ADCS.estimators.initialization module

Quantities a warm start needs, read straight off a measurement vector.

vector_observations() turns the attitude sensors’ readings into pairs of unit directions, one in the body frame and one in the inertial frame, each with an angular standard deviation, ready for attitude_determination. Single-axis sensors (magnetometers, sun sensors, sun pairs) are combined into one direction per kind by weighted least squares; vector sensors (Earth horizon, star tracker) are taken as they are. angular_rate_from_readings() does the same for the gyros, and wheel_momentum_from_readings() collects the reaction wheel readings.

class ADCS.estimators.initialization.VectorObservation(kind, body, reference, sigma, sources)

Bases: object

One direction seen in the body frame and known in the inertial frame.

Parameters:

• kind (str) – What was observed ("magnetic_field", "sun", "nadir", "star").

• body (ndarray) – Unit direction in the body frame.

• reference (ndarray) – Unit direction in the inertial frame.

• sigma (float) – Angular standard deviation of body in radians, the same in every direction perpendicular to it.

• sources (tuple[str, ...]) – Names of the measurement-stack entries that produced it.

body: ndarray

kind: str

reference: ndarray

sigma: float

sources: tuple[str, ...]

class ADCS.estimators.initialization.WarmStart(method='auto', rate='gyro', wheel_momentum='readings', act_bias=None, sens_bias=None, dist_param=None, attitude_std=None, rate_std=None, wheel_momentum_std=None, act_bias_std=None, sens_bias_std=None, dist_param_std=None, process_noise=None, star_references=None, max_attitude_std=3.141592653589793)

Bases: object

How to build an estimator’s initial state from its first readings.

Pass an instance in place of the state of any attitude estimator, or to from_readings(). The attitude is solved from the direction observations (see attitude_from_readings()), the angular rate is read off the gyros assuming zero bias, and the wheel momenta off the wheels. Biases and disturbance parameters start at zero unless given. Every *_std is an initial standard deviation, a single number or one per element; the attitude, rate and wheel-momentum ones default to what the sensors’ noise implies, the bias and disturbance ones must be given whenever the satellite estimates such parameters, and a value you supply yourself (a rate, wheel momenta) needs its standard deviation too.

Parameters:

• method (str) – "auto" (a quaternion star tracker when one has a reading, otherwise QUEST), "quest", "triad" (the two most precise directions) or "tracker".

• rate (Any) – "gyro" or the initial angular rate in rad/s.

• wheel_momentum (Any) – "readings" or the initial wheel momenta.

• act_bias (Any) – Initial actuator biases (default zeros).

• sens_bias (Any) – Initial sensor biases (default zeros).

• dist_param (Any) – Initial disturbance parameters (default zeros).

• attitude_std (Any) – Attitude standard deviation in rad, per body axis; default from the observations.

• rate_std (Any) – Rate standard deviation in rad/s; default from the gyro noise.

• wheel_momentum_std (Any) – Wheel-momentum standard deviation; default from the wheels’ momentum-measurement noise.

• act_bias_std (Any) – Actuator-bias standard deviations.

• sens_bias_std (Any) – Sensor-bias standard deviations.

• dist_param_std (Any) – Disturbance-parameter standard deviations.

• process_noise (Any) – The per-step process covariance the filter adds (int_cov), in the filter’s covariance coordinates; default zeros.

• star_references (Mapping[Any, Any] | None) – Inertial directions for vector star trackers, see vector_observations().

• max_attitude_std (float) – Cap, in rad, for an attitude axis the observations barely determine (nearly parallel directions); the default, pi, means “unknown” and leaves the filter’s first corrections to settle it.

act_bias: Any = None

act_bias_std: Any = None

attitude_std: Any = None

dist_param: Any = None

dist_param_std: Any = None

max_attitude_std: float = 3.141592653589793

method: str = 'auto'

process_noise: Any = None

rate: Any = 'gyro'

rate_std: Any = None

sens_bias: Any = None

sens_bias_std: Any = None

star_references: Mapping[Any, Any] | None = None

wheel_momentum: Any = 'readings'

wheel_momentum_std: Any = None

ADCS.estimators.initialization.angular_rate_from_readings(satellite, readings)

Body angular rate from the gyro readings, assuming zero gyro bias.

