Michael Schneider

Kerianne Pruett, Nathan McNaughton, Michael Schneider

Accurately detecting rendezvous and proximity operations (RPO) is crucial for understanding how objects are behaving in the space domain. However, detecting closely-spaced objects (CSO) is challenging for ground-based optical space domain awareness (SDA) algorithms as two objects close together along the line-of-sight can appear blended as a single object within the point-spread function (PSF) of the optical system. Traditional machine learning methods can be useful for differentiating between singular objects and closely-spaced objects, but many methods require large training sample sizes or high signal-to-noise conditions. The quality and quantity of realistic data make probabilistic classification methods a superior approach, as they are better suited to handle these data inadequacies. We present CSO classification results using the Gaussian process python package, MuyGPyS, and examine classification accuracy as a function of angular separation and magnitude difference between the simulated satellites. This orbit-independent analysis is done on highly accurate simulated SDA images that emulate realistic ground-based commercial-of-the-shelf (COTS) optical sensor observations of CSOs. We find that MuyGPyS outperforms traditional machine learning methods, especially under more challenging circumstances.

Amanda Muyskens, Benjamin Priest, Imène Goumiri et al.

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, naïve GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the likelihood function. These bottlenecks have driven much investment in the development of approximate GP alternatives that scale to the large data sizes common in modern data-driven applications. We present in this manuscript MuyGPs, a novel efficient GP hyperparameter estimation method. MuyGPs builds upon prior methods that take advantage of the nearest neighbors structure of the data, and uses leave-one-out cross-validation to optimize covariance (kernel) hyperparameters without realizing a possibly expensive likelihood. We describe our model and methods in detail, and compare our implementations against the state-of-the-art competitors in a benchmark spatial statistics problem. We show that our method outperforms all known competitors both in terms of time-to-solution and the root mean squared error of the predictions.

Felix Fontein, Michael Schneider, Urs Wagner

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in practice but the running time seems to explode. Weaker variants of DeepLLL, where the insertions are restricted to blocks, behave nicely in practice concerning the running time. However no proof of polynomial running time is known. In this paper PotLLL, a new variant of DeepLLL with provably polynomial running time, is presented. We compare the practical behavior of the new algorithm to classical LLL, BKZ as well as blockwise variants of DeepLLL regarding both the output quality and running time.