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Example 2.4 Bad Measurement Identification Example
ОглавлениеThe considered covariance matrix R is
Matrices P and Ω are computed using expressions (2.19) and (2.27), respectively. The residual (from (2.21)) and the normalized residual of measurements (from (2.28)) are also calculated and provided in Table 2.6.
The threshold for detection at a 0.99 confidence level (α = 0.01) is Φ−1(1 − 0.01/2) = 2.5758. The normalized residual with highest absolute value in Table 2.6 (column 3) corresponds to v1, and, because its value is larger than 2.5758, it is identified as a bad measurement, and, therefore, it is removed from z .
After removing this bad measurement, observability is checked again. In this case, the system remains observable, and the state estimation is carried out again. After estimating the state, the objective function , and therefore no additional bad measurement is identified.
TABLE 2.6 Residuals and normalized residuals.
| Measurement | r i | |
|---|---|---|
| P 1 | −0.0154 | 2.2757 |
| P 3 | −0.0183 | 1.5836 |
| P 14 | 0.0078 | −0.5386 |
| P 32 | −0.0127 | 0.8996 |
| P 34 | 0.0275 | −1.9219 |
| v 1 | 0.0258 | −3.6530 |
| v 2 | −0.0245 | 3.5700 |
| Q 1 | −0.0032 | 2.6631 |
| Q 3 | −0.0018 | 1.0033 |
| Q 34 | 0.0041 | −1.0586 |
