def findStopsGlobalForRTK(track,
std_max=2e-2,
duration=5,
downsampling=1,
verbose=True):
"""Find stop points in a track based on maximal size of a stop and minimal
time duration
Two parameters:
- Maximal size of a stop (as the standard deviation per axis, in ground units)
- Minimal time duration (in seconds)
Use downsampling parameter > 1 to speed up the process.
Default is set for precise RTK GNSS survey (2 cm for 5 sec)
"""
# If down-sampling is required
if downsampling > 1:
track = track.copy()
track **= track.size() / downsampling
# ---------------------------------------------------------------------------
# Computes cost matrix as :
# Cij = 0 if sqrt(0.33*(std_x^2 + std_y^2 + std_Z^2)) > std_max
# Cij = 0 if time duration between pi and p-1 is < duration
# Cij = (j-i)**2 = square of the number of points of segment otherwise
# ---------------------------------------------------------------------------
C = np.zeros((track.size(), track.size()))
RANGE = range(track.size() - 2)
if verbose:
print("Minimal enclosing circles computation:")
RANGE = progressbar.progressbar(RANGE)
for i in RANGE:
for j in range(i + 1, track.size() - 1):
if track[i].distanceTo(track[j - 1]) > 3 * std_max:
C[i, j] = 0
break
if track[j - 1].timestamp - track[i].timestamp <= duration:
C[i, j] = 0
continue
portion = track.extract(i, j - 1)
varx = portion.operate(Operator.Operator.VARIANCE, "x")
vary = portion.operate(Operator.Operator.VARIANCE, "y")
varz = portion.operate(Operator.Operator.VARIANCE, "z")
C[i, j] = math.sqrt(varx + vary + varz)
C[i, j] = (C[i, j] < std_max) * (j - i)**2
C = C + np.transpose(C)
# ---------------------------------------------------------------------------
# Computes optimal partition with dynamic programing
# ---------------------------------------------------------------------------
segmentation = optimalPartition(C, MODE_SEGMENTATION_MAXIMIZE, verbose)
stops = Track()
TMP_RADIUS = []
TMP_MEAN_X = []
TMP_MEAN_Y = []
TMP_MEAN_Z = []
TMP_IDSTART = []
TMP_IDEND = []
TMP_STD_X = []
TMP_STD_Y = []
TMP_STD_Z = []
TMP_DURATION = []
TMP_NBPOINTS = []
for i in range(len(segmentation) - 1):
portion = track.extract(segmentation[i], segmentation[i + 1] - 1)
radius = C[segmentation[i], segmentation[i + 1]]
if radius == 0:
continue
xm = portion.operate(Operator.Operator.AVERAGER, "x")
ym = portion.operate(Operator.Operator.AVERAGER, "y")
zm = portion.operate(Operator.Operator.AVERAGER, "z")
xv = portion.operate(Operator.Operator.VARIANCE, "x")
yv = portion.operate(Operator.Operator.VARIANCE, "y")
zv = portion.operate(Operator.Operator.VARIANCE, "z")
pt = portion[0].position.copy()
pt.setX(xm)
pt.setY(ym)
pt.setZ(zm)
stops.addObs(Obs(pt, portion[0].timestamp))
TMP_RADIUS.append(math.sqrt(xv + yv + zv))
TMP_MEAN_X.append(xm)
TMP_MEAN_Y.append(ym)
TMP_MEAN_Z.append(zm)
TMP_STD_X.append(xv**0.5)
TMP_STD_Y.append(yv**0.5)
TMP_STD_Z.append(zv**0.5)
TMP_IDSTART.append(segmentation[i] * downsampling)
TMP_IDEND.append((segmentation[i + 1] - 1) * downsampling)
TMP_NBPOINTS.append(segmentation[i + 1] - segmentation[i])
TMP_DURATION.append(portion.duration())
if stops.size() == 0:
return stops
stops.createAnalyticalFeature("radius", TMP_RADIUS)
stops.createAnalyticalFeature("mean_x", TMP_MEAN_X)
stops.createAnalyticalFeature("mean_y", TMP_MEAN_Y)
stops.createAnalyticalFeature("mean_z", TMP_MEAN_Z)
stops.createAnalyticalFeature("id_ini", TMP_IDSTART)
stops.createAnalyticalFeature("id_end", TMP_IDEND)
stops.createAnalyticalFeature("sigma_x", TMP_STD_X)
stops.createAnalyticalFeature("sigma_y", TMP_STD_Y)
stops.createAnalyticalFeature("sigma_z", TMP_STD_Z)
