Page 206 - Glucose Monitoring Devices

CGM denoising by Kalman filter 209

Step 2
2
2
For the rest of the data, the values of l and s found in Step 1 are used inside Eqs.
(10.5) and (10.8), allowing both real-time application of KF and individualization of
KF parameters.

In silico assessment
To demonstrate the necessity of the individualization of filter parameters and the
reliability of the new methodology, a Monte Carlo simulation study has been
performed.

Accuracy in SNR determination
A reference noise-free 3-min sampled glucose profile (Fig. 10.2, top panel, thick
gray line) was first created. Then, N sim ¼ 300 noisy time series have been generated
by adding to the reference profile a zero-mean white Gaussian noise sequence [7]
2
2
2
with variance s randomly sampled in the interval (1100) mg /dL . Two represen-
2
tative profiles with high and low SNR (obtained for realizations of s equal to 2
and 51, respectively) are shown in the middle and bottom panels of Fig. 10.2 (thick
2
2
gray lines), respectively. In both panels, s and l estimates, obtained applying the
procedure of described previously, are reported inside the gray box, which represents
the 6 h tuning interval that has been selected for this example (here, the number of
2
CGM samples is N ¼ 120). Estimated s values are 2.4 and 46.2, very similar to true
values. The KF output (tuned with parameters estimated in the 6 h window) is
displayed by a thin black line. In these two realizations, the root means square error
(RMSE) is equal to 1.2 and 4.5 mg/dL, respectively.
Results of the application of the criterion of Eq. (10.11) for all N sim ¼ 300
2
simulations show that the measurement noise variance s is estimated very well.
2
Fig. 10.3 displays the comparison between true and estimated s values in
2
N sim ¼ 300 runs, with a correlation coefficient R ¼ 0.986. Looking at the
so-called Q/R ratio, estimated g values are very different, with an average value
of 21.6, and 10th and 90th percentile of 3.3 and 48.2, respectively. In addition,
2
the estimation of the process noise variance l for all the N sim ¼ 300 realizations
2
returned an average value of 1.5, with 10th and 90th percentile of 1.0 mg /dL 2
2
2
2
and 2.1 mg /dL , respectively (meaning that the variability of l is correctly
estimated, irrespectively of the SNR).
Importance of filter parameters accuracy
Here we demonstrate the necessity of filter parameters individualization. The top
panel of Fig. 10.4 displays a zoom of what happens if the signal of Fig. 10.2 (middle
panel) is filtered using parameters obtained for the signal of Fig. 10.2 (bottom
panel). As apparent, the use of suboptimal parameters, in this case, leads to over-
smoothing, introducing possibly critical under/overshoots when signal derivative
changes and large temporal delay (e.g., 6 min around hour 20.7). Conversely, if
the signal of Fig. 10.2 (bottom panel) is filtered with the parameters obtained for