From 3be6e9fd6e8c129a352ebbca714429dc8d468654 Mon Sep 17 00:00:00 2001 From: Nick Foster Date: Tue, 11 Dec 2012 09:44:21 -0800 Subject: [PATCH] Remove altitude-based extra station. I don't now believe there's a way to construct a "fake" station as you don't have the originating time of the transmission as a known quantity. --- python/mlat.py | 60 +++++--------------------------------------------- 1 file changed, 6 insertions(+), 54 deletions(-) diff --git a/python/mlat.py b/python/mlat.py index 47d9741..9cce2e5 100755 --- a/python/mlat.py +++ b/python/mlat.py @@ -107,30 +107,15 @@ def mlat_iter(stations, prange_obs, guess = [0,0,0], limit = 20, maxrounds = 100 #create a matrix of partial differentials to find the slope of the error in X,Y,Z,t directions H = numpy.array([(numpy.array(-stations[row,:])+guess) / prange_est[row] for row in range(len(stations))]) H = numpy.append(H, numpy.ones(len(prange_obs)).reshape(len(prange_obs),1)*c, axis=1) - #print "H: ", H #now we have H, the Jacobian, and can solve for residual error solved = numpy.linalg.lstsq(H, dphat) xerr = solved[0].flatten() - #print "s: ", solved[3] - #print "xerr: ", xerr guess += xerr[:3] #we ignore the time error for xguess - #print "Estimated position and change: ", guess, numpy.linalg.norm(xerr[:3]) rounds += 1 if rounds > maxrounds: raise Exception("Failed to converge!") return (guess, xerr[3]) -#gets the emulated Arne Saknussemm Memorial Radio Station report -#here we calc the estimated pseudorange to the center of the earth, using station[0] as a reference point -#in other words, we say "if the aircraft were directly overhead of me, this is the pseudorange to the center of the earth" -#if the dang earth were actually round this wouldn't be an issue -#this lets us use the altitude of the mode S reply as info to construct an additional reporting station -#i haven't really thought about it but I think the geometry (re: *DOP) of this "station" is pretty lousy -#but it lets us solve with 3 stations -def get_fake_prange(surface_position, altitude): - fake_xyz = numpy.array(llh2ecef((surface_position[0], surface_position[1], altitude))) - return [numpy.linalg.norm(fake_xyz)-numpy.linalg.norm(llh2geoid(surface_position))] #use ECEF not geoid since alt is MSL not GPS - #func mlat: #uses a modified GPS pseudorange solver to locate aircraft by multilateration. #replies is a list of reports, in ([lat, lon, alt], timestamp) format @@ -142,58 +127,25 @@ def mlat(replies, altitude): stations = [sorted_reply[0] for sorted_reply in sorted_replies] timestamps = [sorted_reply[1] for sorted_reply in sorted_replies] - print "Timestamps: ", timestamps - nearest_llh = stations[0] - #nearest_xyz = numpy.array(llh2geoid(stations[0])) - - stations_xyz = [numpy.array(llh2geoid(station)) for station in stations] + stations_xyz = numpy.array([llh2geoid(station) for station in stations]) - #add in a center-of-the-earth station if we have altitude -# if altitude is not None: -# stations_xyz.append([0,0,0]) - - stations_xyz = numpy.array(stations_xyz) #convert list of arrays to 2d array - - #get TDOA relative to station 0, multiply by c to get pseudorange #the absolute time shouldn't matter at all except perhaps in #maintaining floating-point precision; in other words you can - #add a constant here and it should fall out in the solver as time - #error - prange_obs = [[c*(stamp)] for stamp in timestamps] + #add a constant here and it should fall out in the solver as time error + prange_obs = [[c*stamp] for stamp in timestamps] -# if altitude is not None: -# prange_obs.append(get_fake_prange(stations[0], altitude)) - - #if no alt, use a very large number - #this guarantees monotonicity in the error function + #if no alt, use a reasonably large number (in meters) #since if all your stations lie in a plane (they basically will), #there's a reasonable solution at negative altitude as well if altitude is None: altitude = 20000 - - print "Initial pranges: ", prange_obs - print "Stations: ", stations_xyz + firstguess = numpy.array(llh2ecef((nearest_llh[0], nearest_llh[1], altitude))) prange_obs = numpy.array(prange_obs) - #use the nearest station (we sorted by timestamp earlier) as the initial guess - firstguess = numpy.array(llh2ecef((nearest_llh[0], nearest_llh[1], altitude))) xyzpos, time_offset = mlat_iter(stations_xyz, prange_obs, firstguess, maxrounds=100) - print "xyzpos: ", xyzpos llhpos = ecef2llh(xyzpos) - #now, we could return llhpos right now and be done with it. - #but the assumption we made above, namely that the aircraft is directly above the - #nearest station, results in significant error due to the oblateness of the Earth's geometry. - #so now we solve AGAIN, but this time with the corrected pseudorange of the aircraft altitude - #this might not be really useful in practice but the sim shows >50m errors without it - #and <4cm errors with it, not that we'll get that close in reality but hey let's do it right - -# if altitude is not None: -# prange_obs[-1] = [numpy.linalg.norm(llh2ecef((llhpos[0], llhpos[1], altitude)))] -# xyzpos_corr, time_offset = mlat_iter(stations, prange_obs, xyzpos) #start off with a really close guess -# llhpos = ecef2llh(xyzpos_corr+nearest_xyz) - return (llhpos, time_offset) #tests the mlat_iter algorithm using sample data from Farrell & Barth (p.147) @@ -235,7 +187,7 @@ if __name__ == '__main__': replies = [(station, stamp) for station,stamp in zip(teststations, teststamps)] - ans, offset = mlat(replies, None) + ans, offset = mlat(replies, testalt) error = numpy.linalg.norm(numpy.array(llh2ecef(ans))-numpy.array(testplane)) rng = numpy.linalg.norm(llh2geoid(ans)-numpy.array(llh2geoid(teststations[0]))) print "Resolved lat/lon/alt: ", ans