stops.createAnalyticalFeature("duration", TMP_DURATION)
stops.createAnalyticalFeature("nb_points", TMP_NBPOINTS)
stops.operate(Operator.Operator.QUAD_ADDER, "sigma_x", "sigma_y", "rmse")
stops.base = track.base
return stops
def findStopsGlobal(track,
diameter=20,
duration=60,
downsampling=1,
verbose=True):
"""Find stop points in a track based on two parameters:
Maximal size of a stop (as the diameter of enclosing circle,
in ground units) and minimal time duration (in seconds)
Use downsampling parameter > 1 to speed up the process"""
# If down-sampling is required
if downsampling > 1:
track = track.copy()
track **= track.size() / downsampling
# ---------------------------------------------------------------------------
# Computes cost matrix as :
# Cij = 0 if size of enclosing circle of pi, pi+1, ... pj-1 is > diameter
# Cij = 0 if time duration between pi and p-1 is < duration
# Cij = (j-i)**2 = square of the number of points of segment otherwise
# ---------------------------------------------------------------------------
C = np.zeros((track.size(), track.size()))
RANGE = range(track.size() - 2)
if verbose:
print("Minimal enclosing circles computation:")
RANGE = progressbar.progressbar(RANGE)
for i in RANGE:
for j in range(i + 1, track.size() - 1):
if track[i].distance2DTo(track[j - 1]) > diameter:
C[i, j] = 0
break
if track[j - 1].timestamp - track[i].timestamp <= duration:
C[i, j] = 0
continue
C[i, j] = 2 * minCircle(track.extract(i, j - 1))[1]
C[i, j] = (C[i, j] < diameter) * (j - i)**2
C = C + np.transpose(C)
# ---------------------------------------------------------------------------
# Computes optimal partition with dynamic programing
# ---------------------------------------------------------------------------
segmentation = optimalPartition(C, MODE_SEGMENTATION_MAXIMIZE, verbose)
stops = Track()
TMP_RADIUS = []
TMP_MEAN_X = []
TMP_MEAN_Y = []
TMP_MEAN_Z = []
TMP_IDSTART = []
TMP_IDEND = []
TMP_STD_X = []
TMP_STD_Y = []
TMP_STD_Z = []
TMP_DURATION = []
TMP_NBPOINTS = []
for i in range(len(segmentation) - 1):
portion = track.extract(segmentation[i], segmentation[i + 1] - 1)
C = minCircle(portion)
if (C[1] > diameter / 2) or (portion.duration() < duration):
continue
stops.addObs(Obs(C[0], portion.getFirstObs().timestamp))
TMP_RADIUS.append(C[1])
TMP_MEAN_X.append(portion.operate(Operator.Operator.AVERAGER, "x"))
TMP_MEAN_Y.append(portion.operate(Operator.Operator.AVERAGER, "y"))
TMP_MEAN_Z.append(portion.operate(Operator.Operator.AVERAGER, "z"))
TMP_STD_X.append(portion.operate(Operator.Operator.STDDEV, "x"))
TMP_STD_Y.append(portion.operate(Operator.Operator.STDDEV, "y"))
TMP_STD_Z.append(portion.operate(Operator.Operator.STDDEV, "z"))
TMP_IDSTART.append(segmentation[i] * downsampling)
TMP_IDEND.append((segmentation[i + 1] - 1) * downsampling)
TMP_NBPOINTS.append(segmentation[i + 1] - segmentation[i])
TMP_DURATION.append(portion.duration())
if stops.size() == 0:
return stops
stops.createAnalyticalFeature("radius", TMP_RADIUS)
stops.createAnalyticalFeature("mean_x", TMP_MEAN_X)
stops.createAnalyticalFeature("mean_y", TMP_MEAN_Y)
stops.createAnalyticalFeature("mean_z", TMP_MEAN_Z)
stops.createAnalyticalFeature("id_ini", TMP_IDSTART)
stops.createAnalyticalFeature("id_end", TMP_IDEND)
stops.createAnalyticalFeature("sigma_x", TMP_STD_X)
stops.createAnalyticalFeature("sigma_y", TMP_STD_Y)
stops.createAnalyticalFeature("sigma_z", TMP_STD_Z)
stops.createAnalyticalFeature("duration", TMP_DURATION)
stops.createAnalyticalFeature("nb_points", TMP_NBPOINTS)
stops.operate(Operator.Operator.QUAD_ADDER, "sigma_x", "sigma_y", "rmse")
stops.base = track.base
return stops