Page 213 - Glucose Monitoring Devices

216 CHAPTER 10 CGM filtering and denoising techniques

interval 25e28 h is greater than in 10e13 h. Therefore, different filtering would be
needed for denoising these two portions of the same signal.
To deal with the intraindividual variability of the SNR, the KF proposed so far
needs to be modified. In an online setting, the procedure of Eqs. (10.10)e(10.12),
instead of been used only at the beginning of the monitoring, that is, at time t on
the first time window containing N samples, should be repeated at time t þ 1,
t þ 2, ., with the N-size vector y, u, and v referred to a sliding temporal window
of length N. Obviously, in practical applications, N determines also the length of
a burn-in interval where no filtered data can be provided (in the previous application
on Menarini Glucoday system the length of the initial tuning interval was set to 6 h,
but this value may vary due to the sampling frequency of the CGM sensor).
Remark: so far, we assumed the measurement noise v(t)of Eq. (10.1) to be white
and Gaussian. In any case, the method we propose is general and flexible to these
assumptions. As far as whiteness is concerned, this implies that in Eq. (10.10) the
matrix B ¼ I N , where I N is an N-size identity matrix, should be suitably modified
to properly describe correlated noise, for example, autoregressive [4,35]. In addition,
Gaussanity is not strictly required because it simply ensures the global optimality of
the estimator in Eq. (10.9).

Conclusions
CGM data are affected by several sources of error, including bias errors due to
imperfect/loss of calibration or to the physics/chemistry of the sensor, and random
noise, which dominates the true signal at high frequency. Although calibration errors
were discussed in Chapter 9 of this book, in this chapter we have discussed the
denoising problem by online digital filtering. In particular, after having revised
the major challenges of CGM filtering, that is, it is impossible to determine real-
time filter parameters, and to adapt them to the individual SNR, we presented a
KF-based methodology and assessed its performance on both Monte Carlo simula-
tion and CGM data. The method has general applicability, also outside from the
CGM context, and can be also used to quantify the variance of measurement noise
on CGM data.

References
[1] Facchinetti A, Sparacino G, Cobelli C. Reconstruction of glucose in plasma from inter-
stitial fluid continuous glucose monitoring data: role of sensor calibration. Journal of
Diabetes Science and Technology 2007;1(5):617e23.
[2] Kovatchev B, Anderson S, Heinemann L, Clarke W. Comparison of the numerical and
clinical accuracy of four continuous glucose monitors. Diabetes Care 2008;31(6):
1160e4.
[3] Kuure-Kinsey M, Palerm CC, Bequette BW. A dual-rate Kalman filter for continuous
glucose monitoring. Conference of Proceedings IEEE Engineering in Medicine Biology
Society 2006;1:63e6.