ahrs2 0.1.6

Attitude and heading reference system
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254

# http://www.juddzone.com/ALGORITHMS/least_squares_3D_ellipsoid.html

# https://matplotlib.org/stable/gallery/mplot3d/scatter3d.html#sphx-glr-gallery-mplot3d-scatter3d-py
import matplotlib.pyplot as plt
import numpy as np

points = [
   (0.3051851, -0.27564317, -0.5238197),
   (0.30909148, -0.2745445, -0.52699363),
   (0.36146122, -0.49586475, -0.02783288),
   (0.37647635, -0.46534625, -0.01147496),
   (0.34119692, -0.24683371, -0.5134434),
   (0.3150731, -0.2684408, -0.52833647),
   (0.3706168, -0.16016114, -0.0020752586),
   (0.35145116, -0.23218483, 0.03747673),
   (0.20032349, -0.3177587, -0.53566086),
   (0.20288706, -0.30494094, -0.5294351),
   (0.4471572, -0.21460617, -0.038575396),
   (0.3842891, -0.4954985, -0.35389262),
   (0.3075045, -0.4043092, -0.48365733),
   (0.26953948, -0.3737907, -0.50917083),
   (0.40101323, -0.44373912, -0.050294504),
   (0.37549976, -0.44312876, 0.0026856288),
   (0.3239845, -0.156621, -0.47181615),
   (0.37769708, -0.5294351, -0.28955963),
   (0.40174565, -0.529313, -0.22669148),
   (0.3399762, -0.044312876, -0.311655),
   (0.38380077, -0.049806207, -0.29224524),
   (0.37073886, -0.054200873, -0.16797388),
   (0.35804316, -0.509415, -0.052125614),
   (0.34632406, -0.52577287, -0.07238991),
   (0.32044435, -0.09424116, -0.41871396),
   (0.37537766, -0.105838194, -0.065309614),
   (0.4080935, -0.4034547, 0.003418073),
   (0.31336406, -0.440199, -0.46107364),
   (0.2989593, -0.18909268, -0.5055086),
   (0.039185766, -0.09778131, -0.26172674),
   (0.07751702, -0.059327982, -0.25049594),
   (0.20166631, -0.38575396, -0.5089267),
   (0.16443373, -0.08130131, -0.084109016),
   (0.11670278, -0.529313, -0.21179846),
   (0.4491104, -0.47328106, -0.11243019),
   (0.45338297, -0.4721824, -0.11035493),
   (0.3521836, -0.51564074, -0.11316264),
   (0.31299785, -0.054933317, -0.110965304),
   (0.3150731, -0.2684408, -0.52833647),
   (0.30909148, -0.2745445, -0.52699363),
   (0.20166631, -0.38575396, -0.5089267),
   (0.34815517, -0.40382093, -0.4730369),
   (0.39515367, -0.36805323, -0.4710837),
   (0.39649647, -0.3573107, -0.46632284),
   (0.24292734, -0.38550982, -0.5069735),
   (0.4326304, -0.50379956, -0.20435195),
   (0.30225533, -0.34717858, -0.50428784),
   (0.24744408, -0.34583575, -0.52577287),
   (0.18787195, -0.04504532, -0.2031312),
   (0.30225533, -0.319834, -0.532487),
   (0.37867367, -0.54628134, -0.30286568),
   (0.45594653, -0.49061555, -0.33472702),
   (0.39857173, -0.3668325, -0.003540147),
   (0.4080935, -0.4034547, 0.003418073),
   (0.4804834, -0.45765558, -0.1513718),
   (0.3856319, -0.37354657, -0.47401348),
   (0.41724905, -0.45216224, -0.06860561),
   (0.3075045, -0.4043092, -0.48365733),
   (0.36597797, -0.07373272, -0.09668264),
   (0.32044435, -0.09424116, -0.41871396),
   (0.35743278, -0.29456466, 0.045777764),
   (0.34632406, -0.52577287, -0.07238991),
   (0.28247932, -0.33582568, -0.53456223),
   (0.5215003, -0.29126865, -0.29493088),
   (0.38380077, -0.049806207, -0.29224524),
   (0.38868374, -0.46961883, -0.07483139),
   (0.2924894, -0.36414686, -0.5100253),
   (0.33179724, -0.35804316, -0.49940488),
   (0.13183996, -0.36414686, -0.50843835),
   (0.35145116, -0.23218483, 0.03747673),
   (0.18860438, -0.34644613, -0.52955717),
   (0.19678335, -0.33118686, -0.5252846),
   (0.44605854, -0.38026062, -0.4340953),
   (0.34119692, -0.24683371, -0.5134434),
   (0.27869502, -0.56776637, -0.3408307),
   (0.27503282, -0.32520524, -0.52919096),
   (0.07751702, -0.059327982, -0.25049594),
   (0.043092135, -0.18018128, -0.08899198),
]


x_offset = 0.123
y_offset = 0.071
z_offset = -0.180

for point in points:
   with_cal = np.array([point[0] - x_offset, point[1] - y_offset, point[2] - z_offset])
   mag = np.linalg.norm(with_cal)
   print(f"Mag: {mag}")


def ls_ellipsoid(xx,yy,zz):