Returns:

(rate, covariance) in rad/s and (rad/s)^2, by weighted least squares over the gyros with finite readings.

Raises:

ValueError – when fewer than three non-coplanar gyro axes have readings.

Parameters:

• satellite (Any)

• readings (Any)

ADCS.estimators.initialization.attitude_from_readings(satellite, readings, orbital_state, *, method='auto', star_references=None)

The attitude at the time of one raw measurement vector.

"quest" solves Wahba’s problem over every direction observation (vector_observations()), "triad" uses the two most precise ones, "tracker" takes the reading of a quaternion star tracker, and "auto" takes the tracker when one has a finite reading and QUEST otherwise. The solution’s covariance is the small-angle attitude-error covariance in the body frame, in rad^2.

Raises:

ValueError – when the readings do not determine the attitude (fewer than two usable directions, for example in eclipse with only magnetometers and sun sensors, or parallel directions); the message says to pass the initial attitude explicitly.

Parameters:

• satellite (Any)

• readings (Any)

• orbital_state (Any)

• method (str)

• star_references (Mapping[Any, Any] | None)

Return type:

AttitudeSolution

ADCS.estimators.initialization.initial_state_from_readings(satellite, readings, orbital_state, warm_start=None, *, covariance_coordinates='tangent', quaternion_mode='quaternion_vector')

A complete initial estimator state from one raw measurement vector.

The values come from the readings as the WarmStart recipe says (its defaults: attitude by "auto", rate from the gyros, wheel momenta from the wheels, zero biases and disturbance parameters). The covariance is block diagonal: the attitude solution’s covariance, the gyro least-squares covariance, the wheels’ momentum-measurement noise, and the given bias and disturbance standard deviations. Its attitude block is expressed in the quaternion_mode chart, and for covariance_coordinates="full" (the EKF) the whole matrix is projected onto the four quaternion components.

Parameters:

• satellite (Any) – The EstimatedSatellite the estimator uses.

• readings (Any) – Raw measurement vector, in the measurement stack’s order.

• orbital_state (Any) – Orbital state at the time of the readings.

• warm_start (WarmStart | None) – The recipe; None for the defaults.

• covariance_coordinates (str) – "tangent" (MEKF, UKF, SRUKF) or "full" (EKF).

• quaternion_mode (str) – Chart of the attitude block; the estimator’s quaternion_mode.

Raises:

ValueError – when the readings do not determine the attitude or the rate, or the recipe lacks a required standard deviation.

Return type:

EstimatorState

ADCS.estimators.initialization.vector_observations(satellite, readings, orbital_state, *, star_references=None, lit_threshold_sigmas=3.0, sigma_floor=1e-06)

Direction pairs from the attitude sensors’ readings.

Single-axis sensors of one kind (three magnetometers, a set of sun sensors) are combined by weighted least squares into one direction per kind; at least three non-coplanar axes with finite readings are needed, otherwise that kind is skipped. Sun sensors count only when lit (reading above lit_threshold_sigmas noise standard deviations); in eclipse their readings are NaN and no sun direction results. Vector sensors give one observation each. A vector star tracker needs its star’s inertial direction in star_references (keyed by measurement-stack entry name or sensor index) because the reading does not say which star it saw.

Parameters:

• satellite (Any) – The EstimatedSatellite whose measurement layout the readings follow.

• readings (Any) – Raw measurement vector, in the measurement stack’s order.

• orbital_state (Any) – Orbital state at the time of the readings (reference directions).

• star_references (Mapping[Any, Any] | None) – Inertial unit directions for vector star trackers.

• lit_threshold_sigmas (float) – A sun sensor is lit when its reading exceeds this many noise sigmas.

• sigma_floor (float) – Smallest angular standard deviation reported, in radians; perfect (noise-free) sensors get this value. The default, 1e-6 rad, is well below any real sensor and keeps the weights of a mixed set within what the attitude solvers handle accurately.

Returns:

One VectorObservation per observed direction; possibly empty.

Return type:

list[VectorObservation]

ADCS.estimators.initialization.wheel_momentum_from_readings(satellite, readings)

The reaction-wheel momentum readings, in the satellite’s wheel order.

Parameters:

• satellite (Any)

• readings (Any)

Return type:

ndarray