U. Glaeser

FIGURE 34.40 The phase format.
Position Estimators
Estimating various parameters of a sinusoid is well documented in textbooks [3]. A decade ago position
estimators were mostly implemented by analog circuitry, whereas at present, digital implementation is
the norm and the one considered in this article [21–25]. One way of classifying estimators is to determine
whether the phase and/or the frequency of the incoming waveform are known.
Assume that the amplitude of a noisy sinusoid needs to be determined. If the phase of this waveform
is known, a matched filter can be used to generate the amplitude estimate. This is known as coherent
estimation. Under certain assumptions and performance criteria such a filter becomes optimal. When
the phase of the waveform is not known, but the frequency is known, then two matched filters can be
used, one tuned to a sine waveform while the other filter is tuned to a cosine waveform. The outputs of
the two filters are squared and added to give the energy estimate of the waveform. This is known as
noncoherent estimation and is equivalent to computing the Fourier transform at the first harmonic.
Other ad hoc estimators include the peak estimator and digital area estimators [26], which respectively
estimate the averaged peak and the mean value of the unsigned waveform. Neither of these estimators
requires the phase or the frequency of the waveform.
For the amplitude format, all the estimators mentioned here can be used. For the antipodal format,
the phase of the waveform is needed and therefore a single matched filter is the required estimator. For
dual frequency format, we need two estimators, each tuned to a different frequency. Since the two
waveforms are orthogonal to each other, an estimator tuned to one of the waveforms will not observe
the other waveform. Each estimator can utilize a single matched filter for coherent estimation or two
matched filters for noncoherent estimation. Finally, for phase estimation, two matched filters are utilized,
similar to noncoherent estimation; however, rather than squaring and adding the filter outputs, the
inverse tangent function is performed on the ratio of the filter outputs.
References
1. Comstock, R.L. and Workman, M.L., Data storage in rigid disks, in Magnetic Storage Handbook, 2nd
ed., Mee, C.D. and Daniel, E.D., Eds., McGraw-Hill, New York, 1996, chap. 2.
2. Proakis, J.G., Digital Communications, 4th ed., McGraw-Hill, New York, 2000.
3. Kay, S.M., Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall, Englewood
Cliffs, NJ, 1993.
4. Franklin, G.F., Powell, D.J., and Workman, M.L., Digital control of dynamic systems, 3rd ed., Addison-
Wesley, Reading, MA, 1997, chap. 14.
5. Brown, D.H., et al., Self-servo writing file, US patent 06,040,955, 2000.
6. Liu, B., Hu, S.B., and Chen, Q. S., A novel method for reduction of the cross track profile asymmetry
of MR head during self servo-writing, IEEE Trans. on Mag., 34, 1901, 1998.
7. Bernard, W.R. and Buslik, W.S., Magnetic pattern recording, U.S. patent 03,869,711, 1975.
© 2002 by CRC Press LLC
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