# Accuracy Analysis algorithm

Algorithm:

def calc_accuracy(tag,
anch_a,
anch_b,
anch_s,
sig_c):
"""
This function calculates the DRMS(Distance Root Mean Square) value of
position.
"""

# Given coordinates
# T = np.zeros((1,3), dtype=float)
tag_x = tag[0]
tag_y = tag[1]
tag_z = tag[2]
tmp_tag = np.array(tag)

# A = np.zeros((1,3), dtype=float)
a_x = anch_a[0]
a_y = anch_a[1]
# a_z = anch_a[2]     # UNUSED
tmp_anch_a = np.array(anch_a)

# B = np.zeros((1,3), dtype=float)
b_x = anch_b[0]
b_y = anch_b[1]
# b_z = anch_b[2]     # UNUSED
tmp_anch_b = np.array(anch_b)

# S = np.zeros((1,3), dtype=float)
s_x = anch_s[0]
s_y = anch_s[1]
s_z = anch_s[2]
tmp_anch_s = np.array(anch_s)

# see eq.(3), eq.(4) and eq.(5) in document "Annex_II_2D_Positioning"

# see eq.(1) in document "Annex_II_2D_Positioning"

# see eq.(7) in document "Annex_IV_Accuracy Analysis"
matrix_h = np.zeros((2, 2), dtype=float)
matrix_h[0][0] = float(2*(a_x-s_x))
matrix_h[0][1] = float(2*(a_y-s_y))
matrix_h[1][0] = float(2*(b_x-s_x))
matrix_h[1][1] = float(2*(b_y-s_y))

# rank of the H matrix is ??controlled
if matrix_rank(matrix_h) < 2:
drms = float("inf")
else:
# see eq.(8) in document "Annex_IV_Accuracy Analysis"
# K is pseudo inverse of matrix H
matrix_k = np.zeros((2, 2), dtype=float)

# K = ( H.transpose() * H ) \ ( H.transpose() )
matrix_k = LA.pinv(matrix_h)

k11 = matrix_k[0][0]
k12 = matrix_k[0][1]
k21 = matrix_k[1][0]
k22 = matrix_k[1][1]

# print("k11: " + str(k11))
# print("k12: " + str(k12))
# print("k21: " + str(k21))
# print("k22: " + str(k22))

anch_s = np.array([s_x, s_y, s_z])

# initial condition and threshold value for loop
sig_r = 0
flag = 1
thr = 0.5

while flag == 1:
# see eq.(20) in document "Annex_IV_Accuracy Analysis"
x11 = 4*pow(das, 2)*pow(sig_r, 2) + \

x12 = 4*das*dbs*pow(sig_r, 2) + 4*das*radius_s*sig_r*sig_c + \

x21 = x12

x22 = 4*pow(dbs, 2)*pow(sig_r, 2) + 8*dbs*(radius_s+dbs)*sig_r*sig_c + \

# see eq.(24), eq.(25) and eq(26) in document "Annex_IV_Accuracy Analysis"
# sig_x = sqrt(pow(k11, 2)*x11 + 2*k11*k12*x12 + pow(k12, 2)*x22)
# sig_y = sqrt(pow(k21, 2)*x11 + 2*k21*k22*x12 + pow(k22, 2)*x22)

try:
sig_x = sqrt(pow(k11, 2)*x11 + 2*k11*k12*x12 + pow(k12, 2)*x22)
except ValueError: # as err:
print "Gx ValueError"
return -1

try:
sig_y = sqrt(pow(k21, 2)*x11 + 2*k21*k22*x12 + pow(k22, 2)*x22)
except ValueError: # as err:
print "Gy ValueError"
return -1

sig_x_sig_y = (k11*x11+k12*x21)*k21 + (k11*x12+k12*x22)*k22

# see Step 9 in iterative solution in document "Annex_IV_Accuracy Analysis"
if sig_x_sig_y >= 0:
p_2 = np.array([tag_x + sig_x/2, tag_y + sig_y/2, tag_z])
p_1 = np.array([tag_x - sig_x/2, tag_y - sig_y/2, tag_z])
else:
p_2 = np.array([tag_x - sig_x/2, tag_y + sig_y/2, tag_z])
p_1 = np.array([tag_x ...
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1

So... what's your question?

( 2019-12-10 07:11:41 -0600 )edit

I want to know the detailed Accuracy Analysis algorithm derivation because I want to do 3D calculations.Do you have relevant information? Greatful

( 2019-12-10 07:28:34 -0600 )edit
2

Please edit your question and add more context. I have no idea what you are talking about.

( 2019-12-10 07:31:26 -0600 )edit

I am doing research on indoor positioning of objects. The method of selecting an appropriate anchor point with reference to GPS positioning, that is, calculating the minimum PDOP (Position Dilution of Precision)value. The code of this calculation process is what I show. But I don't understand the loop of this program. can you help me？

( 2019-12-10 07:38:33 -0600 )edit

sig_c is Standard deviation of distance measurement about TDOA

( 2019-12-10 07:42:36 -0600 )edit