dcm2latlon

Convert direction cosine matrix to geodetic latitude and longitude

Syntax

[lat lon] = dcm2latlon(dcm)

[lat lon] = dcm2latlon(dcm,action)

[lat lon] = dcm2latlon(dcm,action,tolerance)

Description

[lat lon] = dcm2latlon(dcm) calculates the geodetic latitude and longitude lat and lon for the direction cosine matrix dcm.

[lat lon] = dcm2latlon(dcm,action) performs an, action, if the direction cosine matrix is invalid, that is, not orthogonal.

[lat lon] = dcm2latlon(dcm,action,tolerance) uses a tolerance level, tolerance, to evaluate if the direction cosine matrix is within tolerance.

Examples

Determine Geodetic Latitude and Longitude from Direction Cosine Matrix

Determine the geodetic latitude and longitude from direction cosine matrix dcm.

dcm = [ 0.3747    0.5997    0.7071; ...
        0.8480   -0.5299         0; ...
        0.3747    0.5997   -0.7071]; 
[lat, lon] = dcm2latlon(dcm)

lat = 
44.9995

lon = 
-122.0005

Determine Geodetic Latitude and Longitude with Multiple Direction Cosine Matrices

Determine the geodetic latitude and longitude from multiple direction cosine matrices.

dcm = [ 0.3747    0.5997    0.7071; ...
        0.8480   -0.5299         0; ...
        0.3747    0.5997   -0.7071]; 
dcm(:,:,2) = [-0.0531    0.6064    0.7934; ...
               0.9962    0.0872         0; ...
              -0.0691    0.7903   -0.6088]; 
[lat, lon] = dcm2latlon(dcm)

lat = 2×1

   44.9995
   37.5028

lon = 2×1

 -122.0005
  -84.9975

Determine Geodetic Latitude and Longitude from Direction Cosine Matrix Within Tolerance

Determine the geodetic latitude and longitude from the direction cosine matrix dcm within tolerance.

dcm = [ 0.3747    0.5997    0.7071; ...
        0.8480   -0.5299         0; ...
        0.3747    0.5997   -0.7071]; 
[lat, lon] = dcm2latlon(dcm,'Warning',0.1)

lat = 
44.9995

lon = 
-122.0005

Input Arguments

dcm — Direction cosine matrix

3-by-3-by-M matrix

Direction cosine matrix, specified as a 3-by-3-by-M containing M orthogonal direction cosine matrices. dcm performs the coordinate transformation of a vector in Earth-centered Earth-fixed (ECEF) axes into a vector in North-East-down (NED) axes.

Data Types: double

action — Function behavior

'None' (default) | 'Error' | 'Warning'

Function behavior when direction cosine matrix is invalid, that is not orthogonal.

• 'Warning' — Displays warning and indicates that the direction cosine matrix is invalid.

• 'Error' — Displays error and indicates that the direction cosine matrix is invalid.

• 'None' — Does not display warning or error.

Data Types: char | string

tolerance — Tolerance

eps(2) (4.4409e-16) (default) | scalar

Tolerance of direction cosine matrix validity, specified as a scalar. The function considers the direction cosine matrix valid if these conditions are true:

• The transpose of the direction cosine matrix times itself equals 1 within the specified tolerance (transpose(dcm)*dcm == 1±tolerance).

• The determinant of the direction cosine matrix equals 1 within the specified tolerance (det(dcm) == 1±tolerance).

Data Types: double

Output Arguments

lat — Geodetic latitude

M array

Geodetic latitude, returned as an M array in degrees.

lon — Geodetic longitude

M array

Geodetic longitude, returned as a M array in degrees.

Version History

Introduced in R2006b