well suited for real-time applications because it depends only on previous measurements to obtain the filtered value. Figures 9-8 through 9-11 illustrate the use of various data filters on simulated attitude data which has been contaminated with Gaussian noise. In Fig. 9-8, a constant input signal plus noise is processed by a Butterworth (order=50, wc = 2w/50 sec-1), least-squares quadratic or LSQ («, = m2- m= 25), and averaging* filter. In the figure, points denote the noisy input data, and the dotted, dashed, and solid lines denote the data after processing with a Butterworth, LSQ, and averaging filter, respectively. Except for'the initial transient in the Butterworth filter's response, all three filters effectively attenuate the noise.
In Fig. 9-9, a sinusoidal input signal, V=> 1 +cos«i (<o=2w/50 sec-1), has been contaminated as before. The averaging filter removes both the noise and the signal, whereas the Butterworth and LSQ filters remove the noise and only
* Each data sample is replaced with the arithmetic mean of the 25 preceding and subsequent samples.
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