Wrong total error computation by TPPA

[Armando Beneduce]

Hi,

currently TPPA wrongly computes total error:

CurrentMountAxisTotalError = Angle.ByDegree(Accord.Math.Tools.Hypotenuse(InitialMountAxisAltitudeError.Degree, InitialMountAxisAzimuthError.Degree));

If we assume

Ra_id=[0;cos(lat);sin(lat)], Ra_mount=[x;y;z] with norm(Ra_mount)=1 (i.e. x^2+y^2+z^2=1), Az_err= atan(x/y) and Alt_err=atan(z/y)-lat

then

Tot_err=sqrt(Az_err^2+Alt_err^2)

Tot_err=acos<Ra_id,Ra_mount>=acos(cos(lat)y+sin(lat)z)

[Armando Beneduce]

Hi Stefan,
I evaluated how to compute Total alignment error. I'm considering the mount aligned to North Pole (i.e. lat>0) and lat+Alt_err = mountAlt accordingly to TPPA source.

Let's set:
Ra_id=[0;cos(lat);sin(lat)]
Ra_mount=[x;y;z] with norm(Ra_mount)=1 (i.e. x^2+y^2+z^2=1)
Az_err= atan(x/y) and Alt_err=atan(z/y)-lat

I would compute Tot_err as follows:

Tot_err = acos <Ra_id,Ra_mount> = acos(cos(lat)y+sin(lat)z)

If y and z are known then the problem is solved...

If not, we can calculate y and z by lat, alt_err and az_err. We can consider x^2+y^2+z^2=1

x^2/y^2 + 1 +z^2/y^2 = 1/y^2 -> (tan(az_err))^2 + 1 + (tan(lat+lat_err))^2 = 1/y^2

y^2 = sqrt(1/...)
z = y * tan(lat+alt_err)

Tot_err = acos (cos(lat)y+sin(lat)z)

‌

[Armando Beneduce]

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