I have been reading about outlier detection algorithm for improving determinations based on realistic data.
Outlier exclusion is an important tool in any analysis of realistic noisy data. There are many ways to detect/identify outliers, and some may be better than others for orbit determination.
I've been reading the book Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook by Bruce P. Gibbs. The author mentions outlier detection but it is discuss for only a few pages. He introduced two ways which are De-Weighting Large Residual and Data Editing. He said that data editing is used with much more success in satellite orbit determination.
I'd like to better understand if this is in fact true, and if so, why. Any other tips on the topic would be appreciated as well.
1) 𝑿^𝟐=〖(𝒚−𝒉(𝒙))〗^𝑻 𝑺^(−𝟏) (𝒚−𝒉(𝒙))
2) Residual(i) > 3√(HP 𝐻^𝑇 + R)
EDITED: I want to share what I learn from outlier detection if I am wrong, Please improve me!
The RMS of the residuals
(eq.7.4-4) is computed first, and then significance of the residual is checked under the n.RMS value
(eq.7.4-3). When the significance of the residual is larger than the n.RMS
(eq.7.4-3) value, the corresponding observation is marked. If there exists any outlier in the observations, the OD process is repeated in which the marked observations are not used.
Also, to find the significance of residual instead of (eq.7.4-3), only 3*RMS can be used but I don't know how much it is sensitive.
Therefore, If I am not wrong, OD process will run minimum two times if there is at least one outlier. The process: first-calculate residuals and RMS and Second-If there is an outlier, don't calculate and skip that measurement for next in OD performance.
I think the
eq7.4-5 is not correct because For example, if you have 3 measurement data(range, azimuth, and elevation), you can obtain one significance of residual such as matrix
(3x1)^T*(3x3)*(3x1)= (1,1) so that the result should be
3x1 because the significance of residuals should be calculated for each sensor type. Otherwise, limit of the significance of residuals will be same for all different sensors.