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Register a new userMaximum a posteriori estimation through simulated annealing for binary asteroid orbit determination
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This paper considers a new method for the binary asteroid orbit determination problem. The method is based on the Bayesian approach with a global optimisation algorithm. The orbital parameters to be determined are modelled through an a posteriori distribution made of a priori and likelihood terms. The first term constrains the parameters space and it allows the introduction of available knowledge about the orbit. The second term is based on given observations and it allows us to use and compare different observational error models. Once the a posteriori model is built, the estimator of the orbital parameters is computed using a global optimisation procedure: the simulated annealing algorithm. The maximum a posteriori (MAP) techniques are verified using simulated and real data. The obtained results validate the proposed method. The new approach guarantees independence of the initial parameters estimation and theoretical convergence towards the global optimisation solution. It is particularly useful in these situations, whenever a good initial orbit estimation is difficult to get, whenever observations are not well-sampled, and whenever the statistical behaviour of the observational errors cannot be stated Gaussian like.
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Using classical simulated annealing to maximise a function $psi$ defined on a subset of $R^d$, the probability $p(psi(theta_n)leq psi_{max}-epsilon)$ tends to zero at a logarithmic rate as $n$ increases; here $theta_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $psi_{max}$ is the maximal value of $psi$. We propose a modified scheme for which this probability is of order $n^{-1/3}log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replaced by a more heavy-tailed function, and the system is cooled faster. We also show how the algorithm may be applied to functions that cannot be computed exactly but only approximated, and give an example of maximising the log-likelihood function for a state-space model.
A significant opportunity for synergy between pure research and asteroid resource research exists. We provide an overview of the state of the art in asteroid resource utilization, and highlight where we can accelerate the closing of knowledge gaps, leading to the utilization of asteroid resources for growing economic productivity in space.
Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, $rm{LensIt}$, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor $simeq 2 $ compared to the quadratic estimator in a CMB stage IV configuration.
In this paper we present the orbital elements of Linus satellite of 22 Kalliope asteroid. Orbital element determination is based on the speckle interferometry data obtained with the 6-meter BTA telescope operated by SAO RAS. We processed 9 accurate positions of Linus orbiting around the main component of 22 Kalliope between 10 and 16 December, 2011. In order to determine the orbital elements of the Linus we have applied the direct geometric method. The formal errors are about 5 mas. This accuracy makes it possible to study the variations of the Linus orbital elements influenced by different perturbations over the course of time. Estimates of six classical orbital elements, such as the semi-major axis of the Linus orbit a = 1109 +- 6 km, eccentricity e = 0.016 +- 0.004, inclination i = 101{deg} +- 1{deg} to the ecliptic plane and others, are presented in this work.
We introduce a new algorithm for reinforcement learning called Maximum aposteriori Policy Optimisation (MPO) based on coordinate ascent on a relative entropy objective. We show that several existing methods can directly be related to our derivation. We develop two off-policy algorithms and demonstrate that they are competitive with the state-of-the-art in deep reinforcement learning. In particular, for continuous control, our method outperforms existing methods with respect to sample efficiency, premature convergence and robustness to hyperparameter settings while achieving similar or better final performance.
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