Disk drive to estimate repeatable runout (RRO) based upon on an optimal mean square estimation (MSE) learning method
View Patent ↗Disclosed is a method of estimating repeatable runout (RRO) for a disk drive. The method includes: determining a plurality of position error signal (PES) values for a plurality of servo wedges of a track of a disk; and estimating repeatable runout (RRO) in the PES values for the servo wedges of the track by averaging determined PES values over a pre-determined number of revolutions of the disk of the disk drive and scaling the averaged PES values by a pre-determined ratio of the variance of non-repeatable runout (NRRO) to the variance of an optimal estimation of the RRO for the disk drive.
1. A method of estimating repeatable runout (RRO) for a disk drive comprising:
determining a plurality of position error signal (PES) values for a plurality of servo wedges of a track of a disk; and
estimating repeatable runout (RRO) in the PES values for the servo wedges of the track by averaging determined PES values over a pre-determined number of revolutions of the disk of the disk drive and scaling the averaged PES values by a pre-determined ratio of the variance of non-repeatable runout (NRRO) to the variance of an optimal estimation of the RRO for the disk drive, wherein the RRO value is governed by an equation:
R
R
^
O
=
1
n
+
r
∑
i
=
1
n
PES
(
n
)
;
wherein n is a number of revolutions of the disk of the disk drive, PES(n) is a summed PES value for the plurality of servo wedges of the track at an n-th revolution, and r is the pre-determined ratio of the variance of NRRO to the variance of the optimal estimation of the RRO for the disk drive.
2. The method of claim 1 , wherein r is governed by an equation:
r
=
σ
︵
NRO
2
μ
^
RRO
2
;
wherein 2 NRO =the variance of NRRO of the disk drive and {circumflex over (μ)} 2 RRO =the variance of the optimal estimation of the RRO for the disk drive based upon an RRO estimator defined as
θ
︵
=
1
n
+
r
∑
i
=
1
n
X
i
in which X i equals a determined PES value at an n-th sample and E[X i ]={circumflex over (μ)} RRO and Var[X i ]= 2 NRO .
3. The method of claim 2 , further comprising determining an optimal estimation of the RRO estimator by determining a minimum mean square error (MSE) for the RRO estimator defined by the equation, MSE( )=E[( −μ) 2 ] wherein:
MSE
(
θ
︵
)
=
Var
[
θ
︵
]
+
(
Bias
[
θ
︵
]
)
2
=
(
1
n
+
r
)
2
n
σ
2
+
(
r
n
+
r
)
2
μ
2
;
and wherein a solution to a derivative of MSE( ),
∂
MSE
(
θ
︵
)
∂
r
=
0
,
yields an optimal solution:
r
=
σ
︵
NRO
2
μ
^
RRO
2
.
4. The method of claim 1 , wherein the ratio is determined for a first disk drive during a calibration process and the ratio is thereafter utilized for subsequent disk drives.
5. The method of claim 1 , wherein the ratio is determined by the disk drive itself during a self servo-calibration process.
6. The method of claim 1 , wherein the ratio is written to a reserved track of the disk.
7. The method of claim 1 wherein the RRO value is written in the servo wedge of the disk.
8. A disk drive to estimate repeatable runout (RRO), the disk drive comprising:
a disk including at least one track having a plurality of servo wedges;
a moveable head; and
a servo controller for controlling the position of the moveable head to perform track following on the plurality of servo wedges of the track and to measure a plurality of position error signal (PES) values, the servo controller to:
determine a plurality of position error signal (PES) values for a plurality of servo wedges of the track of the disk; and
estimate repeatable runout (RRO) in the PES values for the servo wedges of the track by averaging determined PES values over a pre-determined number of revolutions of the disk of the disk drive and scaling the averaged PES values by a pre-determined ratio of the variance of non-repeatable runout (NRRO) to the variance of an optimal estimation of the RRO for the disk drive, wherein the RRO value is governed by an equation:
R
R
^
O
=
1
n
+
r
∑
i
=
1
n
PES
(
n
)
;
wherein n is a number of revolutions of the disk of the disk drive, PES(n) is a summed PES value for the plurality of servo wedges of the track at an n-th revolution, and r is the pre-determined ratio of the variance of NRRO to the variance of the optimal estimation of the RRO for the disk drive.
9. The disk drive of claim 8 , wherein r is governed by an equation:
r
=
σ
︵
NRO
2
μ
^
RRO
2
;
wherein 2 NRO =the variance of NRRO of the disk drive and {circumflex over (μ)} 2 RRO =the variance of the optimal estimation of the RRO for the disk drive based upon an RRO estimator defined as
θ
︵
=
1
n
+
r
∑
i
=
1
n
X
i
in which X i equals a determined PES value at an n-th sample and E[X i ]={circumflex over (μ)} RRO and Var[X i ]= 2 NRO .
10. The disk drive of claim 9 , wherein an optimal estimation of the RRO estimator is estimated by determining a minimum mean square error (MSE) for the RRO estimator defined by the equation, MSE( ) E[( −μ) 2 ] wherein:
MSE
(
θ
︵
)
=
Var
[
θ
︵
]
+
(
Bias
[
θ
︵
]
)
2
=
(
1
n
+
r
)
2
n
σ
2
+
(
r
n
+
r
)
2
μ
2
;
and wherein a solution to a derivative of MSE( ),
∂
MSE
(
θ
︵
)
∂
r
=
0
,
yields an optimal solution:
r
=
σ
︵
NRO
2
μ
^
RRO
2
.
11. The disk drive of claim 8 , wherein the ratio is determined for a first disk drive during a calibration process and the ratio is thereafter utilized for subsequent disk drives.
12. The disk drive of claim 8 , wherein the ratio is determined during a self servo-calibration process.
13. The disk drive of claim 8 , wherein the ratio is written to a reserved track of the disk.
14. The disk drive of claim 8 wherein the RRO value is written in the servo wedge of the disk.