Geoscience Reference
In-Depth Information
Fig. 6. MSE of estimated noise power in the proposed method
In addition to have a high precision, the moment method is non-recursive, trustable from the
beginning, and provides a rapid reaction.
The second point in figures (7) and (8) is the existence of a bulge around the time 25 seconds,
where the third component of the speed has changed and made a nonlinear motion. There is
no bulge in the curves relating to the moment method, because in this method, the estimation
at any time is independent from the other times, so it has no problem in nonlinear motions.
In the figures we magnify the results around time 25 seconds and show them in linear scale
to depict the bulge obviously. We cannot present all results together in linear scale, because
moment results are too small in comparison with EKF and PF results.
To further examine the ability of the proposed method, the test is done at different SNRs. The
results of this experiment is showed in figures (9) and (10). In the figures, MSE of the position
and velocity estimation is portrayed for our moment method.
In figures (7) and (8), MSE is versus time , and SNR is constant and equal to +10dB. Thus the
figures (7) and (8) show the superiority of the proposed method on the two other ones. But
in figures (9) and (10), MSE is versus SNR. The power of moment method in the low SNR is
quite satisfactory, while the other methods, the EKF and PF, either do not respond or provide
answers that are not reliable.
Finally, a necessary point should be noted. We see that our method has much better results
in comparison with other ones. The better results are not only because of using moments.
Moment method helps us as a tool to encounter the undesired signals logically. In fact, in the
first step, we recognize the environment more precisely by a suitable model of noise. Then
after the modelling, although the noise is unknown, but the moments of its model are known
and used for our estimations. So we can control the noise behaviour. This procedure cannot
be found in other methods.
