API

Angles

High-level computation of incidence, look, squint, and other angles from sensor trajectories.

Attributes

all `module-attribute`

Python

__all__ = ['compute_incidence_angles', 'compute_look_angles']

Classes

Functions:

compute_incidence_angles

Python

compute_incidence_angles(trajectory: Trajectory, azimuth_time: PreciseDateTime | datetime64, range_times: float | NDArray[floating], look_direction: SensorLookDirection, geodetic_altitude: float | None = None, doppler_frequencies: float | NDArray[floating] | None = None, carrier_wavelength: float | None = None, *, radians: bool = True) -> float | npt.NDArray[np.floating]

Compute incidence angles in radians/degrees from sensor trajectory.

Parameters:

Name	Type	Description	Default
`trajectory`	`Trajectory`	sensor trajectory	required
`azimuth_time`	`PreciseDateTime \| datetime64`	azimuth time at which compute the incidence angles corresponding to the input range times	required
`range_times`	`float \| NDArray[floating]`	range times where to compute the incidence angles, a float or a (N,) array	required
`look_direction`	`SensorLookDirection`	sensor looking side where to perform geocoding, "RIGHT" or "LEFT"	required
`geodetic_altitude`	`float \| None`	the altitude over wgs84, if None is set to 0, by default None	`None`
`doppler_frequencies`	`float \| NDArray[floating] \| None`	frequency_doppler_centroid value or set of values, one for each range time, if None is set to 0, by default None	`None`
`carrier_wavelength`	`float \| None`	carrier signal wavelength, if None is set to 1, by default None	`None`
`radians`	`bool`	output angles are expressed in radians if this flag is set to True (default), if False are expressed in degrees	`True`

Returns:

Type	Description
`float \| NDArray[floating]`	incidence angles in radians/degrees corresponding to the input range times at the given azimuth time

compute_look_angles

Python

compute_look_angles(trajectory: Trajectory, azimuth_time: PreciseDateTime | datetime64, range_times: float | NDArray[floating], look_direction: SensorLookDirection, geodetic_altitude: float | None = None, doppler_frequencies: float | NDArray[floating] | None = None, carrier_wavelength: float | None = None, *, radians: bool = True) -> float | npt.NDArray[np.floating]

Compute look angles in radians/degrees from sensor trajectory.

Parameters:

Name	Type	Description	Default
`trajectory`	`Trajectory`	sensor trajectory	required
`azimuth_time`	`PreciseDateTime \| datetime64`	azimuth time at which compute the look a angles corresponding to the input range times	required
`range_times`	`float \| NDArray[floating]`	range times where to compute the look angles, a float or a (N,) array	required
`look_direction`	`SensorLookDirection`	sensor looking side where to perform geocoding, "RIGHT" or "LEFT"	required
`geodetic_altitude`	`float \| None`	the altitude over wgs84, if None is set to 0, by default None,	`None`
`doppler_frequencies`	`float \| NDArray[floating] \| None`	doppler frequencies values, if None is set to 0, by default None	`None`
`carrier_wavelength`	`float \| None`	carrier signal wavelength, if None is set to 1, by default None	`None`
`radians`	`bool`	output angles are expressed in radians if this flag is set to True (default), if False are expressed in degrees	`True`

Returns:

Type	Description
`float \| NDArray[floating]`	look angles in radians/degrees corresponding to the input range times at the given azimuth time

Doppler

Computation of Doppler-related quantities.

Classes

Functions:

doppler_equation

Python

doppler_equation(wavelength: float, pv_scalar: float | NDArray[floating], distance: float | NDArray[floating], doppler_frequency: float | NDArray[floating], sensor_velocity: NDArray[floating], los: NDArray[floating]) -> tuple[float | npt.NDArray[np.floating], npt.NDArray[np.floating]]

Doppler equation solver.