   # change xx from vector of length N to Nx1 matrix so we can use hstack
   x = xx[:,np.newaxis]
   y = yy[:,np.newaxis]
   z = zz[:,np.newaxis]

   #  Ax^2 + By^2 + Cz^2 +  Dxy +  Exz +  Fyz +  Gx +  Hy +  Iz = 1
   J = np.hstack((x*x,y*y,z*z,x*y,x*z,y*z, x, y, z))
   K = np.ones_like(x) #column of ones

   # print(J.shape, "J SHAPE")

   # print("\n\nJ: ", J);

   # print("K", K)

   #np.hstack performs a loop over all samples and creates
   #a row in J for each x,y,z sample:
   # J[ix,0] = x[ix]*x[ix]
   # J[ix,1] = y[ix]*y[ix]
   # etc.

   JT=J.transpose()
   JTJ = np.dot(JT,J)
   InvJTJ=np.linalg.inv(JTJ);
   ABC= np.dot(InvJTJ, np.dot(JT,K))

   # Rearrange, move the 1 to the other side
   #  Ax^2 + By^2 + Cz^2 +  Dxy +  Exz +  Fyz +  Gx +  Hy +  Iz - 1 = 0
   #    or
   #  Ax^2 + By^2 + Cz^2 +  Dxy +  Exz +  Fyz +  Gx +  Hy +  Iz + J = 0
   #  where J = -1
   eansa=np.append(ABC,-1)

   return eansa


def polyToParams3D(vec):

   # convert the polynomial form of the 3D-ellipsoid to parameters
   # center, axes, and transformation matrix
   # vec is the vector whose elements are the polynomial
   # coefficients A..J
   # returns (center, axes, rotation matrix)

   #Algebraic form: X.T * Amat * X --> polynomial form

   print('\npolynomial\n',vec)

   Amat=np.array(
      [
         [ vec[0],     vec[3]/2.0, vec[4]/2.0, vec[6]/2.0 ],
         [ vec[3]/2.0, vec[1],     vec[5]/2.0, vec[7]/2.0 ],
         [ vec[4]/2.0, vec[5]/2.0, vec[2],     vec[8]/2.0 ],
         [ vec[6]/2.0, vec[7]/2.0, vec[8]/2.0, vec[9]     ]
      ])

   print('\nAlgebraic form of polynomial\n',Amat)

   #See B.Bartoni, Preprint SMU-HEP-10-14 Multi-dimensional Ellipsoidal Fitting
   # equation 20 for the following method for finding the center
   A3=Amat[0:3,0:3]
   A3inv=np.linalg.inv(A3)
   ofs=vec[6:9]/2.0
   center=-np.dot(A3inv,ofs)

   # Center the ellipsoid at the origin
   Tofs=np.eye(4)
   Tofs[3,0:3]=center
   R = np.dot(Tofs,np.dot(Amat,Tofs.T))
   print ('\nAlgebraic form translated to center\n',R,'\n')

   R3=R[0:3,0:3]
   R3test=R3/R3[0,0]
   print('normed \n',R3test)

   s1=-R[3, 3]
   R3S=R3/s1
   (el,ec)=np.linalg.eig(R3S)

   recip=1.0/np.abs(el)
   axes=np.sqrt(recip)

   print('\nAxes are\n',axes  ,'\n')

   inve=np.linalg.inv(ec) #inverse is actually the transpose here

   return (center,axes,inve)


   # Rearrange, move the 1 to the other side
   #  Ax^2 + By^2 + Cz^2 +  Dxy +  Exz +  Fyz +  Gx +  Hy +  Iz - 1 = 0
   #    or
   #  Ax^2 + By^2 + Cz^2 +  Dxy +  Exz +  Fyz +  Gx +  Hy +  Iz + J = 0
   #  where J = -1
   eansa=np.append(ABC,-1)

   return (eansa)


xx = np.array([pt[0] for pt in points])
yy = np.array([pt[1] for pt in points])
zz = np.array([pt[2] for pt in points])

poly_pts = ls_ellipsoid(xx, yy, zz)

(center, axes, R) = polyToParams3D(poly_pts)

L = np.diag([1/axes[0],1/axes[1],1/axes[2]])
M=np.dot(R.T,np.dot(L,R))

print('\nHard iron\n',center)

print('\nSoft iron\n',M)



# This script plots magnetometer data, for visualizing offsets and
# calibration


fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.set_title("Magnetometer readings, during a calibration maneuver.")
ax.set_xlabel('Mag X')
ax.set_ylabel('Mag Y')
ax.set_zlabel('Mag Z')

# C+P from println console from device as list of (x, y, z) tuples,
# eg (1., 0., 0.)

# ax.set_aspect('equal')

for x, y, z in points:
   ax.scatter(x, y, z)

plt.show()

fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.set_title("Magnetometer readings, with calibration applied.")
ax.set_xlabel('Mag X')
ax.set_ylabel('Mag Y')
ax.set_zlabel('Mag Z')


for x, y, z in points:
   # apply cal
   pts_cal = M @ (np.array([x, y, z]) - center)

   ax.scatter(pts_cal[0], pts_cal[1], pts_cal[2])

plt.show()