Orbit Measurements¶

The astrojax.orbit_measurements module provides measurement functions and noise covariance constructors for orbit determination sensors. These are designed to plug directly into the estimation filters from astrojax.estimation.

Purpose¶

In state estimation, a measurement function h(x) maps the full state vector to an observable quantity (e.g., extracting position from a position-velocity state). A measurement noise covariance R describes the sensor's uncertainty. Together, they define how a filter incorporates sensor data.

This module provides both components for common orbit determination sensors so you can pass them directly to ekf_update or ukf_update.

Available Models¶

GNSS¶

Function	Description
`gnss_position_measurement`	Extracts position `[x, y, z]` from the state vector
`gnss_measurement_noise`	Builds a `(3, 3)` diagonal noise covariance from a position sigma
`gnss_position_velocity_measurement`	Extracts position and velocity `[x, y, z, vx, vy, vz]` from the state vector
`gnss_position_velocity_noise`	Builds a `(6, 6)` diagonal noise covariance from position and velocity sigmas

Usage¶

Position-Only GNSS¶

import jax.numpy as jnp
from astrojax.orbit_measurements import (
    gnss_position_measurement,
    gnss_measurement_noise,
)
from astrojax.estimation import FilterState, ekf_update

# Build the noise covariance: 10 m 1-sigma position noise
R = gnss_measurement_noise(10.0)  # (3, 3) diagonal, 100 on diagonal

# Simulated noisy position observation
z = jnp.array([6878e3 + 5.0, 3.0, -2.0])

# Update a filter state with the observation
state = FilterState(
    x=jnp.array([6878e3, 0.0, 0.0, 0.0, 7612.0, 0.0]),
    P=jnp.diag(jnp.array([1e6, 1e6, 1e6, 1e2, 1e2, 1e2])),
)
result = ekf_update(state, z, gnss_position_measurement, R)

Position-Velocity GNSS¶

from astrojax.orbit_measurements import (
    gnss_position_velocity_measurement,
    gnss_position_velocity_noise,
)

# 10 m position noise, 0.1 m/s velocity noise
R_pv = gnss_position_velocity_noise(10.0, 0.1)  # (6, 6) diagonal

z_pv = jnp.array([6878e3 + 5.0, 3.0, -2.0, 0.01, 7612.0 + 0.05, -0.01])
result = ekf_update(state, z_pv, gnss_position_velocity_measurement, R_pv)

Custom Measurement Functions¶

You can write your own measurement functions following the same pattern: a pure function h(x) -> z that maps a state vector to an observation vector.

def range_measurement(state):
    """Range from the origin to the spacecraft."""
    r = state[:3]
    return jnp.array([jnp.linalg.norm(r)])

R_range = jnp.array([[25.0]])  # 5 m 1-sigma range noise
result = ekf_update(state, z_range, range_measurement, R_range)

The EKF will compute the measurement Jacobian automatically via jax.jacfwd. The UKF evaluates the function at sigma points, so no Jacobian is needed. See the Estimation user guide for full filter usage patterns.

Configurable precision

All measurement functions and noise constructors respect astrojax.set_dtype(). Call set_dtype() before JIT compilation to control float32 vs float64 precision.