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I'm trying to calculate the DOP values for a set of GPS satellites in Python 2.7.2 using numpy 1.9.3.

I found a guide on how to do this but I'm having trouble translating it to python.

Here's what I tried so far:

import numpy as np

# First I defined 3 variables for each satellite as described in the guide.  

sat_1_1 =  np.sin(np.deg2rad(136)) * np.cos(np.deg2rad(14))
sat_1_2 =  np.cos(np.deg2rad(136)) * np.cos(np.deg2rad(14))
sat_1_3 =  np.sin(np.deg2rad(14))

sat_2_1 = np.sin(np.deg2rad(329)) * np.cos(np.deg2rad(48))
sat_2_2 = np.cos(np.deg2rad(329)) * np.cos(np.deg2rad(48))
sat_2_3 = np.sin(np.deg2rad(48))

sat_3_1 = np.sin(np.deg2rad(253)) * np.cos(np.deg2rad(36))
sat_3_2 = np.cos(np.deg2rad(253)) * np.cos(np.deg2rad(36))
sat_3_3 = np.sin(np.deg2rad(36))

sat_4_1 = np.sin(np.deg2rad(188)) * np.cos(np.deg2rad(9))
sat_4_2 = np.cos(np.deg2rad(188)) * np.cos(np.deg2rad(9))
sat_4_3 = np.sin(np.deg2rad(9)) 

# Next I created the line-of-sight matrix: 

LOS_Matrix = np.array([[sat_1_1, sat_1_2, sat_1_3, 1.0], [sat_2_1, sat_2_2, sat_2_3, 1.0], [sat_3_1, sat_3_2, sat_3_3, 1.0], [sat_4_1, sat_4_2, sat_4_3, 1.0]])

# Then its transpose:

LOS_Matrix_t = LOS_Matrix.transpose()

# Next the guide says to compute the covariance matrix which is said to be equal to the inverse of LOS_Matrix * LOS_Matrix_t, so:

cov_matrix = np.linalg.inv(LOS_Matrix * LOS_Matrix_t)

# This should now lets me calculate the DOP values such as GDOP, PDOP, etc

PDOP = np.sqrt(cov_matrix[0, 0] + cov_matrix[1, 1] + cov_matrix[2, 2])

# This comes out as 2.25575033021 which is possbile though it seems suspiciously low

# Also TDOP can't be computed since cov_matrix[3, 3] is a negative number so something must be wrong I guess?

I'm a python noob and math isn't my strong suit either, I only got this far by googling error message after error message.

I'm now at a point it runs without any error message but it doesn't seem correct either, otherwise the TDOP value should be computable for example .

Does anyone have an idea where the issue lies?

Cheers

Sutta
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2 Answers2

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cov_matrix = np.linalg.inv(LOS_Matrix * LOS_Matrix_t)

Should probably be

cov_matrix = np.linalg.inv(LOS_Matrix.dot(LOS_Matrix_t))

I know I know, it's confusing. But in numpy you have two different types, one is the ndarray which you should use and another is matrix which your should not use. For ndarray multiplication defaults to element-wise multiplication.

iliar
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    Thanks! That's confusing indeed. I tried it out and the values seem more reasonable now. I'll test it with a bunch of different azimuts and elevations later to see if it all makes sense. – Sutta Nov 22 '19 at 16:16
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If you take more than 4 sats you would see that the cov matrix needs to be build like:

cov_matrix = np.linalg.inv(LOS_Matrix_t.dot(LOS_Matrix))

to always obtain a 4x4.

mketelhut
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