RADAR

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Description

The RADAR (Radio Detection and Ranging) is a Sensor that detects objects by simulating radio wave transmission and reflection. It calculates received signal power using the radar equation, compares it against thermal noise to determine signal-to-noise ratio, and reports detection when the SNR exceeds a configurable threshold.

The sensor automatically adds the orbited celestial body (and the Moon for Earth-orbiting spacecraft) as default targets on initialization.

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Example Use Cases

• Proximity Detection: Detect nearby spacecraft or debris during rendezvous operations.
• Altimetry: Measure distance to planetary surfaces for landing or orbital analysis.
• Target Tracking: Monitor distance to tracked objects within the sensor’s field of view.

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Module Implementation

The RADAR sensor calculates signal strength using the monostatic radar equation and determines detection based on signal-to-noise ratio.

Radar Equation

The received power from a target is calculated using the monostatic radar equation:

$$P_r=\frac{P_t{G}^2{\lambda }^2\sigma }{(4\pi {)}^3{R}^4}$$

where $P_t$ is the transmit power, $G$ is the antenna gain (linear scale), $\lambda$ is the wavelength, $\sigma$ is the radar cross-section, and $R$ is the distance to the target surface.

The antenna gain is converted from decibels to linear scale:

$$G=10^{G_{\text{dB}}/10}$$

Radar Cross-Section

For spherical targets, the radar cross-section is approximated as the geometric cross-section:

$$\sigma =\pi {\left(\frac{d}{2}\right)}^2$$

where $d$ is the target diameter. If the target’s angular size exceeds the field of view, the effective cross-section is scaled by the visible fraction.

Thermal Noise

The system thermal noise power is:

$$N=k_{B}TB$$

where $k_B$ is Boltzmann’s constant, $T$ is the system temperature, and $B$ is the receiver bandwidth.

Signal-to-Noise Ratio

The signal-to-noise ratio is computed from the total received signal power and noise:

$$\text{SNR}=10{\log }_{10}\left(\frac{P_{\text{total}}}{N}\right)\text{ dB}$$

A target is considered detected when the SNR exceeds the detection threshold.

Distance Measurement

The reported distance corresponds to the strongest detected target, with optional noise applied as a fraction of the true distance:

$$R_{\text{measured}}=R_{\text{true}}(1+ϵ)$$

where $ϵ$ is a random value within $\pm$ the configured distance noise fraction.

Field of View

Only targets within the sensor’s conical field of view are considered. A target at direction $\hat{d}$ from the sensor is visible if:

$$\hat{u}\cdot \hat{d}\ge \cos \left(\frac{{\theta }_{\text{FOV}}}{2}\right)$$

where $\hat{u}$ is the sensor’s boresight direction and ${\theta }_{\text{FOV}}$ is the field of view angle.

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Assumptions/Limitations

• Targets must be added to the sensor’s target list; only listed objects are considered for detection.
• Line-of-sight checks are performed against celestial bodies; occluded targets are not detected.
• The radar cross-section uses a spherical approximation based on target diameter.
• Multiple targets within the field of view contribute to total signal; the reported distance is to the strongest return.
• The sensor must be in operational state to capture data.