Filtering is a term used to describe methods that estimate the values of partially observed states, such as the position, velocity, and attitude of a vehicle, using current observations that are corrupted due to various sources, such as measurement noise, transmission dropouts, and spurious information. The study of filtering has been an active focus of research for decades, and the resulting filters have been the cornerstone of many of humankind\u27s greatest technological achievements. However, these achievements are enabled principally by the use of specialized techniques that seek to, in some way, combat the negative impacts that processor roundoff and truncation error have on filtering.
Two of these specialized techniques are known as square-root filters and consider filters. The former alleviates the fragility induced from estimating error covariance matrices by, instead, managing a factorized representation of that matrix, known as a square-root factor. The latter chooses to account for the statistical impacts a troublesome system parameter has on the overall state estimate without directly estimating it, and the result is a substantial reduction in numerical sensitivity to errors in that parameter. While both of these techniques have found widespread use in practical application, they have never been unified in a common square-root consider framework. Furthermore, consider filters are historically rooted to standard, vector-valued estimation techniques, and they have yet to be generalized to the emerging, set-valued estimation tools for multitarget tracking.
In this dissertation, formulae for the square-root consider filter are derived, and the result is extended to finite set statistics-based multitarget tracking tools. These results are used to propose a terrain-aided navigation concept wherein data regarding a vehicle\u27s environment is used to improve its state estimate, and square-root consider techniques provide the numerical stability necessary for an onboard navigation application. The newly developed square-root consider techniques are shown to be much more stable than standard formulations, and the terrain-aided navigation concept is applied to a lunar landing scenario to illustrate its applicability to navigating in challenging environments --Abstract, page iii
