The adaptive Kalman filter model

For a time-invariant system, the expected standard deviation of the innovation consists of two parts the measurement variance (r(/)), and the variance due to the uncertainty in the parameters (P(y)), given by [4]  

The above example illustrates the self adaptive capacity of the Kalman filter. The large interferences introduced at the wavelengths 26 and 28 10 cm have not really influenced the end result. At wavelengths 26 and 28 10 cm , the innovation is large due to the interfered. At 30 10 cm the innovation is high because the concentration estimates obtained in the foregoing step are poor. However, the observation at 30 10 cm is unaffected by which the concentration estimates are restored within the true value. In contrast, the OLS estimates obtained for the above example are inaccurate (j , = 0.148 and JCj = 0.217) demonstrating the sensitivity of OLS for model errors. 

Non-adaptive Kalman filter with interference at 26 and 28 10 3 cm- (see Table 41.5 for the starting conditions) 

Step j Wavelength jc, CI2 X2 Br Absorbance Measured ) Estimated ) Innovation 

2 Calculated with the absorbtivity coefficients from Table 41.4. 

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