Patent Publication Number: US-2012033317-A1

Title: Position error signal demodulation with target-based blending

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     Embodiments of the present invention relate generally to disk drives and, more particularly, to systems and methods for demodulating position error signals in such drives. 
     2. Description of the Related Art 
     A disk drive is a data storage device that stores digital data in concentric tracks on the surface of a data storage disk. The data storage disk is a rotatable hard disk with a layer of magnetic material thereon, and data is read from or written to a desired track on the data storage disk using a read/write head that is held proximate to the track while the disk spins about its center at a constant angular velocity. 
     To properly align the read/write head with a desired track during a read or write operation, disk drives generally use a closed-loop servo system that relies on servo data stored in servo sectors written on the disk surface when the disk drive is manufactured. These servo sectors form “servo wedges” or “servo spokes” from the outer to inner diameter of the disk, and are either written on the disk surface by an external device, such as a servo track writer, or by the drive itself using a self servo-writing procedure. The read/write head can be positioned with respect to the data storage disk by using feedback control based on servo information read from the servo wedges with the read element of the read/write head. The servo sectors provide position information about the radial location of the read/write head with respect to the disk surface in the form of servo patterns. 
     A typical servo pattern consists of a preamble field, a Gray code area and servo bursts, where the servo bursts are used to determine the fine position of the read/write head relative to a specific track.  FIG. 1  illustrates servo burst patterns  100 ,  150  written in adjacent servo sectors k, k+1 on a disk surface. Servo burst pattern  100  includes an AB burst pair  101  and a CD burst pair  102  for track N. Similarly, servo burst pattern  150  includes an AB burst pair  151  and a CD burst pair  152  for track N. For reference, a portion of burst pairs  198 ,  199  for adjacent track N+1 are also shown in  FIG. 1 . As a read head  160  travels over servo burst patterns  100 ,  150  the magnetic transition of the servo bursts generates electrical signals in read head  160 . The amplitude of the electrical signals depends on the overlap between read head  160  and the various bursts associated with track N, i.e., AB burst pair  101 , CD burst pair  102 , AB burst pair  151 , CD burst pair  152 , and so on. This amplitude information can be used to determine the fine position of the head relative to the servo bursts. 
     Ideally, when written on a disk surface the servo bursts are uniformly positioned, so that the distance between the AB null point  140  and CD null point  141  are equally spaced for each track and within each sector. In servo sector k, this distance is X1, and in servo sector k−1, this distance is X2. In practice, due to servo writer inaccuracies, distance X1 and X2 vary from track-to-track and from sector-to-sector. The track-to-track variation of average track spacing is typically referred to as DC squeeze or DC track spacing variation and the sector-to-sector variation of track spacing within one track is typically referred to as AC squeeze or AC track spacing variation. 
     Various burst-decoding schemes are known in the art and can be affected by track squeeze, including stitched demodulation schemes and seamless demodulation schemes. When read head  160  is positioned at some track locations, e.g., between 0 track location (N) and ⅛ track location (N+0.125), the AB burst pairs provide the majority of electrical signals for determining the position of read head  160 , while at other track locations, e.g., ½ track location (N+0.5), the CD burst pairs provide the majority of electrical signals. At ¼ track location (N+0.25), however, both the AB burst pairs and the CD burst pairs provide a strong position signal, and generally there is some discontinuity between these two signals at this transition zone, known as “stitching error.” 
     Stitched burst-decoding demodulation schemes use a weighted combination of the signal provided by an AB burst pair and a CD burst pair to determine a position for read head  160 . Stitched demodulation schemes can mathematically ensure that the measured and actual head positions are exactly equal when read head  160  is at the 0 and ½ track locations. Stitched demodulation schemes can be calibrated to accommodate for stitching error that occurs between AB burst pairs and CD burst pairs for nominal track pitch, but because stitching error is greatly exaggerated by track squeeze, such calibration is of limited utility for “squeezed” tracks. Using stitched demodulation schemes, squeezed tracks generally can have undesirable position error signal (PES) noise, or “chatter” at the ¼ track location, which is known to cause data integrity problems. 
     Seamless burst-decoding demodulation schemes are constructed so that the measured position of read head  160  has no discontinuity between the signals provided by AB burst pairs and CD burst pairs, i.e., the measured position of read head  160  is represented by a continuous curve connecting the AB null and CD null points. This is accomplished by designing seamless demodulation schemes to ensure that the measured and actual head positions are exactly equal when read head  160  is at the 0, ¼, and ½ track locations.  FIG. 2  is a graph representing the measured position (ordinate) of read head  160  as a function of the physical position (abscissa) of read head  160 , according to a typical seamless burst-decoding demodulation scheme. Curve  201  depicts the measured position of read head  160  for a track having nominal track pitch. As shown, curve  201  is constructed so that at the 0, ¼, and ½ track locations, the measured position is set equal to the physical position of read head  160 , thereby defining a continuous curve from the 0 track to the ½ track locations. Because the measured position of read head  160  is defined by such a continuous curve, PES chatter cannot occur. This holds true even when physical track spacing changes due to track squeeze. Curve  202  depicts the measured position of read head  160  for a squeezed track having substantially less than nominal track pitch. Although the physical position of the ¼ track and ½ track locations have moved due to track squeeze, curve  202  is still a continuous curve defining the measured position of read head  160  and PES chatter cannot occur. But because curve  202  has end points and a middle point that are fixed to the actual (squeezed) track locations and not to the nominal 0, ¼ and ½ track locations, the slope  202 A of curve  202  is necessarily different than the slope  201 A of curve  201 . Because servo loop gain for controlling the position of read head  160  is proportional to the slope of curves  201 ,  202 , the servo loop gain changes whenever actual track pitch varies between servo sectors, such as when track squeeze occurs. When the actual track pitch varies between adjacent or proximate servo sectors, as illustrated between servo sectors k and k+1 in  FIG. 1 , changes in servo loop gain can cause servo loop stability problems, resulting in unwanted oscillations of read head  160 . 
