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Expansion of Check-Cases for 6DOF Simulation

This is the Appendix containing a description of the solution for Case 1 in the assessment, “Expansion of Check-Cases for 6DOF Simulation”. For cases of spherical gravity, it is possible to provide a two-body solution without recourse to numerical integration and thus it is accurate to machine precision. Python code for a Keplerian Propagator (propagate.py) which produced a reference trajectory for Case 1 is provided in this appendix. There is also code for generating test cases which was used as an independent verification of the propagator. This is a high-level description of the algorithm employed. The documentation of each function includes implementation details, including equations for each task.

Modeling

Estimating the Size of Huffman Code Preambles

Data compression via block-adaptive Huffman coding is considered. The compressor consecutively processes blocks of N data symbols, estimates source statistics by computing the relative frequencies of each source symbol in the block, and then synthesizes a Huffman code based on these estimates. In order to let the decompressor know which Huffman code is being used, the compressor must begin the transmission of each compressed block with a short preamble or header file. This file is an encoding of the list n = (n 1 , n 2 ....,n m ), where n i is the length of the Hufffman codeword associated with the ith source symbol. A simple method of doing this encoding is to individually encode each n i into a fixed-length binary word of length log 2 l, where l is an a priori upper bound on the codeword length. This method produces a maximum preamble length of mlog 2 l bits. The object is to show that, in most cases, no substantially shorter header of any kind is possible.

R J McEliece