Design & Development of an Optimized Sensor Scheduling & Tasking Program for Tracking Space Objects

The Industrial Sciences Group (ISG) and SERC (Research Programme 3) collaborated on the development/analysis of mathematical models and software, to perform sensor scheduling and tasking for a network of sensors over a 12-hour schedule. The program optimizes sensor utilization by producing sensor-object assignments that maximize the information gain - that is, the reduction in object covariances - for each assignment window throughout the schedule. The success of this project required a multi-disciplinary team with expertise in astrodynamics, statistics, information theory and software engineering.

The program takes in a catalog of Earth-orbiting satellites, with initial state vectors and covariances, and a set of active and passive optical sensors across Australia. Each object is simulated over a 12-hour period to determine visible passes that may be tracked by each sensor. The program outputs a schedule for each sensor detailing the tracking times of selected objects over the 12-hour period.

Objects are propagated forward using an unscented Kalman filter, allowing for a range of propagators to be used at different stages throughout the program, depending on requirements. For example, when propagating objects for the purpose of calculating information gain, program run-time takes precedence over accuracy, so a simpler analytical propagator can be used (e.g. SGP4). Similarly, when propagating objects forward in real-time, calculating the position of objects, accuracy is of more importance and a more accurate propagator can be utilized (e.g. numerical propagators).

Object selection is made using Rényi divergence as an Information Gain criterion, comparing the potential reduction in each object's covariance during an object's visible pass. Multiple observations from each sensor are simulated over a configurable assignment window, which is then passed into an unscented Kalman filter to compute the new covariance that would result if a sensor was tasked to that object. Using Rényi divergence as a measure of information gain, an auction-style algorithm is used to select a single, unique object for each sensor over the assignment window that maximizes the total information gain of the sensor network. Once tasks are executed, actual measurements from sensors can be passed to the unscented Kalman filter to update the object's position in real-time.

The program now accounts for asynchronous assignment windows, computing the cumulative information gain from multiple observations, scaling the information gain for high priority targets, and adding constraints on laser measurements. The program and algorithms were successfully tested by SERC on a catalogue of 20,000 objects with 6 sensors. The assignments will be used by SERC to produce daily schedules for their sensor network. The program can be scaled to maintain pace with the ever-growing number of objects in orbit. Following the implementation of this program, several key practical insights were gained. Firstly, as the program is required to produce results with a real-time deadline, it is important that runtime performance is minimised. This was achieved through various methods, including the translation of the original Python program into C++, the use of run-time analysis and optimization, the implementation of multithreading, and the use of faster propagators at non-critical stages. Secondly, as the program is required to process up to 100 000 objects against multiple sensors, memory utilization is important to consider. This was addressed by identifying generated data that is not used in future calculations, regularly archiving data to files and subsequently deleting that data from memory.

Future developments include applications of methods from industrial statistics to simulation of collision probabilities. This includes the use of optimized sampling schemes known as 'space-filling' designs as an alternative to 'brute force' Monte Carlo approach to simulate a known 'true' probability of collision. Initial results show a significant reduction of up to 50% in the number of Monte Carlo runs required required for convergence. This applied to simulations of both linear and nonlinear collision models. Finally, the methodology used is adaptable and scalable to range of complex multi-sensor/multi-object problems where optimal tasking is required. Additionally, dynamic scheduling could be used to account for changes in weather effecting visibility, and target priorities.