Parameters:

Name	Type	Description	Default
`wavelength`	`float`	carrier signal wavelength	required
`pv_scalar`	`(float \| NDArray[floating],)`	scalar product between sensor velocity and line of sight scalar or shape (N,)	required
`distance`	`float`	ground point - sensor position distance scalar or shape (N,)	required
`doppler_frequency`	`float`	doppler frequency scalar or shape (N,)	required
`sensor_velocity`	`NDArray[floating]`	sensor velocity (3,) or shape (N, 3)	required
`los`	`NDArray[floating]`	ground point - sensor position (3,) or shape (N, 3)	required

Returns:

Type	Description
`float \| NDArray[floating]`	doppler equation solution scalar or shape (N,)
`NDArray[floating]`	doppler equation gradient (3,) or shape (N, 3)

doppler_equation_monostatic_residuals

Python

doppler_equation_monostatic_residuals(ground_point: NDArray[floating], sensor_positions: NDArray[floating], sensor_velocities: NDArray[floating], doppler_frequency: float, wavelength: float) -> float | npt.NDArray[np.floating]

Evaluate SAR doppler equation residual, assuming monostatic approximation.

Doppler Equation

\[ f_{doppler} = \\frac{2}{\\lambda} \\frac{v_{sensor} \\cdot LOS}{\\|LOS\\|} \]

Doppler Equation Residual

\[ residual = \\frac{2}{\\lambda} \\frac{v_{sensor} \\cdot LOS}{\\|LOS\\|} - f_{doppler} \]

where LOS is defined as the line of sight, a.k.a. the position difference between the ground point and the sensor positions.

Parameters:

Name	Type	Description	Default
`ground_point`	`NDArray[floating]`	ground point in ECEF coordinates, with shape (3,)	required
`sensor_positions`	`NDArray[floating]`	sensor positions, with shape (3,) or (N, 3)	required
`sensor_velocities`	`NDArray[floating]`	sensor velocities, with shape (3,) or (N, 3)	required
`doppler_frequency`	`float`	frequency doppler centroid in Hz	required
`wavelength`	`float`	signal carrier wavelength in meters	required

Returns:

Type	Description
`float \| NDArray[floating]`	doppler equation residual (Hz) for each input sensor position, scalar or (N,)

doppler_equation_bistatic_residuals

Python

doppler_equation_bistatic_residuals(sensor_pos_rx: NDArray[floating], sensor_pos_tx: NDArray[floating], sensor_vel_rx: NDArray[floating], sensor_vel_tx: NDArray[floating], ground_points: NDArray[floating], wavelength: float, doppler_frequency: float) -> float | npt.NDArray[np.floating]

Evaluate doppler equation residual for bistatic sensors.

Parameters:

Name	Type	Description	Default
`sensor_pos_rx`	`NDArray[floating]`	sensor rx position, (3,) or (N, 3)	required
`sensor_pos_tx`	`NDArray[floating]`	sensor tx position, (3,) or (N, 3)	required
`sensor_vel_rx`	`NDArray[floating]`	sensor rx velocity, (3,) or (N, 3)	required
`sensor_vel_tx`	`NDArray[floating]`	sensor tx velocity, (3,) or (N, 3)	required
`ground_points`	`NDArray[floating]`	ground points from direct geocoding solution, (3,) or (N, 3)	required
`wavelength`	`float`	carrier signal wavelength in meters	required
`doppler_frequency`	`float`	doppler frequency in Hz	required

Returns:

Type	Description
`float \| NDArray[floating]`	doppler equation residual, scalar or (N,)

get_geometric_doppler_centroid

Python

get_geometric_doppler_centroid(sensor_positions: NDArray[floating], sensor_velocities: NDArray[floating], ground_points: NDArray[floating], wavelength: float) -> float

Compute doppler centroid (geometrically) from squint angle.

Parameters:

Name	Type	Description	Default
`sensor_positions`	`NDArray[floating]`	sensor positions array, in the form (3,) or (N, 3)	required
`sensor_velocities`	`NDArray[floating]`	sensor velocities array, in the form (3,) or (N, 3)	required
`ground_points`	`NDArray[floating]`	ground points array, in the form (3,) or (N, 3)	required
`wavelength`	`int`	carrier signal wavelength in meters	required

Returns:

Type	Description
`float \| NDArray[floating]`	doppler centroid in Hz, scalar or with shape (N,)

compute_theoretical_doppler_rate

Python

compute_theoretical_doppler_rate(trajectory: Trajectory, azimuth_time: PreciseDateTime | datetime64, ground_points: NDArray[floating], carrier_frequency: float) -> float | npt.NDArray[np.floating]

Compute theoretical doppler rate.

