] 300
#> [1] 1893
summary(mt_time_lags(leroy_5min, units = "min"))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.     NAs 
#> 0.09997 4.45000 5.00000 4.20965 5.00000 5.00000       1

The "5 mins" string is passed through lubridate::floor_date(), so you can use any interval format that accepts ("30 secs", "2 hours", "1 day", …). max_time_lag is the policy for gaps: any original lag longer than this cutoff is not bridged; the output track has a break there rather than a dense string of interpolated points across the gap.

B. Interpolate at a specific set of timestamps

t0 <- min(mt_time(leroy))
target_t <- t0 + as.difftime(c(10, 20, 30, 60, 120), units = "mins")
leroy_at <- mt_interpolate(leroy, time = target_t, omit = FALSE)
## the new locations
head(leroy_at[mt_time(leroy_at) %in% target_t, ])
#> A <move2> with `track_id_column` "individual-local-identifier" and
#> `time_column` "timestamp"
#> Containing 1 track lasting 1.83 hours in a
#> Simple feature collection with 5 features and 20 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: -73.89874 ymin: 42.74363 xmax: -73.89869 ymax: 42.74369
#> Geodetic CRS:  WGS 84
#> # A tibble: 5 × 21
#>   `individual-local-identifier` `event-id` visible timestamp          
#> * <fct>                            <int64> <lgl>   <dttm>             
#> 1 M1                                    NA NA      2009-02-11 12:26:45
#> 2 M1                                    NA NA      2009-02-11 12:36:45
#> 3 M1                                    NA NA      2009-02-11 12:46:45
#> 4 M1                                    NA NA      2009-02-11 13:16:45
#> 5 M1                                    NA NA      2009-02-11 14:16:45
#> # ℹ 17 more variables: `behavioural-classification` <fct>,
#> #   `eobs:battery-voltage` [mV], `eobs:fix-battery-voltage` [mV],
#> #   `eobs:horizontal-accuracy-estimate` [m], `eobs:key-bin-checksum` <int64>,
#> #   `eobs:speed-accuracy-estimate` [m/s], `eobs:start-timestamp` <dttm>,
#> #   `eobs:status` <ord>, `eobs:temperature` [°C], `eobs:type-of-fix` <fct>,
#> #   `eobs:used-time-to-get-fix` [s], `ground-speed` [m/s], heading [°],
#> #   `height-above-ellipsoid` [m], `manually-marked-outlier` <lgl>, …
#> Track features:
#>   individual-local-identifier individual-taxon-canonical-name
#> 1                          M1                 Martes pennanti
#>                         study-name tag-local-identifier
#> 1 Martes pennanti LaPoint New York                   74

Setting omit = TRUE returns only the requested timestamps and discards the originals.

C. Interpolate to where a line crosses the track

Useful for finding when an animal crossed a boundary — a road, a home-range edge, a territory line.

## example: bounding square line (plug in your own geometry in practice)
line <- sf::st_sfc(
  sf::st_linestring(cbind(c(-1, 1, 1, -1, -1), c(-1, -1, 1, 1, -1))),
  crs = sf::st_crs(leroy)
)
crossings <- mt_interpolate(leroy, sf = line)

Comparison with legacy `move::interpolateTime()`

move	move2
`interpolateTime(x, time = 500)` (count)	`mt_interpolate(x, time = seq(min(t), max(t), length.out = 500))`
`interpolateTime(x, time = as.difftime(5, "mins"))`	`mt_interpolate(x, time = "5 mins", max_time_lag = ...)`
`interpolateTime(x, time = timestamp_vec)`	`mt_interpolate(x, time = timestamp_vec)`

The explicit max_time_lag is slightly more disciplined than the legacy default — you decide what counts as “too long to interpolate” rather than letting the function silently fill every gap.

Time-thinning

The question “give me ~one fix per 45 min” has two sensibly different answers. move2::mt_filter_per_interval() gives the bucketed answer: divide time into 45-minute windows (aligned to wall-clock intervals via floor_date), and pick one fix per window.

leroy_45 <- mt_filter_per_interval(leroy, unit = "45 min",
                                    criterion = "first")
nrow(leroy); nrow(leroy_45)
#> [1] 300
#> [1] 157
summary(mt_time_lags(leroy_45, units = "min"))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.     NAs 
#>   14.28   15.10   37.48   51.06   45.00  779.53       1

The criterion can be "first", "last", or "random". Because the buckets are aligned to the wall clock, the actual time lag between retained fixes is not guaranteed to equal 45 minutes; if the first observed fix of a window falls at 10:55 and the next at 11:00, both are kept (they belong to different hour windows but are only 5 minutes apart in time).

Tolerance-constrained thinning with `mt_thin_time()`

mt_filter_per_interval() is fine for visualisation, quick-look downsampling, or feeding a method that is tolerant of irregular sampling.

mt_thin_time() solves a stricter problem: find the largest subset of fixes such that every successive retained pair is within [interval - tolerance, interval + tolerance]. The answer is the longest path in a small DAG on sorted timestamps; it is computed with a linear-time dynamic-programming sweep rather than the memoised recursion of the legacy implementation, so it scales cleanly to + fixes.

thinned <- mt_thin_time(leroy,
                         interval  = "30 min",
                         tolerance = "5 min",
                         remove    = TRUE)
nrow(leroy); nrow(thinned)
#> [1] 300
#> [1] 153

lags <- mt_time_lags(thinned, units = "min")
summary(lags[!is.na(lags)])
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   28.35   29.78   30.08   52.30   30.47  794.25

The retained-lag distribution shows the two regimes the function produces by construction:

Within-run lags fall inside [interval - tolerance, interval + tolerance] — these are the tolerance-admissible transitions that the DP maximised.
Between-run lags exceed interval + tolerance — they are the original gaps that were too long to bridge; the run-splitter pre-pass decomposed the track at these gaps so that thinning never pretends to bridge them.

No retained lag is ever shorter than interval - tolerance; that is the hard contract the function enforces.

Tie-breaking when several chains are equally long:

criterion = "closest" (default) — minimum summed deviation from the target interval, preferring chains that hit the target most evenly.
criterion = "first" — earliest-starting chain, matching the legacy "first" behaviour.

Distance-thinning

A further common pattern — “give me one fix every 300 metres of travel” — is handled by mt_thin_distance(). It walks along the track, accumulates great-circle (lon/lat) or planar (projected) distance via move2::mt_distance(), and retains a fix each time the cumulative distance crosses a new multiple of the distance step.

leroy_300m <- mt_thin_distance(leroy, distance = 300)
nrow(leroy); sum(leroy_300m$thin_selected)
#> [1] 300
#> [1] 95

## filtered output for downstream use
leroy_300m_kept <- mt_thin_distance(leroy, distance = 300, remove = TRUE)

Multi-track input is thinned per individual, the first fix of each track is always retained, and the output is labelled in place with a thin_selected column (matching the mt_thin_time() convention). distance can be a numeric metre count or a units object (units::set_units(0.5, "km")), so the call can read naturally.

Summary

Task	Function
Interpolate at regular intervals	`mt_interpolate(x, time = "5 mins", max_time_lag = ...)`
Interpolate at specific timestamps	`mt_interpolate(x, time = t_vec)`
Interpolate where a line crosses	`mt_interpolate(x, sf = line)`
Time-thin (bucketed)	`mt_filter_per_interval(x, unit = "45 min", criterion = "first")`
Time-thin (tolerance-constrained)	`mt_thin_time(x, interval, tolerance)`
Distance-thin	`mt_thin_distance(x, distance)`