Rachel Oliver, Cornell University; Brian McReynolds, ETH Zurich; Dmitry Savransky, Cornell University
Keywords: multiple hypothesis tracker, event-based sensor, neuromorphic sensor, data association, hypothesis testing
Abstract:
The process of maintaining awareness in space is growing in complexity. Larger constellations of satellites and collisions in orbit are exponentially increasing the number of objects that need to be tracked so that the domain remains usable. Augmenting the current Space Domain Awareness (SDA) platforms with new technologies that can identify and track resident space objects (RSOs) autonomously is one possibility to improve the SDA process. Event-based sensors are one such technology through their unique change detection capabilities. These sensors are distinct because each of their pixels operate independently and only record binary events. An event is recorded when a pixel reaches a set logarithmic threshold change in photocurrent. The resulting event data is a timestamped list of pixel locations with the positive or negative polarity of photocurrent change. The high dynamic range and temporal sensitivity of the sensors has prompted proof of concept demonstrations with these sensors for SDA. Given the growing database of on-sky collections, we demonstrate a novel method to implement a multiple hypothesis tracker (MHT) based off the statistics and characteristics of the collected data sets. Such an MHT provides online track detection without reassembling traditional frames used in traditional electro-optical recognition and tracking algorithms.
The difficulty in applying the disaggregated data stream for online object tracking is distinguishing binary event signals from satellites, stars, and noise. A single event without context has minimal information to infer where the signal originated. To overcome this drawback other researchers have identified tracks in event-based data with two methods: through reassembly of traditional frames without filtering and by filtering event-data with an assumption of a Poisson distribution of satellite events. We take a different approach to a MHT by extracting spatial, temporal, and event profile characteristics from the data stream to improve the inference of a satellite detection. Based on statistics collected from 30 second duration of a staring Prophesee VGA-CD camera, the probability that a certain cluster of events grouped spatially and temporally belongs to a true satellite track is compared to that of non-satellite detections through a hypothesis test. By rejecting data in this manner, returned hypothesis tracks from the MHT are primarily resemble those of prior satellite detections.
The first step towards our hypothesis testing method is processing data to serve as prior knowledge about the detection probability and its corresponding characteristics. It is impractical to assign events, on the orders of thousands per data set, individually to the categories of satellite, star, noise, and hot pixel. Starting with a density-based clustering algorithm and the spatial coordinates, clusters are chosen with a maximum distance and minimum number of points within that radius. This method reliably groups well-spaced data. However, many data sets include tracks that the human eye can identify that have a larger Euclidean distance between portions of the track than an adjacent track. Slightly better results are achieved by incorporating the timestamp with either a three-dimensional density clustering algorithm or an algorithm that clusters the events in the order that they were recorded. While the latter does the best at delineating between nearby tracks, it is computationally more expensive. Additionally, even though the methods including the timestamp are generally more effective, they are not perfect because some adjacent tracks are close in both time and space. In these cases, choosing a conservative threshold to maintain unique clusters for distinct tracks results in multiple clusters for a single track. By applying a Hough transformation, the clusters that are most likely on the same track because they are colinear are combined. Following the clustering algorithms, we manually assign track labels as positive satellite identifications to generate the prior information. This assignment of labels is on the order of a couple satellite tracks instead of thousands due to the clustering.
The next step in our MHT development is examination of different attributes within the clustered data to develop a hypothesis test that will better delineate between the true and false positives. It is not immediately evident that events associated with each pixel or track has a stronger correlation to the track classification, so we investigate both possibilities. The correlation of variables such as the average time between events on a pixel and the distance between the next pixel on the track justifies removing redundant information. We also analyze which variables provide the greatest separation between satellite and other detections for improved data association. Taking these variable attributes into regard, we choose a test statistic for a hypothesis test at both the pixel and track level and create discrete probability distributions for use in the MHT.
Finally, we implement and evaluate multiple MHT configurations. First, prior to data inclusion in a global hypothesis list of all possible track configurations, the aforementioned hypothesis test is applied until the data association with a satellite detection is strong enough. This measurement rejection reduces the amount of data considered in the hypothesis list reducing complexity in the hypothesis evaluation. Alternatively, the track hypothesis list considers all the incoming events and applies the test statistic as part of the track evaluation. Besides these unique filters, standard MHT practices to limit the hypothesis list such as applying a Euclidean gate to the incoming events are also applied. We examine the computational time and resulting sensitivity and specificity of each MHT configuration as a basis for which will best support online satellite track identification.
The statistical response of the event-based camera changes due to differences in the operational setup, sensing environment, and a specific camera’s response to certain settings. Therefore, anyone applying this method will require our outlined steps to create their own probability distributions and test statistic unique to their SDA sensing situation. By utilizing the resulting open-source code for data processing and the MHT, the SDA community can conveniently augment their current capabilities with an event-based sensor.
Date of Conference: September 27-20, 2022
Track: Optical Systems & Instrumentation