## ---- message=F, warning=FALSE------------------------------------------------
library(navigation)

## -----------------------------------------------------------------------------
data("lemniscate_traj_ned") # trajectory in proper format as shown bellow
head(lemniscate_traj_ned)

## -----------------------------------------------------------------------------
traj <- make_trajectory(data = lemniscate_traj_ned, system = "ned")
class(traj)

## -----------------------------------------------------------------------------
timing <- make_timing(
  nav.start = 0, # time at which to begin filtering
  nav.end = 15,
  freq.imu = 100, # frequency of the IMU, can be slower wrt trajectory frequency
  freq.gps = 1, # gnss frequency
  freq.baro = 1, # barometer frequency (to disable, put it very low, e.g. 1e-5)
  gps.out.start = 8, # to simulate a GNSS outage, set a time before nav.end
  gps.out.end = 13
)

## -----------------------------------------------------------------------------
snsr.mdl <- list()
acc.mdl <- WN(sigma2 = 5.989778e-05) + AR1(phi = 9.982454e-01, sigma2 = 1.848297e-10) + AR1(phi = 9.999121e-01, sigma2 = 2.435414e-11) + AR1(phi = 9.999998e-01, sigma2 = 1.026718e-12)
gyr.mdl <- WN(sigma2 = 1.503793e-06) + AR1(phi = 9.968999e-01, sigma2 = 2.428980e-11) + AR1(phi = 9.999001e-01, sigma2 = 1.238142e-12)

snsr.mdl$imu <- make_sensor(name = "imu", frequency = timing$freq.imu, error_model1 = acc.mdl, error_model2 = gyr.mdl)

## -----------------------------------------------------------------------------
gps.mdl.pos.hor <- WN(sigma2 = 0.025^2)
gps.mdl.pos.ver <- WN(sigma2 = 0.05^2)
gps.mdl.vel.hor <- WN(sigma2 = 0.01^2)
gps.mdl.vel.ver <- WN(sigma2 = 0.02^2)
snsr.mdl$gps <- make_sensor(
  name = "gps", frequency = timing$freq.gps,
  error_model1 = gps.mdl.pos.hor,
  error_model2 = gps.mdl.pos.ver,
  error_model3 = gps.mdl.vel.hor,
  error_model4 = gps.mdl.vel.ver
)

## -----------------------------------------------------------------------------
baro.mdl <- WN(sigma2 = 0.5^2)
snsr.mdl$baro <- make_sensor(name = "baro", frequency = timing$freq.baro, error_model1 = baro.mdl)

## -----------------------------------------------------------------------------
KF.mdl <- list()

KF.mdl$imu <- make_sensor(name = "imu", frequency = timing$freq.imu, error_model1 = acc.mdl, error_model2 = gyr.mdl)
KF.mdl$gps <- snsr.mdl$gps
KF.mdl$baro <- snsr.mdl$baro

## -----------------------------------------------------------------------------
wrong_acc.mdl <- WN(sigma2 = 5.989778e-05)
wrong_gyr.mdl <- WN(sigma2 = 1.503793e-06)
wrong_KF.mdl <- list()
wrong_KF.mdl$imu <- make_sensor(name = "imu", frequency = timing$freq.imu, error_model1 = wrong_acc.mdl, error_model2 = wrong_gyr.mdl)
wrong_KF.mdl$gps <- snsr.mdl$gps
wrong_KF.mdl$baro <- snsr.mdl$baro

## ---- message=FALSE, results='hide', eval=T-----------------------------------
num.runs <- 5 # number of Monte-Carlo simulations
res <- navigation(
  traj.ref = traj,
  timing = timing,
  snsr.mdl = snsr.mdl,
  KF.mdl = KF.mdl,
  num.runs = num.runs,
  noProgressBar = TRUE,
  PhiQ_method = "1",
  parallel.ncores = 1,
  P_subsampling = timing$freq.imu,
  compute_PhiQ_each_n = 50
) # keep one covariance every second

## ---- message=FALSE, results='hide', eval=T-----------------------------------
wrong_res <- navigation(
  traj.ref = traj,
  timing = timing,
  snsr.mdl = snsr.mdl,
  KF.mdl = wrong_KF.mdl, # < here the model is the wrong one
  num.runs = num.runs,
  noProgressBar = TRUE,
  PhiQ_method = "1",
  parallel.ncores = 1,
  P_subsampling = timing$freq.imu,
  compute_PhiQ_each_n = 50
) # keep one covariance every second

## ---- eval=T------------------------------------------------------------------
pe_res <- compute_mean_position_err(res, step = 25)
pe_wrong_res <- compute_mean_position_err(wrong_res, step = 25)

oe_res <- compute_mean_orientation_err(res, step = 25)
oe_wrong_res <- compute_mean_orientation_err(wrong_res, step = 25)

## ---- results='hide', fig.align='center', fig.width=7, fig.height=5, eval=T----
nees <- compute_nees(res, step = timing$freq.imu)
wrong_nees <- compute_nees(wrong_res, step = timing$freq.imu)

coverage <- compute_coverage(res, alpha = 0.7, step = timing$freq.imu)
wrong_coverage <- compute_coverage(wrong_res, alpha = 0.7, step = timing$freq.imu)

## ----  fig.height=5, fig.align='center', fig.width=6, eval=T------------------
plot(pe_res, pe_wrong_res, legend = c("correct model", "wrong model"))

plot(oe_res, oe_wrong_res, legend = c("correct model", "wrong model"))

plot(nees, wrong_nees, legend = c("correct model", "wrong model"))

plot(coverage, wrong_coverage, legend = c("correct model", "wrong model"))