Parameters:

Name	Type	Description	Default
`trajectory`	`Trajectory`	sensor trajectory	required
`azimuth_time`	`PreciseDateTime \| datetime64`	azimuth time when to evaluate the doppler rate	required
`ground_points`	`NDArray[floating]`	ground point coordinates, with shape (3,) or (N, 3)	required
`carrier_frequency`	`float`	signal carrier frequency in Hz	required

Returns:

Type	Description
`float \| NDArray[floating]`	theoretical doppler rate in Hz/s, scalar or with shape (N,) if multiple ground points are provided

compute_steering_doppler_frequency

Python

compute_steering_doppler_frequency(trajectory: Trajectory, azimuth_time: PreciseDateTime | datetime64, az_mid_burst_time: PreciseDateTime | datetime64, doppler_rate: float, az_steering_rate: float, carrier_frequency: float) -> float

Compute doppler frequency related to the antenna electrical steering.

Parameters:

Name	Type	Description	Default
`trajectory`	`Trajectory`	sensor trajectory	required
`azimuth_time`	`PreciseDateTime \| datetime64`	azimuth time at which compute the steering frequency	required
`az_mid_burst_time`	`PreciseDateTime \| datetime64`	azimuth mid burst time	required
`doppler_rate`	`float`	sensor doppler rate in Hz/s	required
`az_steering_rate`	`float`	azimuth steering rate in rad/s	required
`carrier_frequency`	`float`	signal carrier frequency	required

Returns:

Type	Description
`float`	steering doppler frequency in Hz

Velocities

Computation of sensor velocity quantities.

Attributes

all `module-attribute`

Python

__all__ = ['compute_ground_velocity']

Classes

Functions:

compute_ground_velocity

Python

compute_ground_velocity(trajectory: Trajectory, azimuth_time: PreciseDateTime | datetime64, look_angles_rad: NDArray[floating], reference_frame: ReferenceFrame = 'ZERODOPPLER', geodetic_altitude: float = 0, averaging_interval_relative_origin: float = 0, averaging_interval_duration: float = 1, averaging_interval_num_points: int = 11) -> npt.NDArray[np.floating] | float

Numerical computation of the ground velocity [m/s] at given look angles.

The algorithm is based on the direct geocoding, via look angles, of points at different azimuth times in a averaging interval.

Parameters:

Name	Type	Description	Default
`trajectory`	`Trajectory`	sensor trajectory	required
`azimuth_time`	`PreciseDateTime \| datetime64`	azimuth time at which compute the ground velocity	required
`look_angles_rad`	`NDArray[floating]`	look angles in radians, float or array with shape (N,)	required
`reference_frame`	`('GEOCENTRIC', 'GEODETIC', 'ZERODOPPLER')`	the reference frames in which the look angles are intended, by default "ZERODOPPLER"	`'ZERODOPPLER'`
`geodetic_altitude`	`float`	altitude of the points over wgs84, by default 0	`0`
`averaging_interval_relative_origin`	`float`	averaging interval starts at time_point + averaging_interval_relative_origin, by default 0	`0`
`averaging_interval_duration`	`float`	total duration of the averaging interval, by default 1.0	`1`
`averaging_interval_num_points`	`int`	number of time points in the averaging interval, by default 11	`11`

Returns:

Type	Description
`NDArray[floating] \| float`	ground velocity in m/s

API

Angles

Attributes

__all__ module-attribute

Classes

Functions:

compute_incidence_angles

compute_look_angles

Doppler

Classes

Functions:

doppler_equation

doppler_equation_monostatic_residuals

doppler_equation_bistatic_residuals

get_geometric_doppler_centroid

compute_theoretical_doppler_rate

compute_steering_doppler_frequency

Velocities

Attributes

__all__ module-attribute

Classes

Functions:

compute_ground_velocity

all `module-attribute`

all `module-attribute`