Proximity Navigation Software

Description

The Proximity Navigation Software fuses laser range finder and boresight bearing measurements to estimate relative position and velocity for proximity operations. It converts spherical sensor measurements to Cartesian coordinates and applies an alpha filter for noise smoothing without the complexity of a full extended Kalman filter. The software is designed for close-range rendezvous and docking scenarios where direct sensor measurements provide the primary navigation solution.

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Example Use Cases

• Rendezvous Operations: Estimate relative state during final approach to a target spacecraft.
• Docking Alignment: Provide real-time position and velocity feedback for docking control systems.
• Proximity Maneuvering: Support station-keeping and inspection operations near a target.

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Module Implementation

Coordinate Conversion

The software converts spherical measurements from the laser range finder and boresight sensor to Cartesian position in the body frame. Given range $r$, azimuth $\theta$, and elevation $\varphi$:

$${\mathbf{r}}_B=\left[\begin{array}{c}r\cos \varphi \cos \theta \\ r\cos \varphi \sin \theta \\ r\sin \varphi \end{array}\right]$$

where the X-axis aligns with the sensor boresight, Y-axis is cross-track, and Z-axis is elevation.

Alpha Filter

An alpha filter smooths the position estimate to reduce measurement noise:

$${\mathbf{r}}_{\text{filtered}}=\alpha \cdot {\mathbf{r}}_{\text{new}}+(1-\alpha )\cdot {\mathbf{r}}_{\text{prev}}$$

where $\alpha$ is the filter coefficient. A value of $\alpha =1$ passes measurements through unfiltered, while lower values provide increased smoothing at the cost of response lag. The default value of 0.3 provides moderate noise reduction.

Velocity Estimation

Relative velocity is computed from the position change between time steps:

$${\mathbf{v}}_B=\frac{{\mathbf{r}}_{\text{current}}-{\mathbf{r}}_{\text{previous}}}{\Delta t}$$

When enabled, the radial velocity component can be replaced with the laser range finder’s direct range rate measurement for improved accuracy:

$${\mathbf{v}}_B=\dot{r}\hat{\mathbf{r}}+{\mathbf{v}}_{\perp }$$

where $\dot{r}$ is the measured range rate, $\hat{\mathbf{r}}$ is the unit vector toward the target, and ${\mathbf{v}}_{\perp }$ is the transverse velocity from position differencing.

Frame Transformation

When attitude information is available, the body-frame estimates are transformed to the LVLH (Local Vertical Local Horizontal) frame for use by guidance algorithms. The transformation uses the navigation attitude to rotate from body to inertial coordinates.

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Assumptions/Limitations

• The software requires valid laser range finder detection to produce outputs; invalid measurements result in no solution.
• The alpha filter introduces lag proportional to the smoothing level; aggressive filtering delays response to target motion.
• Velocity estimation from position differencing amplifies noise; enabling range rate substitution improves radial accuracy.
• The LVLH transformation assumes the body frame is approximately aligned with LVLH during proximity operations.
• The software does not perform full state estimation with covariance tracking; use a navigation filter for higher-fidelity applications.
• Boresight angles default to zero if the boresight sensor message is not connected.