Guidelines For Multisensor System Calibration With And Without Regularization

Calibration of multisensor systems (MSS) with linear response usually involves some form of regression analysis, e.g. ordinary least square regression (OLSR) or ridge regression (RR), between n(c) calibration combinations of ni measurands (loads) applied to the system and the corresponding signals extracted from its n(s) sensors. The selection of a suitable n(c) is delicate, especially with redundant systems, where n(s) > n(1). Furthermore, the effectiveness of regularization critically depends on the value of n(1) and n(c) with respect to n and adds effort, e.g., by the necessity to identify an optimal regularization parameter a in RR. This work addresses these trade-offs. A numerical study was used to identify the relevant features of MSS calibration and to formulate general conclusions applicable to redundant MSS. The minimally required number of calibration load cases is n(1). For n(1) < n(c) < n(s), OLSR achieves reasonably high measurement accuracies for n(c) approximate to (n(l) + n(s))/2. An unfavorable case is n(c) = n(s) where OLSR fails due to overfitting, which can be cured by RR. A validation study is carried out using a force/moment transducer with n(s) = 32 and n(1) = 6. As expected, RR improves the accuracy of the measured moments m(x), m(y), and m(z) comparison to OLSR, namely by respective factors of 45, 12 and 40.