Abstract

A method for comparing the relative phase of carrier signals received from GPS satellites to determine the roll, pitch and azimuth attitude of ships, aircraft, land vehicles, or survey instruments, accomplishes a maximum likelihood estimation (MLE) optimum solution over the full range of integers and vehicle attitudes. The problem is formulated as an MLE optimization, where vehicle attitude and integers are regarded as parameters to be adjusted to maximize probability of first-difference carrier phase measurements that are actually generated by hardware. Formulation results in weighted-fit error W as the objective criterion to minimize. A Kalman filter is introduced, having same objective criterion. Minimizing computation in Kalman filter leads to a decision tree for the integers. Two ways are shown to prune decision tree. The first is to exclude impossible combinations, such as those that produce an antenna upside down. The second is to generate a lower bound for W at each branch of the tree. A running sum is kept at each stage moving down the tree. When that sum exceeds a reasonableness bound or the current best W found elsewhere in the search, it is guaranteed that all subsequent integer combinations further down the current branch will produce a larger W and the remainder of the current branch can be cut off, speeding up the search.

Other References

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