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Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying themore » technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.« less

Evidence of the $$K^+\to\mu^+\nu\bar\nu\nu$$ decay was searched for using E949 experimental data with an exposure of $$1.70\times 10^{12}$$ stopped kaons. The data sample is dominated by the backgrond process $$K^+\to\mu^+\nu_\mu\gamma$$. An upper limit on the decay rate $$\Gamma(K^+\to\mu^+\nu\bar\nu\nu)< 2.4\times 10^{-6}\Gamma(K^+\to all)$$ at 90% confidence level was set assuming the Standard Model muon spectrum. The data are presented in such a way as to allow calculation of rates for any assumed $$\mu^+$$ spectrum.