This paper discusses the development of a particle filter for attitude and angular rate estimation of a space object using light curve observations. The particle filter approach used is based on the generalized Rodrigues parameters (GRPs) local error representation. The global state used is the quaternion to avoid singularity in the attitude states. Uniform quaternions are generated to approxim...

An exact formula for the expected length of the minimum spanning tree of a connected graph, with independent and identical edge distribution, is given, which generalizes Steele’s formula in the uniform case. For a complete graph, the difference of expected lengths between exponential distribution, with rate one, and uniform distribution on the interval (0, 1) is shown to be positive and of rate...

Abstract—In this paper, we study the achievable rate region of Gaussian multiuser channels with the messages transmitted being from finite input alphabets and the outputs being quantized at the receiver. In particular, we focus on the achievable rate region of i) Gaussian broadcast channel (GBC) and ii) Gaussian multiple access channel (GMAC). First, we study the achievable rate region of two-u...

For double trigonometric Fourier series, Móricz and Rhoades studied the rate of uniform approximation by Nörlund means of the rectangular partial sums of double Fourier series of a function belonging to the class Lipα (0 < α 1) [12] and the class of continuous functions [13], on the two-dimensional torus. As a special case, they obtained the rate of uniform approximation by double Cesàro means....

Effective parallel tempering simulations rely crucially on a properly chosen sequence of temperatures. While it is desirable to achieve a uniform exchange acceptance rate across neighboring replicas, finding a set of temperatures that achieves this end is often a difficult task, in particular for systems undergoing phase transitions. Here we present a method for determination of optimal replica...

Uniform deviation bounds limit the difference between a model’s expected loss and its loss on a random sample uniformly for all models in a learning problem. In this paper, we provide a novel framework to obtain uniform deviation bounds for unbounded loss functions. As a result, we obtain competitive uniform deviation bounds for k-Means clustering under weak assumptions on the underlying distri...