Topocentric Coordinates¶

Functions for working with local topocentric coordinate frames including East-North-Up (ENZ), South-East-Zenith (SEZ), and Azimuth-Elevation-Range.

ENZ (East-North-Up) Frame¶

Rotation Matrices¶

rotation_ellipsoid_to_enz `builtin` ¶

rotation_ellipsoid_to_enz(x_ellipsoid: ndarray, angle_format: AngleFormat) -> Any

Compute rotation matrix from ellipsoidal coordinates to East-North-Up (ENZ) frame.

Calculates the rotation matrix that transforms vectors from an ellipsoidal coordinate frame (geocentric or geodetic) to the local East-North-Up (ENZ) topocentric frame at the specified location.

Parameters:

Name	Type	Description	Default
`x_ellipsoid`	`ndarray`	Ellipsoidal position `[latitude, longitude, altitude/radius]` where latitude is in radians or degrees, longitude is in radians or degrees.	required
`angle_format`	`AngleFormat`	Angle format for input angular coordinates (`RADIANS` or `DEGREES`).	required

Returns:

Type	Description
`ndarray`	3x3 rotation matrix from ellipsoidal frame to `ENZ` frame.

rotation_enz_to_ellipsoid `builtin` ¶

rotation_enz_to_ellipsoid(x_ellipsoid: ndarray, angle_format: AngleFormat) -> Any

Compute rotation matrix from East-North-Up (ENZ) frame to ellipsoidal coordinates.

Calculates the rotation matrix that transforms vectors from the local East-North-Up (ENZ) topocentric frame to an ellipsoidal coordinate frame (geocentric or geodetic) at the specified location.

Parameters:

Name	Type	Description	Default
`x_ellipsoid`	`ndarray`	Ellipsoidal position `[latitude, longitude, altitude/radius]` where latitude is in radians or degrees, longitude is in radians or degrees.	required
`angle_format`	`AngleFormat`	Angle format for input angular coordinates (`RADIANS` or `DEGREES`).	required

Returns:

Type	Description
`ndarray`	3x3 rotation matrix from `ENZ` frame to ellipsoidal frame.

Position Conversions¶

relative_position_ecef_to_enz `builtin` ¶

relative_position_ecef_to_enz(location_ecef: ndarray, r_ecef: ndarray, conversion_type: EllipsoidalConversionType) -> Any

Convert relative position from ECEF to East-North-Up (ENZ) frame.

Transforms a relative position vector from Earth-Centered Earth-Fixed (ECEF) coordinates to the local East-North-Up (ENZ) topocentric frame at the specified location.

Parameters:

Name	Type	Description	Default
`location_ecef`	`ndarray`	Reference location in `ECEF` coordinates `[x, y, z]` in meters.	required
`r_ecef`	`ndarray`	Position vector in `ECEF` coordinates `[x, y, z]` in meters.	required
`conversion_type`	`EllipsoidalConversionType`	Type of ellipsoidal conversion (`GEOCENTRIC` or `GEODETIC`).	required

Returns:

Type	Description
`ndarray`	Relative position in `ENZ` frame `[east, north, up]` in meters.

Example

import brahe as bh
import numpy as np

# Ground station and satellite positions
station_ecef = np.array([4000000.0, 3000000.0, 4000000.0])
sat_ecef = np.array([4100000.0, 3100000.0, 4100000.0])
enz = bh.relative_position_ecef_to_enz(station_ecef, sat_ecef, bh.EllipsoidalConversionType.GEODETIC)
print(f"ENZ: East={enz[0]/1000:.1f}km, North={enz[1]/1000:.1f}km, Up={enz[2]/1000:.1f}km")

relative_position_enz_to_ecef `builtin` ¶

relative_position_enz_to_ecef(location_ecef: ndarray, r_enz: ndarray, conversion_type: EllipsoidalConversionType) -> Any

Convert relative position from East-North-Up (ENZ) frame to ECEF.

Transforms a relative position vector from the local East-North-Up (ENZ) topocentric frame to Earth-Centered Earth-Fixed (ECEF) coordinates at the specified location.

Parameters:

Name	Type	Description	Default
`location_ecef`	`ndarray`	Reference location in `ECEF` coordinates `[x, y, z]` in meters.	required
`r_enz`	`ndarray`	Relative position in `ENZ` frame `[east, north, up]` in meters.	required
`conversion_type`	`EllipsoidalConversionType`	Type of ellipsoidal conversion (`GEOCENTRIC` or `GEODETIC`).	required

Returns:

Type	Description
`ndarray`	Position vector in `ECEF` coordinates `[x, y, z]` in meters.

