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GNSS

GNSS measurement models for orbit determination.

Provides measurement functions and noise covariance constructors for GNSS-based (GPS, Galileo, etc.) orbit determination. These are designed to be passed directly to ekf_update or ukf_update as the measurement_fn and R arguments.

Measurement functions extract observable quantities from the full state vector. Noise covariance constructors build the corresponding R matrix from sensor noise parameters.

gnss_measurement_noise(sigma_pos)

Construct measurement noise covariance for position-only GNSS.

Builds a diagonal (3, 3) noise covariance matrix assuming independent, identically distributed position errors.

Parameters:

Name Type Description Default
sigma_pos float

Position measurement standard deviation in the same units as the state vector (typically meters).

 required

Returns:

Type Description
Array

jax.Array: Diagonal noise covariance matrix of shape (3, 3) with sigma_pos**2 on the diagonal.

Examples:

from astrojax.orbit_measurements import gnss_measurement_noise

R = gnss_measurement_noise(10.0)  # 10 m 1-sigma noise
# R = [[100, 0, 0], [0, 100, 0], [0, 0, 100]]

gnss_position_measurement(state)

Extract position from an orbital state vector.

Measurement model for a GNSS receiver that provides position-only observations. Extracts the first three components of the state vector.

Parameters:

Name Type Description Default
state ArrayLike

State vector of shape (n,) where n >= 3. The first three elements are interpreted as position [x, y, z].

 required

Returns:

Type Description
Array

jax.Array: Position vector of shape (3,).

Examples:

import jax.numpy as jnp
from astrojax.orbit_measurements import gnss_position_measurement

state = jnp.array([6878e3, 0.0, 0.0, 0.0, 7612.0, 0.0])
z = gnss_position_measurement(state)  # [6878e3, 0.0, 0.0]

gnss_position_velocity_measurement(state)

Extract position and velocity from an orbital state vector.

Measurement model for a GNSS receiver that provides both position and velocity observations. Extracts the first six components of the state vector.

Parameters:

Name Type Description Default
state ArrayLike

State vector of shape (n,) where n >= 6. The first six elements are interpreted as [x, y, z, vx, vy, vz].

 required

Returns:

Type Description
Array

jax.Array: Position-velocity vector of shape (6,).

Examples:

import jax.numpy as jnp
from astrojax.orbit_measurements import gnss_position_velocity_measurement

state = jnp.array([6878e3, 0.0, 0.0, 0.0, 7612.0, 0.0])
z = gnss_position_velocity_measurement(state)  # full 6-element vector

gnss_position_velocity_noise(sigma_pos, sigma_vel)

Construct measurement noise covariance for position-velocity GNSS.

Builds a diagonal (6, 6) noise covariance matrix assuming independent position and velocity errors.

Parameters:

Name Type Description Default
sigma_pos float

Position measurement standard deviation (typically meters).

 required
sigma_vel float

Velocity measurement standard deviation (typically m/s).

 required

Returns:

Type Description
Array

jax.Array: Diagonal noise covariance matrix of shape (6, 6) with sigma_pos**2 for the first three and sigma_vel**2 for the last three diagonal elements.

Examples:

from astrojax.orbit_measurements import gnss_position_velocity_noise

R = gnss_position_velocity_noise(10.0, 0.1)  # 10 m, 0.1 m/s