Colored noise effects on batch attitude accuracy estimates

The effects of colored noise on the accuracy of batch least squares parameter estimates with applications to attitude determination cases are investigated. The standard approaches used for estimating the accuracy of a computed attitude commonly assume uncorrelated (white) measurement noise, while in actual flight experience measurement noise often contains significant time correlations and thus is colored. For example, horizon scanner measurements from low Earth orbit were observed to show correlations over many minutes in response to large scale atmospheric phenomena. A general approach to the analysis of the effects of colored noise is investigated, and interpretation of the resulting equations provides insight into the effects of any particular noise color and the worst case noise coloring for any particular parameter estimate. It is shown that for certain cases, the effects of relatively short term correlations can be accommodated by a simple correction factor. The errors in the predicted accuracy assuming white noise and the reduced accuracy due to the suboptimal nature of estimators that do not take into account the noise color characteristics are discussed. The appearance of a variety of sample noise color characteristics are demonstrated through simulation, and their effects are discussed for sample estimation cases. Based on the analysis, options for dealing with the effects of colored noise are discussed.