Example

import brahe as bh
import numpy as np

# Convert ENZ offset back to ECEF
station_ecef = np.array([4000000.0, 3000000.0, 4000000.0])
enz_offset = np.array([50000.0, 30000.0, 100000.0])  # 50km east, 30km north, 100km up
target_ecef = bh.relative_position_enz_to_ecef(station_ecef, enz_offset, bh.EllipsoidalConversionType.GEODETIC)
print(f"Target ECEF: {target_ecef}")

position_enz_to_azel `builtin` ¶

position_enz_to_azel(x_enz: ndarray, angle_format: AngleFormat) -> Any

Convert position from East-North-Up (ENZ) frame to azimuth-elevation-range.

Transforms a position from the local East-North-Up (ENZ) topocentric frame to azimuth-elevation-range spherical coordinates.

Parameters:

Name	Type	Description	Default
`x_enz`	`ndarray`	Position in `ENZ` frame `[east, north, up]` in meters.	required
`angle_format`	`AngleFormat`	Angle format for output angular coordinates (`RADIANS` or `DEGREES`).	required

Returns:

Type	Description
`ndarray`	Azimuth-elevation-range `[azimuth, elevation, range]` where azimuth and elevation are in radians or degrees, and range is in meters.

Example

import brahe as bh
import numpy as np

# Convert ENZ to azimuth-elevation for satellite tracking
enz = np.array([50000.0, 100000.0, 200000.0])  # East, North, Up (meters)
azel = bh.position_enz_to_azel(enz, bh.AngleFormat.DEGREES)
print(f"Az={azel[0]:.1f}°, El={azel[1]:.1f}°, Range={azel[2]/1000:.1f}km")

SEZ (South-East-Zenith) Frame¶

Rotation Matrices¶

rotation_ellipsoid_to_sez `builtin` ¶

rotation_ellipsoid_to_sez(x_ellipsoid: ndarray, angle_format: AngleFormat) -> Any

Compute rotation matrix from ellipsoidal coordinates to South-East-Zenith (SEZ) frame.

Calculates the rotation matrix that transforms vectors from an ellipsoidal coordinate frame (geocentric or geodetic) to the local South-East-Zenith (SEZ) topocentric frame at the specified location.

Parameters:

Name	Type	Description	Default
`x_ellipsoid`	`ndarray`	Ellipsoidal position `[latitude, longitude, altitude/radius]` where latitude is in radians or degrees, longitude is in radians or degrees.	required
`angle_format`	`AngleFormat`	Angle format for input angular coordinates (`RADIANS` or `DEGREES`).	required

Returns:

Type	Description
`ndarray`	3x3 rotation matrix from ellipsoidal frame to `SEZ` frame.

Example

import brahe as bh
import numpy as np

# Get rotation matrix for ground station in SEZ frame
lat, lon, alt = 0.7, -1.5, 100.0  # radians, meters
x_geod = np.array([lat, lon, alt])
R_sez = bh.rotation_ellipsoid_to_sez(x_geod, bh.AngleFormat.RADIANS)
print(f"Rotation matrix shape: {R_sez.shape}")

rotation_sez_to_ellipsoid `builtin` ¶

rotation_sez_to_ellipsoid(x_ellipsoid: ndarray, angle_format: AngleFormat) -> Any

Compute rotation matrix from South-East-Zenith (SEZ) frame to ellipsoidal coordinates.

Calculates the rotation matrix that transforms vectors from the local South-East-Zenith (SEZ) topocentric frame to an ellipsoidal coordinate frame (geocentric or geodetic) at the specified location.

Parameters:

Name	Type	Description	Default
`x_ellipsoid`	`ndarray`	Ellipsoidal position `[latitude, longitude, altitude/radius]` where latitude is in radians or degrees, longitude is in radians or degrees.	required
`angle_format`	`AngleFormat`	Angle format for input angular coordinates (`RADIANS` or `DEGREES`).	required

Returns:

Type	Description
`ndarray`	3x3 rotation matrix from `SEZ` frame to ellipsoidal frame.

Example

import brahe as bh
import numpy as np

# Get inverse rotation matrix from SEZ to ellipsoidal
lat, lon, alt = 0.7, -1.5, 100.0  # radians, meters
x_geod = np.array([lat, lon, alt])
R_ellipsoid = bh.rotation_sez_to_ellipsoid(x_geod, bh.AngleFormat.RADIANS)
print(f"Rotation matrix shape: {R_ellipsoid.shape}")

Position Conversions¶

relative_position_ecef_to_sez `builtin` ¶

relative_position_ecef_to_sez(location_ecef: ndarray, r_ecef: ndarray, conversion_type: EllipsoidalConversionType) -> Any

Convert relative position from ECEF to South-East-Zenith (SEZ) frame.

Transforms a relative position vector from Earth-Centered Earth-Fixed (ECEF) coordinates to the local South-East-Zenith (SEZ) topocentric frame at the specified location.

