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kalman.py
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kalman.py
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import numpy as np
import matplotlib.pyplot as plt
import matplotlib.dates as mdates
from datetime import datetime
from datetime import time
import os
import matplotlib
from celluloid import Camera
def to_polar(X,Y,Z):
a = 6378137.000
b = 6356752.3141
c = a**2 / b
e1 = np.sqrt((a**2 - b**2) / a**2)
e2 = np.sqrt((a**2 - b**2) / b**2)
p = np.sqrt(X**2 + Y**2)
lam = np.arctan2(Y , X)
beta = np.arctan2(a * Z , (b*p))
fi = np.arctan2((Z+e2**2 * b *np.sin(beta)**3),(p-e1**2 * a * np.cos(beta)**3))
N = c / np.sqrt(1 + e2**2 * np.cos(fi)**2)
h = p / np.cos(fi) - N
return fi,lam,h
def to_SagYukarı(fi,lam):
a = 6378137.000
b = 6356752.3141
c = a**2 / b
e1 = np.sqrt((a**2 - b**2) / a**2)
e2 = np.sqrt((a**2 - b**2) / b**2)
N = c / np.sqrt(1 + e2**2 * np.cos(fi)**2)
der = 27 *np.pi/ 180
A0 = 1- e1**2 /4 - 3*e1**4 /64 -5*e1**6 /256 -175*e1**8 /16384
A2 = 3/8 *(e1**2 +e1**4 /4+ 15*e1**6 /128- 455*e1**8 /4096)
A4 = 15/256*(e1**4 +3*e1**6 /4 - 77*e1**8/128)
A6 = 35/3072*(e1**6 -41*e1**8 /32)
A8 = (-315)/131072 *e1**8
Sfi = a*(A0*fi-A2*np.sin(2*fi) + A4* np.sin(4*fi) - A6 *np.sin(6*fi) + A8 *np.sin(8*fi))
lam = lam - der
u = lam*np.cos(fi)
t = np.tan(fi)
n_squared = (e2**2)*np.cos(fi)**2
x = N*(u+u**3 /6*(1-t**2 +n_squared)+ u**5 /120 *(5- 18*t**2 + t**4 +14*n_squared - 58*t**2
* n_squared+ 13*n_squared**2 +4 *n_squared**3 -64 *n_squared**2 *t**2 -24*n_squared**3
*t**2)+ u**7 /5040 *(61- 479*t**2 +179*t**4 -t**6))
y = N*(Sfi/N+lam**2 *np.sin(fi)* np.cos(fi)/ 2+ lam**4 *np.sin(fi)* np.cos(fi)**3 / 24 *
(5-t**2 +9*n_squared +4*n_squared**2)+lam**6 *np.sin(fi)* np.cos(fi)**5 /720 *(61-
58 *t**2 +t**4 +270*n_squared +445*n_squared**2 +324*n_squared**3- 680*n_squared**2 *
t**2 +88*n_squared**4 -600*n_squared**4 -600*n_squared**3 *t**2 -192*n_squared**4 *t**2)+
lam**8 *np.sin(fi)* np.cos(fi)**7 /40320 *(1385- 311*t**2 +543*t**4 -t**6))
conv = lam*np.sin(fi)*(1+ lam**2 *np.cos(fi)**2 /3 *(1+3*n_squared+2*n_squared**2)+lam**4 * np.cos(fi)**4 /15* (2-t**2))
yukari = y*0.9996
saga = x*0.9996 + 500000
return saga,yukari
def grafnav_read(fname):
f = open(fname,"r")
data = f.readlines()
f.close()
for i in range(len(data)):
if len(data[i].split()) != 0 and data[i].split()[0] == "(HMS)":
break
else:
continue
del data[:i+1]
easting = []
northing = []
height = []
epoch = []
for i in range(len(data)):
if len(data[i].split()) == 0:
break
else:
epoch.append(datetime.strptime(("2021-10-26"+" "+str(data[i].split()[0])),"%Y-%m-%d %H:%M:%S.%f"))
height.append(float(data[i].split()[3]))
easting.append(float(data[i].split()[1]))
northing.append(float(data[i].split()[2]))
return epoch, easting, northing, height
def output_read(fname):
# PPP-WIZARD output reader (verbose on)
f = open(fname,"r")
data = f.readlines()
f.close()
easting = []
northing = []
height = []
X_list = []
Y_list = []
Z_list = []
XS_list = []
YS_list = []
ZS_list = []
epoch = []
for i in range(len(data)):
epoch.append(datetime.strptime(("20"+str(data[i].split()[0])+" "+str(data[i].split()[1])),"%Y-%m-%d %H:%M:%S.%f"))
