James Helferty, KBR; Jennifer Smith, KBR, Inc; Edgar Ryan, KBR / Pacific Defense Solutions; Manual Thomas, KBR / Pacific Defense Solutions
Keywords: SDA Modeling Track Before Detection Imaging
Abstract:
In a wide area search scenario, a telescope must scan a wide volume of the sky, track known satellites, and identify unexpected and unknown objects. A number of collections on a target area is necessary to help differentiate the star clutter from the moving satellite objects. This also allows for redundancy in the collection to help improve detection performance and remove false alarms with a track before detect strategy.
The satellites are point sources and their intensity can be modeled using a common Visual Magnitude equation that models the satellite as a sphere. This visual magnitude equation depends on the slant range, reflectance of the satellite, CATS angle and cross section area. The intensity of the signal from the satellite in Watts/m^2 can be calculated from the satellite Visual magnitude assuming the reflected energy follows the solar spectrum. This is the intensity immediately before the aperture. The signal at the detector is calculated from converting the watts to photons using the photon energy formula. The signal in electrons is this intensity times the transmission, aperture area, integration time, quantum efficiency, and MTF attenuation (ensquared energy factor).
This signal in electrons is divided by noise to get SNR for detection performance. In summary the SNR determines the ability to detect the satellite in a single image and the false alarm performance. With Gaussian statistics on the noise, think of an example detection threshold with an SNR of 5 will lead to an expectation of about 1 false alarm in every megapixel of detector area. In a satellite detection search, it is possible to improve the detection performance by considering multiple images to remove false alarms. In a track before detect system a lower threshold is allowed so that there are more false alarms in a single image and the tracking system will identify the true detection through frame-to-frame correlation and remove many of these false detections. It is possible to model the detection and false alarms probability of the multiple collections assuming a window where correlations are allowed to reduce false alarms. This updated detection logic can be analyzed using binomial distributions. The detection law with multiple images allows for improved detection performance overall with reduced false alarms.
So now we have an overall expression for This detection law will be based on combining the SNR expression based on signal calculations and detection and false alarm statistics based on binomial distractions with considering tracking parameters. This expression will be further verified using simulations of various satellite sizes, reflectance, aperture area, integration times, geometries, tracking strategies.
This expression has value in planning the best collection parameters and balance the number of frames, the integration times and tracking windows to ensure that the search time and is optimized while the detection statistics are achieved.
Date of Conference: September 19-22, 2023
Track: Space Domain Awareness