The packages we need:

> library(sp)     # coordinates, loaded anyway by raster
> library(raster) # crs, extract

The 2009 land cover data, which is a raster file with 300 m resolution:

> gcvn <- globcoverVN::getgcvn()
> legend <- globcoverVN::show_legend(gcvn)
 11 : Post-flooding or irrigated croplands (or aquatic)
 14 : Rainfed croplands
 20 : Mosaic cropland (50-70%) / vegetation (grassland/shrubland/forest) (20-50%)
 30 : Mosaic vegetation (grassland/shrubland/forest) (50-70%) / cropland (20-50%)
 40 : Closed to open (>15%) broadleaved evergreen or semi-deciduous forest (>5m)
 50 : Closed (>40%) broadleaved deciduous forest (>5m)
 60 : Open (15-40%) broadleaved deciduous forest/woodland (>5m)
 70 : Closed (>40%) needleleaved evergreen forest (>5m)
100 : Closed to open (>15%) mixed broadleaved and needleleaved forest (>5m)
110 : Mosaic forest or shrubland (50-70%) / grassland (20-50%)
120 : Mosaic grassland (50-70%) / forest or shrubland (20-50%)
130 : Closed to open (>15%) (broadleaved or needleleaved, evergreen or deciduous) shrubland (<5m)
140 : Closed to open (>15%) herbaceous vegetation (grassland, savannas or lichens/mosses)
150 : Sparse (<15%) vegetation
160 : Closed to open (>15%) broadleaved forest regularly flooded (semi-permanently or temporarily) - Fresh or brackish water
170 : Closed (>40%) broadleaved forest or shrubland permanently flooded - Saline or brackish water
190 : Artificial surfaces and associated areas (Urban areas >50%)
200 : Bare areas
210 : Water bodies
220 : Permanent snow and ice
> legend <- with(legend, setNames(landtype, code))
> legend <- c(legend, "NA" = NA)

The GPS coordinates:

> gps <- readxl::read_excel("GPS coordinates.xlsx")
> coordinates(gps) <- ~ Longitude + Latitude
> crs(gps) <- crs(gcvn)

Extracting (takes a loooooooong time (a few days)):

> buffer10m <- extract(gcvn, gps, buffer = 10)
> buffer100m <- extract(gcvn, gps, buffer = 100)

10-m and 100-m buffers just give same thing:

> identical(buffer10m, buffer100m)
[1] TRUE

Furthermore, each coordinate has only one value of land cover:

> unique(sapply(buffer10m, length))
[1] 1

which makes our life easier! So, we can easily merge it back with the data frame of the coordinates:

> land_cover <- as.character(unlist(buffer10m))
> land_cover[is.na(land_cover)] <- "NA"
> land_cover <- data.frame(coordinates(gps), land_cover = legend[land_cover])

The number of GPS coordinates:

> nrow(land_cover)
[1] 730320

The number of missing values:

> sum(is.na(land_cover$land_cover))
[1] 73
> 100 * sum(is.na(land_cover$land_cover)) / nrow(land_cover)
[1] 0.009995618

Calculating proportions:

> land_cover2 <- na.exclude(land_cover)
> 100 * sort(table(land_cover$land_cover) / nrow(land_cover), TRUE)

                                                                          Rainfed croplands 
                                                                               5.927224e+01 
                Mosaic vegetation (grassland/shrubland/forest) (50-70%) / cropland (20-50%) 
                                                                               3.617469e+01 
                Mosaic cropland (50-70%) / vegetation (grassland/shrubland/forest) (20-50%) 
                                                                               3.832567e+00 
                                                                               Water bodies 
                                                                               2.327747e-01 
                                          Post-flooding or irrigated croplands (or aquatic) 
                                                                               1.204951e-01 
Closed to open (>15%) (broadleaved or needleleaved, evergreen or deciduous) shrubland (<5m) 
                                                                               1.066656e-01 
                 Closed to open (>15%) broadleaved evergreen or semi-deciduous forest (>5m) 
                                                                               9.776536e-02 
                      Closed to open (>15%) mixed broadleaved and needleleaved forest (>5m) 
                                                                               7.407712e-02 
        Closed to open (>15%) herbaceous vegetation (grassland, savannas or lichens/mosses) 
                                                                               4.463797e-02 
                                Artificial surfaces and associated areas (Urban areas >50%) 
                                                                               1.916968e-02 
                                          Closed (>40%) needleleaved evergreen forest (>5m) 
                                                                               8.626356e-03 
                                  Open (15-40%) broadleaved deciduous forest/woodland (>5m) 
                                                                               6.161683e-03 
                                                                                 Bare areas 
                                                                               1.369263e-04

A pie chart:

> pie(sort(table(land_cover$land_cover) / nrow(land_cover)))

So, basically, we have: