Aerospace and Electronic Systems - August 2018 - 34

Online Calibration Platform with Applications to Inertial Sensors

Figure 7.

Summary of the parameters of the last iteration as seen in the online
GUI corresponding to iteration (c) of Table 2.

the confidence intervals at the last (larger) scales. In any case, it
would be appropriate that the model that is chosen in the end lies
within the confidence interval of the empirical WV (blue color). In
this case, we can stop the iterative model identification (which can
also result in a set of different models) and go to the next step to
extract the parameters of these models.

PARAMETER ESTIMATION

Figure 6.

Evolution of iterative model identification. The figures are directly
generated by the online tool and can be saved easily by clicking on
them. (a) First iteration: QN+WN+GM with objective function: 144.5.
(b) Second iteration: QN+WN+2*GM with objective function: 52.6. (c)
Third iteration: QN+WN+3*GM with objective function: 17.3.

model (orange line) does not entirely lie within the confidence intervals of the empirical WV (blue line), we decide to add an additional GM, since the middle and larger scales show a significant
difference between the empirical and the theoretical WV. The result is plotted in Figure 6b, where we see that the model appears to
better fit the empirical WV.
Although adding a GM model has greatly improved the visual
fit as well as the objective function around the middle scales, there
still persists a small difference at some scales. Therefore, we decided to add another GM process to our model. This final solution is
presented in Figure 6c, showing an overall (almost) perfect match,
which, however, could be considered excessive, given the size of
34

Once the model is defined, we can retrieve the parameters from
the fitted object by clicking in the upper part on the Summary-tab.
The parameters will appear for each underlying model as well as
the value of the objective function shown in (3), which gives an
estimation of how well the fitted model describes the empirical
WV (Figure 7). The smaller the objective function value, the better
the fit to the observed signal. In addition, the confidence interval
with upper and lower bounds for each parameter is given too. As
stated before, this is an iterative process, and the steps in the previous section can be re-evaluated multiple times, until a suitable fit
is found for further processing.
Table 2 reports the parameter values of the datasheets for the
gyroscopes from the two IMUs Navchip and XSENS MTi-G used in
this example compared with those estimated by the online platform
for different noise structures. It can be seen how these parameter
values change depending on the underlying models in the estimation. In each case, the GMWM matches the empirical and the theoretical WV (implied by the fitted model) as best as possible. It can
be seen that the estimated amplitude of the WN corresponds well
to the values in the datasheet of the Navchip, while it differs by one
order of magnitude for the MTi-G. There is also a difference in
the typology of noises: the MTi-G does, for instance, not contain a
QN. The parameters provided by the datasheet are general across
a product line, but a proper analysis of each individual sensor axis
refines the modeling. The parameters differ between the IMUs;
even each axis on the same IMU has different parameters.

MODEL SELECTION
Once a set of models has been identified as possible candidates
to describe the stochastic error signal, the WVIC can be used as

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Aerospace and Electronic Systems - August 2018

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