Shez Virani, University of Colorado Boulder; Marcus Holzinger, University of Colorado Boulder
Keywords: Multi-Target, Track-before-detect, LMB, Multi-Bernoulli, Matched Filtering
Abstract:
Key elements in Space Domain Awareness (SDA) are the ability to maintain custody of space objects (SOs) and autonomously search and recover SO tracks. This paper leverages a dynamic data-driven approach to improve real-time detection and tracking methodologies to maintain custody of SOs with ultra-low signal-to-noise ratio (SNR). This is accomplished by combining the computational efficiency of a detect-before-track (DBT) method with the sensitivity of a track-before-detect (TBD) method to allow efficient tracking of SOs in various orbit regimes. The algorithms developed in this paper are implemented and tested on real data of GEO objects collected using wide field-of-view (18.2 degrees) electro-optical sensor.
The first section of the paper discusses image processing techniques used for performing photometric and astrometric calibrations. Before the SOs can be detected and tracked, the raw images need to be processed. First, the dark noise from the sensor is estimated and subtracted from the image to remove any biases in magnitude calculations. Then, background estimation algorithms are used to estimate and remove the local background in the frame. This results in a zero-mean background which is ideal for the DBT methods. Additionally, the data is taken by rate-tracking the GEO objects. Hence, the stars streak during the exposure. A Fast Fourier Transform (FFT) based method is used to extract the centroid locations of the stars. The detected stars are then compared to a star catalog to determine the inertial bearings (right ascension, declination, and orientation) of the center of the frame. The photometric flux of the stars is also used for magnitude calculation of the SOs detected. The stars are then subsequently subtracted from the frame. This process results in a frame that only contains low and high SNR targets with a zero-mean background.
The second section of the paper introduces the overall detection and tracking methodology for efficient tracking of high and low SNR targets. The two types of filters used in this paper are as follows: Labeled Multi-Bernoulli (LMB) filter for tracking high SNR targets and the Track-Before-Detect i.e. Detectionless Multi-Bernoulli (DMB) filter for tracking low SNR targets. Both the LMB and DMB filters, unlike Multiple Hypothesis Tracking (MHT) and Joint Probability Data Association (JPDA), are derived from a random finite set framework. The LMB filter is computationally efficient at tracking high SNR targets when compared to the DMB filter. The DMB filter is based on a bank of particle filters and leverages a matched filtering based approach to track targets with ultra-low SNR. Matched filter templates are generated by constraining the length and orientation based on an admissible region for blind detection. Since the DMB filter is particle based which tends to be computationally intensive, this paper proposes a matched filter based likelihood function to make the filter tractable for real-time applications. This paper uses the DMB filter to only track low SNR targets and LMB filter to only track the high SNR targets.
Once the images are processed, all the SOs above a given SNR threshold are detected. The target centroids as well as their flux are then computed for these high SNR targets. Since these targets have high photometric flux, only their centroids are tracked using the efficient LMB filter. This filter is used to estimate the position and velocity of the targets in the image space as well as the target’s appropriate labels. Additionally, targets with very low photometric flux appear in the images with very low SNR, which makes their detection very challenging. These low SNR objects are simultaneously detected and tracked using the DMB filter.
Some uncontrolled defunct SOs glint as they tumble in space, causing their SNR to vary over time. This may result in some targets to drop below the SNR threshold used for detection. To efficiently track these targets, the targets must be tracked with the LMB filter while the SNR is above the detection threshold and they must be switched to tracking with the DMB filter while they are dim. This paper proposes a new method to switch tracks between LMB and DMB filter to combine the computationally efficiency of LMB with the sensitivity of the DMB filter. This method uses a first order Markov process to model the time-varying photometric flux. Hence, the photometric flux of the tracked SOs are estimated from frame-to-frame and objects are passed between the two filters if their SNR becomes lower or higher than the detection threshold. These algorithms will be implemented and tested on a real dataset of GEO objects using an electro-optical sensor with wide field-of-view. This 2-hour long dataset was taken from Haleakala, Hawaii. Visual inspection shows about 10 visible high-SNR SOs per frame.
To summarize, this paper will include the following novel contributions:
1) A method to detect and track SOs with ultra-low SNR using the Track-Before-Detect Multi-Bernoulli filter,
2) A new matched-filter based likelihood function,
3) Photometric SNR based switching of SO tracks between a Labeled Multi-Bernoulli and Track-Before-Detect Multi-Bernoulli filter,
4) Results of this algorithm implementation on an empirical wide field-of-view dataset of GEO targets.
Date of Conference: September 15-18, 2020
Track: SSA/SDA