X = float(data[i].split()[12])
Y = float(data[i].split()[15])
Z = float(data[i].split()[18])
X_list.append(X)
Y_list.append(Y)
Z_list.append(Z)
XS_list.append(float(data[i].split()[14]))
YS_list.append(float(data[i].split()[17]))
ZS_list.append(float(data[i].split()[20]))
fi,lam,h = to_polar(X,Y,Z)
S,Y = to_SagYukarı(fi,lam)
height.append(h)
easting.append(S)
northing.append(Y)
return epoch, easting, northing, height, X_list, Y_list, Z_list,XS_list,YS_list,ZS_list
def Sdisp2vel(data,dt = 1):
vel = []
i = 1
while i < (len(data)):
vel.append((data[i-1]**2 + data[i]**2)**0.5 /dt)
i+=1
return vel
def disp2vel(data,dt = 1):
vel = []
i = 1
while i < (len(data)):
vel.append((data[i] - data[i-1])/dt)
i+=1
return vel
def vel2acc(data,dt = 1):
acc = []
i = 1
while i < (len(data)):
acc.append((data[i]-data[i-1])/dt)
i+=1
return acc
def graph_E_N2(var1,var2,Svar1,Svar2,Tvar1,Tvar2,fname):
var1 = np.array(var1)
var2 = np.array(var2)
Svar1 = np.array(Svar1)
Svar2 = np.array(Svar2)
Tvar1 = np.array(Tvar1)
Tvar2 = np.array(Tvar2)
#matplotlib.use('Agg')
fig = plt.figure(figsize=(10,7))
plt.rcParams.update({'font.size': 9})
plt.grid(True, linestyle='--',linewidth=0.2)
plt.title("2D Scatter Plot", fontsize=10)
plt.ylabel("Northing (\u0394X) (cm)", fontsize=9)
plt.xlabel("Easting (\u0394Y) (cm)", fontsize=9)
xax = plt.gca().axes.get_xaxis()
xax = xax.set_visible(False)
# set visibility of y-axis as False
yax = plt.gca().axes.get_yaxis()
yax = yax.set_visible(False)
for i in range(len(var1)):
plt.scatter(var2[:i],var1[:i],c='b',marker="o",s = 2,label="rover")
plt.scatter(Svar2[:i],Svar1[:i],c='r',marker="o", s = 4,label="filtered rover")
plt.scatter(Tvar2[:i],Tvar1[:i],c='g',marker="o", s = 2,label="Predicted rover")
plt.pause(0.001)
plt.show()
def graph_E_N(var1,var2,Svar1,Svar2,Tvar1,Tvar2,Fvar1,Fvar2,fname):
var1 = np.array(var1)
var2 = np.array(var2)
Svar1 = np.array(Svar1)
Svar2 = np.array(Svar2)
Tvar1 = np.array(Tvar1)
Tvar2 = np.array(Tvar2)
Fvar1 = np.array(Fvar1)
Fvar2 = np.array(Fvar2)
fig = plt.figure(figsize=(20,15))
plt.plot(var2,var1,color='b',marker="o", linestyle="None",markersize = 2,label="rover")
plt.plot(Svar2,Svar1,color='r',marker="o", linestyle="None", markersize = 4,label="filtered rover")
plt.plot(Tvar2,Tvar1,color='g',marker="o", linestyle="None",markersize = 2,label="Predicted rover")
plt.plot(Fvar2,Fvar1,color='black',marker="o", linestyle="None",markersize = 2,label="Fixed rover")
plt.grid(True, linestyle='--',linewidth=0.2)
plt.legend(loc=1, handlelength=1, fontsize=12,markerscale=1)
plt.title("2D Scatter Plot", fontsize=12)
plt.ylabel("Northing (\u0394X) (cm)", fontsize=12)
plt.xlabel("Easting (\u0394Y) (cm)", fontsize=12)
xax = plt.gca().axes.get_xaxis()
xax = xax.set_visible(False)
yax = plt.gca().axes.get_yaxis()
yax = yax.set_visible(False)
plt.tight_layout()
plt.savefig("kalman2d.png")
def kalman(Xmatrx, obs_err, init, pro_err,aX):
i = int(np.size(Xmatrx)/len(Xmatrx))
A = np.identity(i)
pc = 0
while pc < i:
A[pc][pc+1] = init[1]
pc += 2
B = np.identity(i)
pc = 0
while pc < i:
B[pc][pc] = 0.5 * init[1]**2
B[pc+1][pc+1] = init[1]
pc += 2
H = np.identity(i)
for pc in range(i):
if pc % 2 != 0:
H[pc][pc] = 0
C = np.identity(i)
I = np.identity(i)
X_kp = np.ndarray((i,1), dtype = float)
X_k_1 = np.array(Xmatrx[0]).reshape((-1,1))
P_k_1 = np.ndarray((i,i), dtype = float)
for k in range(i):
P_k_1[k][k] = pro_err[k]**2
R = np.ndarray((i,i), dtype = float)
x_k = np.ndarray((len(Xmatrx)-1,3), dtype = float)
x_p = np.ndarray((len(Xmatrx)-1,3), dtype = float)
x_m = np.ndarray((len(Xmatrx)-1,3), dtype = float)
k, j = 0, 1
while j < len(Xmatrx):
for pc in range(i):
R[pc][pc] = obs_err[k][pc]**2
X_kp = np.dot(A, X_k_1) + np.dot(B, np.array([aX[k]]).T)
P_kp = (np.dot(np.dot(A, P_k_1), np.transpose(A)))
for pc in range(i):
for pk in range(i):
if pc !=pk:
P_kp[pc][pk] = 0
KG = np.divide(np.dot(P_kp, H), (np.dot(np.dot(H, P_kp), np.transpose(H)) + R))
for pc in range(i):
for pk in range(i):
if pc !=pk:
KG[pc][pk] = 0
Y_k = np.dot(H, Xmatrx[j].reshape((-1, 1)))
X_k = X_kp + np.dot(KG, (Y_k - np.dot(H, X_kp)))
P_k = np.dot((I - np.dot(KG, H)), P_kp)
X_k_1 = X_k
P_k_1 = P_k
x_k[k] = X_k[0][0],X_k[2][0],X_k[4][0]
x_p[k] = X_kp[0][0],X_kp[2][0],X_kp[4][0]
x_m[k] = Xmatrx[j][0],Xmatrx[j][2],Xmatrx[j][4]
j += 1
k += 1
return x_m, x_k, x_p
epoch, easting, northing, height, X_list, Y_list, Z_list,XS_list,YS_list,ZS_list = output_read("output_lowlevel_itu_kampus_RAIM")
np.seterr(divide = 'ignore', invalid = 'ignore')
vX = disp2vel(X_list)
aX = disp2vel(vX)
SvX = Sdisp2vel(XS_list)
SaX = Sdisp2vel(SvX)
SaX.append(0)
aX.append(0)
del X_list[-1]
del XS_list[-1]
vY = disp2vel(Y_list)
aY = disp2vel(vY)
SvY = Sdisp2vel(YS_list)
SaY = Sdisp2vel(SvY)
SaY.append(0)
aY.append(0)
del Y_list[-1]
del YS_list[-1]
vZ = disp2vel(Z_list)
aZ = disp2vel(vZ)
SvZ = Sdisp2vel(ZS_list)
SaZ = Sdisp2vel(SvZ)
SaZ.append(0)
aZ.append(0)
del Z_list[-1]
del ZS_list[-1]
X = np.array((list(zip(X_list, vX, Y_list, vY ,Z_list, vZ))))
obs_err = np.array((list(zip(XS_list, SvX,YS_list, SvY, ZS_list, SvZ))), dtype = float)
pro_err = np.array(([np.mean(XS_list), np.mean(SvX), np.mean(YS_list), np.mean(SvY), np.mean(ZS_list), np.mean(SvZ)]), dtype = float)
init = np.array(([10],[1],[0]), dtype = float)
A = np.array((list(zip(aX, aX, aY, aY ,aZ, aZ))))
x_m, x_k, x_p = kalman(X, obs_err, init, pro_err,A)
height = []
northing = []
easting = []
height2 = []
northing2 = []
easting2 = []
height3 = []
northing3 = []
easting3 = []
for i in range(len(x_m)):
fi,lam,h = to_polar(x_m[i][0],x_m[i][1],x_m[i][2])
S,Y = to_SagYukarı(fi,lam)
height.append(h)
easting.append(S)
northing.append(Y)
for i in range(len(x_k)):
fi,lam,h = to_polar(x_k[i][0],x_k[i][1],x_k[i][2])
S,Y = to_SagYukarı(fi,lam)
height2.append(h)
easting2.append(S)
northing2.append(Y)
for i in range(len(x_p)):
fi,lam,h = to_polar(x_p[i][0],x_p[i][1],x_p[i][2])
S,Y = to_SagYukarı(fi,lam)
height3.append(h)
easting3.append(S)
northing3.append(Y)
epoch4, easting4, northing4, height4 = grafnav_read("grafnav-brodcastorbitilePPK-chc-rt-ppp-rinex304v2.txt")
graph_E_N(northing,easting,northing2,easting2,northing3,easting3,northing4,easting4,"kalman")
fig = plt.figure()
ax = plt.axes(projection ='3d')
ax.plot3D(northing3,easting3, height3, 'green')
plt.show()
ax.plot3D(northing4,easting4, height4, 'green')
plt.show()