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kalmanSimulated.py
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kalmanSimulated.py
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#!/usr/bin/python
import time
import os
from numpy import *
from kalmanFuncs import *
# This file has a simulated input into the Kalman filter in either the 7 or 13 state implementation
# Currently, the angular rates can only be constant
# Estimate the 9 sensor biases (13) or 3 biases (7)
numberStates = 7
# Environmental constants
g = 9.81
hloc = array([[0.225],[-0.057],[-0.4378]])
# Sensor noise constants
hnoise = array([0.01,0.01,0.01])
anoise = array([0.01,0.01,0.01])
# Process noise constants
hnoisep = array([0.001,0.001,0.001])
anoisep = array([0.001,0.001,0.001])
gnoisep = array([0.01,0.01,0.01])
wnoise = 0.02
# Simulation constants
t = 0.0
filterFreq = 50.0 #hz
dt = 1.0 / filterFreq
outputFreq = 1.0 #hz
counter = filterFreq / outputFreq
e1dot = 0.05
e2dot = 0.03
e3dot = 0.02
if numberStates == 7:
hnoisep *= 0
anoisep *= 0
# Simulation Noise & Bias
hnoises = array([0.01,0.01,0.01])
anoises = array([0.01,0.01,0.01])
gnoises = array([0.01,0.01,0.01])
hbiass = array([0.01,0.01,0.01])
abiass = array([0.01,0.01,0.01])
gbiass = array([0.05,0.05,0.05])
# Initial Conditions
X = array([[1],[0],[0],[0],[0],[0],[0],[0],[0],[0],[0],[0],[0]])
P = diag([0,0,0,0,0,0,0,0,0,0,0,0,0])
uu = array([[e1dot],[e2dot],[e3dot],[0],[0],[0],[0],[0],[0]])
# Main filter Loop
while (True):
# Time update
t += dt
counter -= 1
Q = Qmat(X,dt,wnoise,gnoisep,anoisep,hnoisep)
A = Amat(X,uu,g,dt)
X = Afunc(X,uu,g,dt)
P = dot(dot(A,P),A.T) + Q
H = Hmat(X,hloc,g)
R = Rnmat(hnoise,anoise)
K = dot(dot(P, H.T), linalg.inv(dot(dot(H, P), H.T) + R))
YH = Hfunc(X,g,hloc)
# Measurement generation
e1 = arctan(tan(e1dot * t / 2.)) * 2
e2 = arctan(tan(e2dot * t / 2.)) * 2
e3 = arctan(tan(e3dot * t / 2.)) * 2
q0 = cos(e1/2)*cos(e2/2)*cos(e3/2)+sin(e1/2)*sin(e2/2)*sin(e3/2)
q1 = sin(e1/2)*cos(e2/2)*cos(e3/2)-cos(e1/2)*sin(e2/2)*sin(e3/2)
q2 = cos(e1/2)*sin(e2/2)*cos(e3/2)+sin(e1/2)*cos(e2/2)*sin(e3/2)
q3 = cos(e1/2)*cos(e2/2)*sin(e3/2)-sin(e1/2)*sin(e2/2)*cos(e3/2)
w1 = e1dot * cos(e2) * cos(e3) + e2dot * sin(e3)
w2 = - e1dot * cos(e2) * sin(e3) + e2dot * cos(e3)
w3 = e1dot * sin(e2) + e3dot
# euler angle determination of rotation matrix - seems to require a negative sign on calculation of angles from estimated quaternion?
