ADCS.satellite_hardware.sensors.star_tracker module

class ADCS.satellite_hardware.sensors.star_tracker.StarTracker(sample_time=0.1, bias=None, anisotropic_noise=None, estimate_bias=False, boresight=array([0., 0., 1.]), fov=np.float64(0.06981317007977318), sun_exclusion=np.float64(0.4363323129985824), star_catalog=None)[source]

Bases: Sensor

Star tracker direction sensor model.

This class implements a simplified but estimator-consistent star tracker that provides a vector observation corresponding to the line-of-sight (LOS) from the spacecraft to a selected navigation star, expressed in the spacecraft body frame.

Unlike a full star tracker attitude solution, this model returns a single unit vector measurement, making it suitable for tightly coupled state estimation frameworks such as EKF or UKF.

The class conforms to the generic sensor interface defined by Sensor.

Measurement model

Let

Symbol

Description

\(\mathbf{q}\)

Attitude quaternion (body → inertial)

\(\mathbf{s}_{\mathrm{ECI}}\)

Inertial-frame unit vector to a star

\(\mathbf{C}(\mathbf{q})\)

Rotation matrix (body → inertial)

The clean (ideal) star tracker measurement is

\[\mathbf{y}_{\text{clean}} = \mathbf{C}(\mathbf{q})^\top \mathbf{s}_{\mathrm{ECI}} \in \mathbb{R}^3,\]

which represents the star direction expressed in the body frame.

Including bias and noise, the full measurement is

\[\tilde{\mathbf{y}} = \mathbf{y}_{\text{clean}} + \mathbf{b} + \mathbf{n},\]

where:

  • \(\mathbf{b}\) is an optional additive bias modeled by Bias

  • \(\mathbf{n}\) is anisotropic noise modeled by AnisotropicNoise

After corruption, the measurement is renormalized to enforce a unit-vector constraint:

\[\tilde{\mathbf{y}} \leftarrow \frac{\tilde{\mathbf{y}}}{\lVert \tilde{\mathbf{y}} \rVert}.\]

Star selection

At each measurement epoch, the sensor:

  1. Projects the sensor boresight into the inertial frame

  2. Queries the StarCatalog for visible stars

  3. Applies field-of-view and exclusion constraints (Sun, optional Moon)

  4. Selects the brightest visible star (minimum visual magnitude)

If no valid star is available, the sensor output is NaN.

Estimator properties

  • Output dimension: 3

  • Depends only on attitude quaternion

  • Jacobian is nonzero only w.r.t. quaternion states

  • No coupling to angular velocity or momentum states

See also

StarCatalog, NavigationStar, Sensor

basestate_jac(x, os)[source]

Jacobian of the star tracker measurement with respect to the base state.

The measurement depends only on the attitude quaternion. Therefore,

\[\frac{\partial \mathbf{y}}{\partial \boldsymbol{\omega}} = \mathbf{0}, \qquad \frac{\partial \mathbf{y}}{\partial \mathbf{q}} = D_{\mathbf{q}} \left( \mathbf{C}(\mathbf{q})^\top \mathbf{s}_{\mathrm{ECI}} \right).\]

The quaternion derivative is computed using drotmatTvecdq().

Parameters:

  • x (numpy.ndarray) – Full spacecraft state vector.

  • os (Orbital_State) – Orbital state.

Returns:

Base-state Jacobian stacked as [ω; q], shape (7, 3).

Return type:

numpy.ndarray

bias_jac(x, os)[source]

Jacobian of the measurement with respect to bias states.

The star tracker bias is not included in the estimator state for this model, so the bias Jacobian is empty.

Parameters:

  • x (numpy.ndarray) – Full spacecraft state vector (unused).

  • os (Orbital_State) – Orbital state object (unused).

Returns:

Empty bias Jacobian of shape (0, 3).

Return type:

numpy.ndarray

clean_reading(x, os)[source]

Compute the noise-free, bias-free star tracker measurement.

The attitude quaternion is extracted from the state vector as

\[\mathbf{q} = x_{3:7},\]

and the measurement is computed as

\[\mathbf{y}_{\text{clean}} = \mathbf{C}(\mathbf{q})^\top \mathbf{s}_{\mathrm{ECI}}.\]
Parameters:

  • x (numpy.ndarray) – Full spacecraft state vector.

  • os (Orbital_State) – Orbital state used for star visibility determination.

Returns:

Unit vector pointing toward the selected navigation star in the body frame, or NaN if no star is visible.

Return type:

numpy.ndarray

reading(x, os, dmode=None)[source]

Compute the full star tracker measurement including bias and noise.

Bias and noise are applied using reading(), after which the output is renormalized to enforce a unit-vector constraint.

Parameters:

  • x (numpy.ndarray) – Full spacecraft state vector.

  • os (Orbital_State) – Orbital state.

  • dmode (ErrorMode or None) – Controls whether bias and noise are applied and propagated.

Returns:

Normalized star direction measurement in the body frame.

Return type:

numpy.ndarray

property noise_covariance: ndarray[tuple[int, ...], dtype[float64]]

Measurement noise covariance matrix.

Returns:

Measurement noise covariance expressed in the spacecraft body frame.

Return type:

numpy.ndarray

output_length: int = 3
Parameters:

  • sample_time (float)

  • bias (Bias)

  • anisotropic_noise (AnisotropicNoise)

  • estimate_bias (bool)

  • boresight (ndarray)

  • fov (float)

  • sun_exclusion (float)

  • star_catalog (StarCatalog | None)