Geodetic Observation Model

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Description

The Geodetic Observation Model holds the observation state of one Geodetic Object. The Planet Coverage System writes that state from the Remote Sensor components registered on the same planet. It records whether the object is seen on the current step, how long it has been seen, and the best resolution achieved.

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Example Use Cases

• Target Visibility: Track when coverage sensors see a geodetic object, including a moving Vehicle or Aircraft.
• Detection Quality: Record the best resolution achieved while the object is observed.

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Module Implementation

The model is attached to a geodetic object. One model is used for each object. A model added by the user is kept. Otherwise the coverage system creates it when the first sensor is registered, including for objects that already exist. When the last coverage sensor is removed, the model is disabled and the accumulated state is left in place until coverage is cleared.

The model does not test the sensors itself. On each coverage update, the system writes the result of the test below.

Line of Sight

An operational sensor on the object’s planet sees the object when the line of sight falls inside its field of view and the planet does not block that path. The object is sampled at its inertial position, so an aircraft is tested at altitude rather than at the ground point beneath it.

With sensor position ${\mathbf{r}}_s$ and object position ${\mathbf{r}}_t$,

$$\mathbf{d}={\mathbf{r}}_t-{\mathbf{r}}_s,\rho =|\mathbf{d}|,\hat{\mathbf{d}}=\mathbf{d}/\rho$$

The object is inside a circular field of view of full angle ${\theta }_{\mathrm{FOV}}$ when

$$\hat{\mathbf{b}}\cdot \hat{\mathbf{d}}\ge \cos \left(\frac{{\theta }_{\mathrm{FOV}}}{2}\right)$$

where $\hat{\mathbf{b}}$ is the sensor boresight in the inertial frame. A slant range below $1\mathrm{m}$ is ignored.

The planet is treated as a sphere. If the ray hits that sphere a distance $s$ from the sensor, the path is blocked when

$$s<\rho -50\mathrm{km}$$

The margin keeps a surface object from being hidden by the sphere it sits on.

Observation State

Each step starts with the object marked unseen. If at least one sensor sees it, the object is marked seen for that step and the accumulated time increases once:

$$T\leftarrow T+\Delta t$$

Overlapping sensors do not add extra time. The time of that update is stored as the last time the object was seen.

Each seeing sensor also supplies a resolution ${\delta }_k$ in meters. A camera uses ground sample distance. Any other remote sensor uses the field-of-view footprint $\rho {\theta }_{\mathrm{FOV}}$, with ${\theta }_{\mathrm{FOV}}$ in radians. The stored resolution is the smallest positive value seen so far:

$$\delta \leftarrow \min (\delta ,{\delta }_k)$$

A smaller value is a finer resolution. If the object is not seen, the current flag clears and $T$, $\delta$, and the last seen time stay as they are. Clearing coverage sets $T=0$, $\delta =0$, and clears the last seen time. Zero resolution means the object has not been observed.

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Assumptions/Limitations

• The field of view is a circular cone.
• Several sensors that see the object on the same step add one time increment.
• Occultation uses a spherical planet and a $50\mathrm{km}$ margin. Terrain and other bodies are not tested.
• The test uses the object position, including altitude above the surface.
• A resolution of zero means the object has not yet been seen.
• Shut down or faulted sensors, and sensors registered to another planet, are skipped.
• Disabling coverage clears the current seen flag and leaves the accumulated time and resolution unchanged.