Funded by the NSF CubeSat and NASA ELaNa programs, the Dynamic Ionosphere CubeSat Experiment (DICE) mission consists of two 1.5U CubeSats which were launched into an eccentric low Earth orbit on October 28, 2011. Each identical spacecraft carries two Langmuir probes to measure ionospheric in-situ plasma densities, electric field probes to measure in-situ DC and AC electric fields, and a science grade magnetometer to measure in-situ DC and AC magnetic fields. Given the tight integration of these multiple sensors with the CubeSat platforms, each of the DICE spacecraft is effectively a "sensorsat" capable of comprehensive ionospheric diagnostics. The use of two identical sensor-sats at slightly different orbiting velocities in nearly identical orbits permits the de-convolution of spatial and temporal ambiguities in the observations of the ionosphere from a moving platform. In addition to demonstrating nanosat-based constellation science, the DICE mission is advancing a number of groundbreaking CubeSat technologies including miniaturized mechanisms and high-speed downlink communications.
Abstract-The popular Sudoku puzzle bears structural resemblance to the problem of decoding linear error correction codes: solution is over a discrete set, and several constraints apply. We express the constraint satisfaction using a Tanner graph. The belief propagation algorithm is applied to this graph. Unlike conventional computer-based solvers, which rely on humanly specified tricks for solution, belief propagation is generally applicable, and requires no human insight to solve a problem. The presence of short cycles in the graph creates biases so that not every puzzle is solved by this method. However, all puzzles are at least partly solved by this method. The Sudoku application thus demonstrates the potential effectiveness of BP algorithms on a general class of constraint satisfaction problems.
The conditional probability density function of the state of a stochastic dynamic system represents the complete solution to the nonlinear ltering problem because, with the conditional density in hand, all estimates of the state, optimal or otherwise, can be computed. It is well known that, for systems with continuous dynamics, the conditional density evolves, between measurements, according to Kolmogorov's forward equation. At a measurement, it is updated according to Bayes formula. Therefore, these two equations can be viewed as the dynamic equations of the conditional density and, hence, the exact nonlinear lter. In this paper, Galerkin's method is used to approximate the nonlinear lter by solving for the entire conditional density. Using a discrete cosine transform to approximate the projections required in Galerkin's method leads to a computationally realizable nonlinear lter. The implementation details are given and performance is assessed through simulations.
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