Laser Range Finder

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Description

The Laser Range Finder is a sensor that measures the distance to a target using a laser beam. It operates on the time-of-flight principle and provides range measurements with an accuracy that depends on both a fixed error component and a proportional error component, following the standard mm + ppm model used in surveying instruments. The sensor also computes range-rate (velocity) from successive measurements.

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Example Use Cases

• Proximity Operations: Measure range to a target spacecraft during rendezvous and docking.
• Terrain Sensing: Determine altitude above planetary surfaces for landing or mapping missions.
• Formation Flying: Monitor inter-satellite distances in formation flight scenarios.

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Module Implementation

Range Measurement

The sensor measures range to the nearest valid target within its field of view and operating range. A target is valid when:

1. The target is within the sensor’s field of view
2. The target is within the maximum operating range $R_{\text{max}}$
3. Line of sight to the target is not occluded

The measured range represents the distance from the sensor to the target surface, computed as the distance to the target center minus half the target diameter.

Accuracy Model

Range accuracy follows the standard mm + ppm specification common in laser ranging instruments. The one-sigma accuracy ${\sigma }_R$ is computed as:

$${\sigma }_R=C+P\cdot R$$

where:

• $C$ is the fixed accuracy constant [m]
• $P$ is the proportional accuracy coefficient [dimensionless]
• $R$ is the true range [m]

A proportional coefficient of $1\times 10^{-6}$ corresponds to 1 ppm (1 mm per km of range).

Calibration Model

When a calibration error model is attached, the measured range differs from the true range due to scale and bias errors. The raw measurement is computed as:

$$R_{\text{raw}}=R_{\text{true}}\cdot S_{\text{cal}}+B_{\text{cal}}$$

where $S_{\text{cal}}$ is the calibration scale factor and $B_{\text{cal}}$ is the calibration bias.

If user-applied corrections are configured in the error model, the final measured range is:

$$R_{\text{measured}}=\frac{R_{\text{raw}}-B_{\text{corr}}}{S_{\text{corr}}}$$

where $S_{\text{corr}}$ and $B_{\text{corr}}$ are the correction scale and bias applied by the operator.

Velocity Computation

Range-rate is computed from successive measured range samples using finite differencing:

$$\dot{R}=\frac{R_{\text{current}}-R_{\text{previous}}}{\Delta t}$$

where $\Delta t$ is the time elapsed between samples. The velocity output reflects the calibration-affected measured range, not the true range.

Sampling

The sensor supports both automatic and manual capture modes. When automatic capture is enabled, the sensor takes measurements at intervals defined by the sample rate. A sample rate of zero captures every simulation tick.

Default Targets

On initialization, the sensor automatically registers the orbited celestial body as a target. For spacecraft orbiting Earth, the Moon is also added as a default target.

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Assumptions/Limitations

• The sensor measures range to the nearest valid target only; multiple simultaneous targets are not reported.
• Range is computed to the target surface assuming a spherical target with the specified diameter.
• The accuracy model is one-sigma; actual measurements do not include random noise unless additional error models are attached.
• Field of view is modeled as a circular cone; rectangular or elliptical apertures are not supported.
• Atmospheric effects on laser propagation are not modeled.