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Hierarchial Mixture of Experts


Space Situational Awareness (SSA) involves detecting, tracking, identifying and characterizing resident space objects (RSOs). Electro-optical measurements can be used to estimate important characteristics, such as the size, shape, configuration, rotational dynamics (attitude and angular velocity), and surface properties such as specular and diffuse albedo (reflectivity) of a resident space object (RSO). In addition, estimated features can be used to match or discriminate objects or classes of objects and to identify their behavior.

Under a Phase I SBIR contract sponsored by Air Force Research Laboratory (AFRL), Emergent Space Technologies, Inc. teamed with the University of Colorado Boulder and The University of Texas at Austin to investigate the use of the Hierarchical Mixture of Experts (HME) to process electro-optical measurements to determine an RSO’s attitude profile. The holistic approach involved the integration of Finite Set Statistics (FISST) algorithms and advanced numerical integration techniques and GPU parallelization with the HME for a robust method to improve the Air Force’s capability to detect, track, identify, characterize and catalog RSOs. The mathematical background of the HME and the assumptions, test scenarios, and results of processing simulated apparent magnitude and angles data including experiments to tune the HME learning rate parameter in Phase 1 is available found here:

The results show that the HME is capable of identifying and distinguishing between nadir-pointing, sun-pointing, and spinning objects even though none of the experts in the HME is directly estimating attitude. The paper also shows how the learning parameter selection impacts HME performance.


Emergent’s HME Algorithm.A gating networks assign weights to experts with different state dynamics models. Weights are determined using measurement residuals and their corresponding covariance, with higher weights going to experts that better predict the values of incoming measurements. Experts can be grouped into banks based on what characteristic of the dynamics models they vary from the nominal.