FGFS-4.1/gr-air-modes
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mlat: fixed horrible bug in the solver. also noticed that [0,0,0] cannot contribute meaningful angular data, and so you still really want four stations on receive. there's still a bug in the solver somewhere that results in positions east of here not solving correctly.

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This commit is contained in:
Nick Foster 2011-07-14 18:49:47 -07:00
parent d7e153d281
commit a7e26c5960
2 changed files with 20 additions and 9 deletions
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11
src/python/mlat-test.py
View File

@ -3,21 +3,26 @@ import mlat
import numpy
#here's some test data to validate the algorithm
teststations = [[37.76225, -122.44254, 100], [37.409044, -122.077748, 100], [37.585085, -121.986395, 100]]
teststations = [[37.76225, -122.44254, 100], [37.409044, -122.077748, 100], [37.63816,-122.378082, 100], [37.701207,-122.309418, 100]]
testalt = 8000
testplane = numpy.array(mlat.llh2ecef([37.617175,-122.380843, testalt]))
testplane = numpy.array(mlat.llh2ecef([37.617175,-122.400843, testalt]))
testme = mlat.llh2geoid(teststations[0])
teststamps = [10,
10 + numpy.linalg.norm(testplane-numpy.array(mlat.llh2geoid(teststations[1]))) / mlat.c,
10 + numpy.linalg.norm(testplane-numpy.array(mlat.llh2geoid(teststations[2]))) / mlat.c,
10 + numpy.linalg.norm(testplane-numpy.array(mlat.llh2geoid(teststations[3]))) / mlat.c,
]
print teststamps
replies = []
for i in range(0, len(teststations)):
replies.append((teststations[i], teststamps[i]))
ans = mlat.mlat(replies, testalt)
error = numpy.linalg.norm(numpy.array(mlat.llh2ecef(ans))-numpy.array(testplane))
range = numpy.linalg.norm(mlat.llh2geoid(ans)-numpy.array(mlat.llh2geoid(teststations[0])))
range = numpy.linalg.norm(mlat.llh2geoid(ans)-numpy.array(testme))
print testplane-testme
print ans
print "Error: %.2fm" % (error)
print "Range: %.2fkm (from first station in list)" % (range/1000)

18
src/python/mlat.py
View File

@ -151,7 +151,8 @@ c = 299792458 / 1.0003 #modified for refractive index of air, why not
#we use limit as a goal to stop solving when we get "close enough" (error magnitude in meters for that iteration)
#basically 20 meters is way less than the anticipated error of the system so it doesn't make sense to continue
#it's possible this could fail in situations where the solution converges slowly
def mlat_iter(rel_stations, prange_obs, xguess = [0,0,0], limit = 20, maxrounds = 50):
#TODO: this fails to converge for some seriously advantageous geometry
def mlat_iter(rel_stations, prange_obs, xguess = [0,0,0], limit = 20, maxrounds = 100):
xerr = [1e9, 1e9, 1e9]
rounds = 0
while numpy.linalg.norm(xerr) > limit:
@ -161,11 +162,12 @@ def mlat_iter(rel_stations, prange_obs, xguess = [0,0,0], limit = 20, maxrounds
dphat = prange_obs - prange_est
H = []
for row in range(0,len(rel_stations)):
H.append((numpy.array(-rel_stations[row,:])-xguess) / prange_est[row])
H.append((numpy.array(-rel_stations[row,:])+xguess) / prange_est[row])
H = numpy.array(H)
#now we have H, the Jacobian, and can solve for residual error
xerr = numpy.linalg.lstsq(H, dphat)[0].flatten() #let's not get crazy here
xerr = numpy.linalg.lstsq(H, dphat)[0].flatten()
xguess += xerr
print xguess, xerr
rounds += 1
if rounds > maxrounds:
raise Exception("Failed to converge!")
@ -207,13 +209,17 @@ def mlat(replies, altitude):
prange_obs.append([c * stamp])
#so here we calc the estimated pseudorange to the center of the earth, using station[0] as a reference point for the geoid
#in other words, we say "if the aircraft were directly overhead of station[0], this is the prange to the center of the earth"
#this is a necessary approximation since we don't know the location of the aircraft yet
#if the dang earth were actually round this wouldn't be an issue
prange_obs.append( [numpy.linalg.norm(llh2ecef((me_llh[0], me_llh[1], altitude)))] ) #use ECEF not geoid since alt is MSL not GPS
#prange_obs.append( [numpy.linalg.norm(testplane)]) #test for error
prange_obs = numpy.array(prange_obs)
#xguess = llh2ecef([37.617175,-122.400843, 8000])-numpy.array(me)
xguess = [0,0,0]
#xguess = numpy.array(llh2ecef([stations[2][0], stations[2][1], altitude])) - numpy.array(me)
xyzpos = mlat_iter(rel_stations, prange_obs)
xyzpos = mlat_iter(rel_stations, prange_obs, xguess)
llhpos = ecef2llh(xyzpos+me)
#now, we could return llhpos right now and be done with it.
@ -227,7 +233,7 @@ def mlat(replies, altitude):
llhpos = ecef2llh(xyzpos_corr+me)
#and now, what the hell, let's try to get dilution of precision data
#avec is the vector of relative ranges to the aircraft from each of the stations
#avec is the unit vector of relative ranges to the aircraft from each of the stations
# for i in range(len(avec)):
# avec[i] = numpy.array(avec[i]) / numpy.linalg.norm(numpy.array(avec[i]))
# numpy.append(avec, [[-1],[-1],[-1],[-1]], 1) #must be # of stations