# Tbi = array([[cos(e2)*cos(e3),-cos(e2)*sin(e3),sin(e2)],[sin(e1)*sin(e2)*cos(e3)+sin(e3)*cos(e3),-sin(e1)*sin(e2)*sin(e3)+cos(e3)*cos(e1),-sin(e1)*cos(e2)],[-cos(e1)*sin(e2)*cos(e3)+sin(e3)*sin(e1),cos(e1)*sin(e2)*sin(e3)+cos(e3)*sin(e1),cos(e1)*cos(e2)]])
# quaternion determination of rotation matrix
Tbi = array([[1-2*(q2**2+q3**2),2*(q1*q2+q0*q3),2*(q1*q3-q0*q2)],[2*(q1*q2-q0*q3),1-2*(q1**2+q3**2),2*(q2*q3+q0*q1)],[2*(q1*q3+q0*q2),2*(q2*q3-q0*q1),1-2*(q1**2+q2**2)]])
acc = array([Tbi[0][2]*g,Tbi[1][2]*g,Tbi[2][2]*g])
acc[0] += random.normal(abiass[0],anoises[0])
acc[1] += random.normal(abiass[1],anoises[1])
acc[2] += random.normal(abiass[2],anoises[2])
gyro = array([w1,w2,w3])
gyro[0] += random.normal(gbiass[0],gnoises[0])
gyro[1] += random.normal(gbiass[1],gnoises[1])
gyro[2] += random.normal(gbiass[2],gnoises[2])
mag = dot(Tbi,hloc)
mag[0] += random.normal(hbiass[0],hnoises[0])
mag[1] += random.normal(hbiass[1],hnoises[1])
mag[2] += random.normal(hbiass[2],hnoises[2])
Y = array([[mag[0,0]],[mag[1,0]],[mag[2,0]],[acc[0]],[acc[1]],[acc[2]]])
uu = array([[gyro[0]],[gyro[1]],[gyro[2]],[acc[0]],[acc[1]],[acc[2]],[mag[0]],[mag[1]],[mag[2]]])
# Measurement update
X = X + dot(K,(Y-YH))
P = dot((identity(13)-dot(K,H)),P)
# Output generation
if counter == 0:
counter = filterFreq/outputFreq
Eq0 = X[0][0]
Eq1 = X[1][0]
Eq2 = X[2][0]
Eq3 = X[3][0]
Ewpb= X[4][0]
Ewqb= X[5][0]
Ewrb= X[6][0]
Eaxb= X[7][0]
Eayb= X[8][0]
Eazb= X[9][0]
Ehxb= X[10][0]
Ehyb= X[11][0]
Ehzb= X[12][0]
Ee1 = arctan2(2*(Eq0*Eq1+Eq2*Eq3),1-2*(Eq1**2+Eq2**2))
Ee2 = arcsin(2*(Eq0*Eq2-Eq3*Eq1))
Ee3 = arctan2(2*(Eq0*Eq3+Eq1*Eq2),1-2*(Eq2**2+Eq3**2))
os.system("clear")
print 'time - ',t
print 'meas, calc, error'
set_printoptions(precision = 4, linewidth = 120, suppress = True)
print(Y.T)
print(YH.T)
print(Y.T-YH.T)
print 'Euler angles'
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ee1*180/pi,e1*180/pi,Ee1*180/pi-e1*180/pi)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ee2*180/pi,e2*180/pi,Ee2*180/pi-e2*180/pi)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ee3*180/pi,e3*180/pi,Ee3*180/pi-e3*180/pi)
print sqrt(Eq0**2+Eq1**2+Eq2**2+Eq3**2)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eq0,q0,Eq0-q0)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eq1,q1,Eq1-q1)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eq2,q2,Eq2-q2)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eq3,q3,Eq3-q3)
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ewpb,gbiass[0],Ewpb-gbiass[0])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ewqb,gbiass[1],Ewqb-gbiass[1])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ewrb,gbiass[2],Ewrb-gbiass[2])
if numberStates == 7:
continue
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eaxb,abiass[0],Eaxb-abiass[0])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eayb,abiass[1],Eayb-abiass[1])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Eazb,abiass[2],Eazb-abiass[2])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ehxb,hbiass[0],Ehxb-hbiass[0])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ehyb,hbiass[1],Ehyb-hbiass[1])
print 'est %.4f \t\t real %.4f \t\t error %.4f' % (Ehzb,hbiass[2],Ehzb-hbiass[2])