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position1.py
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position1.py
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# Miscellaneous routines (some interesting) related to covariance
# estimation.
import util, signal, position
def compute_contour(x_hat, f, Q):
''' Find the points that fall within confidence region of the estimate.
Given a point x_hat known to be contained by a contour defined by
f(x) < Q, compute the contour.
'''
S = set(); S.add((x_hat[0], x_hat[1]))
level_set = S.copy()
contour = set()
max_size = 10000 # FIXME Computational stop gap.
while len(S) > 0 and len(S) < max_size and len(level_set) < max_size:
R = set()
for x in S:
if f(x) < Q:
level_set.add(x)
R.add((x[0]+1, x[1]-1)); R.add((x[0]+1, x[1])); R.add((x[0]+1, x[1]+1))
R.add((x[0], x[1]-1)); R.add((x[0] , x[1]+1))
R.add((x[0]-1, x[1]-1)); R.add((x[0]-1, x[1])); R.add((x[0]-1, x[1]+1))
else:
contour.add(x)
S = R.difference(level_set)
if len(S) >= max_size or len(level_set) >= max_size:
return (None, None) # Unbounded confidence region
return (level_set, contour)
def fit_ellipse(x, y):
''' Fit ellipse parameters to a set of points in R^2.
The points should correspond a perfect ellipse.
'''
x_lim = np.array([np.min(x), np.max(x)])
y_lim = np.array([np.min(y), np.max(y)])
x_center = np.array([np.mean(x_lim), np.mean(y_lim)])
X = np.vstack((x,y))
D = (lambda d: np.sqrt(
(d[0] - x_center[0])**2 + (d[1] - x_center[1])**2))(X)
x_major = x_center - X[:,np.argmax(D)]
angle = np.arctan2(x_major[1], x_major[0])
axes = np.array([np.max(D), np.min(D)])
return (x_center, angle, axes)
def fit_noisy_ellipse(x, y):
''' Least squares fit of an ellipse to a set of points in R^2.
The points are allowed to be noisy. Method due to
http://nicky.vanforeest.com/misc/fitEllipse/fitEllipse.html
'''
x = x[:,np.newaxis]
y = y[:,np.newaxis]
D = np.hstack((x*x, x*y, y*y, x, y, np.ones_like(x)))
S = np.dot(D.T,D)
C = np.zeros([6,6])
C[0,2] = C[2,0] = 2; C[1,1] = -1
E, V = np.linalg.eig(np.dot(np.linalg.inv(S), C))
n = np.argmax(np.abs(E))
A = V[:,n]
# Center of ellipse
b,c,d,f,g,a = A[1]/2, A[2], A[3]/2, A[4]/2, A[5], A[0]
num = b*b-a*c
x0=(c*d-b*f)/num
y0=(a*f-b*d)/num
x = np.array([x0,y0])
# Angle of rotation
angle = 0.5*np.arctan(2*b/(a-c))
# Length of Axes
up = 2*(a*f*f+c*d*d+g*b*b-2*b*d*f-a*c*g)
down1=(b*b-a*c)*( (c-a)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
down2=(b*b-a*c)*( (a-c)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
res1=np.sqrt(up/down1)
res2=np.sqrt(up/down2)
axes = np.array([res1, res2])
return (x, angle, axes)
def fit_contour(x, y, N):
''' Fit closed countour to a set of points in R^2.
Convert the Cartesian coordinates (x, y) to polar coordinates (theta, r)
and fit a spline. Sample uniform angles from this spline and compute the
Fourier transform of their distancxe to the centroid of the contour.
`N` is the number of samples.
http://stackoverflow.com/questions/13604611/how-to-fit-a-closed-contour
'''
x0, y0 = np.mean(x), np.mean(y)
C = (x - x0) + 1j * (y - y0)
angles = np.angle(C)
distances = np.abs(C)
sort_index = np.argsort(angles)
angles = angles[sort_index]
distances = distances[sort_index]
angles = np.hstack(([ angles[-1] - 2*np.pi ], angles, [ angles[0] + 2*np.pi ]))
distances = np.hstack(([distances[-1]], distances, [distances[0]]))
f = spline1d(angles, distances)
theta = scipy.linspace(-np.pi, np.pi, num=N, endpoint=False)
distances_uniform = f(theta)
fft_coeffs = np.fft.rfft(distances_uniform)
fft_coeffs[5:] = 0
r = np.fft.irfft(fft_coeffs)
x_fit = x0 + r * np.cos(theta)
y_fit = y0 + r * np.sin(theta)
return (x_fit, y_fit)
### Testing, testing ... ######################################################
def test1():
import time
cal_id = 3
dep_id = 105
t_start = 1407452400
t_end = 1407455985 - (59 * 60)
db_con = util.get_db('reader')
sv = signal1.SteeringVectors(db_con, cal_id)
signal = signal1.Signal(db_con, dep_id, t_start, t_end)
sites = util.get_sites(db_con)
(center, zone) = util.get_center(db_con)
assert zone == util.get_utm_zone(db_con)
start = time.time()
pos = PositionEstimator(dep_id, sites, center, signal, sv,
method=signal1.Signal.MLE)
print "Finished in {0:.2f} seconds.".format(time.time() - start)
print compute_conf(pos.p, pos.num_sites, sites, pos.splines)
if __name__ == '__main__':
#test_exp()
#test_bearing()
#test_mle()
test1()