Parameters:

Name	Type	Description	Default
`location_ecef`	`ndarray`	Reference location in `ECEF` coordinates `[x, y, z]` in meters.	required
`r_ecef`	`ndarray`	Position vector in `ECEF` coordinates `[x, y, z]` in meters.	required
`conversion_type`	`EllipsoidalConversionType`	Type of ellipsoidal conversion (`GEOCENTRIC` or `GEODETIC`).	required

Returns:

Type	Description
`ndarray`	Relative position in `SEZ` frame `[south, east, zenith]` in meters.

Example

import brahe as bh
import numpy as np

# Ground station and satellite positions
station_ecef = np.array([4000000.0, 3000000.0, 4000000.0])
sat_ecef = np.array([4100000.0, 3100000.0, 4100000.0])
sez = bh.relative_position_ecef_to_sez(station_ecef, sat_ecef, bh.EllipsoidalConversionType.GEODETIC)
print(f"SEZ: South={sez[0]/1000:.1f}km, East={sez[1]/1000:.1f}km, Zenith={sez[2]/1000:.1f}km")

relative_position_sez_to_ecef `builtin` ¶

relative_position_sez_to_ecef(location_ecef: ndarray, x_sez: ndarray, conversion_type: EllipsoidalConversionType) -> Any

Convert relative position from South-East-Zenith (SEZ) frame to ECEF.

Transforms a relative position vector from the local South-East-Zenith (SEZ) topocentric frame to Earth-Centered Earth-Fixed (ECEF) coordinates at the specified location.

Parameters:

Name	Type	Description	Default
`location_ecef`	`ndarray`	Reference location in `ECEF` coordinates `[x, y, z]` in meters.	required
`x_sez`	`ndarray`	Relative position in `SEZ` frame `[south, east, zenith]` in meters.	required
`conversion_type`	`EllipsoidalConversionType`	Type of ellipsoidal conversion (`GEOCENTRIC` or `GEODETIC`).	required

Returns:

Type	Description
`ndarray`	Position vector in `ECEF` coordinates `[x, y, z]` in meters.

Example

import brahe as bh
import numpy as np

# Convert SEZ offset back to ECEF
station_ecef = np.array([4000000.0, 3000000.0, 4000000.0])
sez_offset = np.array([30000.0, 50000.0, 100000.0])  # 30km south, 50km east, 100km up
target_ecef = bh.relative_position_sez_to_ecef(station_ecef, sez_offset, bh.EllipsoidalConversionType.GEODETIC)
print(f"Target ECEF: {target_ecef}")

position_sez_to_azel `builtin` ¶

position_sez_to_azel(x_sez: ndarray, angle_format: AngleFormat) -> Any

Convert position from South-East-Zenith (SEZ) frame to azimuth-elevation-range.

Transforms a position from the local South-East-Zenith (SEZ) topocentric frame to azimuth-elevation-range spherical coordinates.

Parameters:

Name	Type	Description	Default
`x_sez`	`ndarray`	Position in `SEZ` frame `[south, east, zenith]` in meters.	required
`angle_format`	`AngleFormat`	Angle format for output angular coordinates (`RADIANS` or `DEGREES`).	required

Returns:

Type	Description
`ndarray`	Azimuth-elevation-range `[azimuth, elevation, range]` where azimuth and elevation are in radians or degrees, and range is in meters.

Example

import brahe as bh
import numpy as np

# Convert SEZ to azimuth-elevation for satellite tracking
sez = np.array([30000.0, 50000.0, 100000.0])  # South, East, Zenith (meters)
azel = bh.position_sez_to_azel(sez, bh.AngleFormat.DEGREES)
print(f"Az={azel[0]:.1f}°, El={azel[1]:.1f}°, Range={azel[2]/1000:.1f}km")

Topocentric Coordinates¶

ENZ (East-North-Up) Frame¶

Rotation Matrices¶

rotation_ellipsoid_to_enz builtin ¶

rotation_enz_to_ellipsoid builtin ¶

Position Conversions¶

relative_position_ecef_to_enz builtin ¶

relative_position_enz_to_ecef builtin ¶

position_enz_to_azel builtin ¶

SEZ (South-East-Zenith) Frame¶

Rotation Matrices¶

rotation_ellipsoid_to_sez builtin ¶

rotation_sez_to_ellipsoid builtin ¶

Position Conversions¶

relative_position_ecef_to_sez builtin ¶

relative_position_sez_to_ecef builtin ¶

position_sez_to_azel builtin ¶

rotation_ellipsoid_to_enz `builtin` ¶

rotation_enz_to_ellipsoid `builtin` ¶

relative_position_ecef_to_enz `builtin` ¶

relative_position_enz_to_ecef `builtin` ¶

position_enz_to_azel `builtin` ¶

rotation_ellipsoid_to_sez `builtin` ¶

rotation_sez_to_ellipsoid `builtin` ¶

relative_position_ecef_to_sez `builtin` ¶

relative_position_sez_to_ecef `builtin` ¶

position_sez_to_azel `builtin` ¶