     In light of the above, there is a need in the art for a burst-decoding demodulation method that prevents PES chatter without introducing servo loop instability. 
     SUMMARY OF THE INVENTION 
     One or more embodiments of the present invention provide a method for servo burst-decoding demodulation in a disk drive that accommodates track pitch variation. Depending on the distance a read head is displaced from a read head target position, a target-based blending scheme, a position-based blending scheme, or a weighted combination of both is used to determine the position of the transducer head. When the transducer head is relatively close to the target position, e.g., within ⅛ of a track, the target-based blending scheme is used to decode servo bursts and calculate the exact head position. When the transducer head is relatively far from the target position, e.g., more than ¼ of a track, the position-based blending scheme is used to decode servo bursts and calculate head position. When the transducer head is an intermediate distance from the target position, a weighted combination of the target-based and position-based blending schemes is used. 
     A method of determining positioning errors of a transducer head of a disk drive, according to an embodiment of the invention, comprises the steps of measuring a position error of the transducer head relative to a nominal target position based on servo bursts written on a recording medium of the disk drive and determining a final position error of the transducer head according to one of a first function, a second function, and a third function. The first function is used when the measured position error is less than a first predetermined number. The second function is used when the measured position error is greater than a second predetermined number. The third function is used when the measured position error is between the first and second predetermined numbers. The first predetermined number represents 12.5% of a nominal track width and the second predetermined number represents 25% of the nominal track width. 
     A non-transitory computer-readable storage medium, according to an embodiment of the invention, comprises instructions for a processing unit of a disk drive to carry out the steps of measuring a position error of a transducer head of the disk drive relative to a nominal target position based on servo bursts written on a recording medium of the disk drive and determining a final position error of the transducer head according to one of a first function, a second function, and a third function. The first function is used when the measured position error is less than a first predetermined number. The second function is used when the measured position error is greater than a second predetermined number. The third function is used when the measured position error is between the first and second predetermined numbers. 
     A disk drive, according to an embodiment of the invention, comprises a transducer head, a recording medium having written thereon servo bursts, and a controller for positioning the transducer head over the recording medium using the servo bursts. The controller is programmed to measure a position error of the transducer head relative to a nominal target position based on the servo bursts and determine a final position error of the transducer head according to one of a first function, a second function, and a third function. The first function is used when the measured position error is less than a first predetermined number. The second function is used when the measured position error is greater than a second predetermined number. The third function is used when the measured position error is between the first and second predetermined numbers. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
         FIG. 1  illustrates two servo burst patterns written in adjacent servo sectors on a disk surface. 
         FIG. 2  is a graph representing the measured position of a read head as a function of the physical position of the read head, according to a typical seamless burst-decoding demodulation scheme. 
         FIG. 3  is a perspective view of a disk drive that can benefit from embodiments of the invention as described herein. 
         FIG. 4  illustrates a storage disk with data organized in a typical manner known in the art. 
         FIG. 5  is a graph illustrating an exemplary embodiment of a hybrid curve that represents the measured position of a read head as a function of the physical position of the read head, as determined according to a hybrid burst-decoding demodulation scheme. 
         FIG. 6  is a graph depicting three curves constructed using a target-based blending scheme for a squeezed track, according to embodiments of the invention. 
         FIG. 7  is a flow chart that summarizes, in a stepwise fashion, a method of determining the position of a transducer head of a hard disk drive, according to embodiments of the invention. 
         FIG. 8  is a graph of servo loop gain in a disk drive using a conventional position-based demodulation scheme. 
         FIG. 9  is a graph of servo loop gain across the sectors of a disk drive using a hybrid demodulation scheme, according to embodiments of the invention. 
     
    
    
     For clarity, identical reference numbers have been used, where applicable, to designate identical elements that are common between figures. It is contemplated that features of one embodiment may be incorporated in other embodiments without further recitation. 
     DETAILED DESCRIPTION 
       FIG. 3  is a perspective view of a disk drive  110  that can benefit from embodiments of the invention as described herein. For clarity, disk drive  110  is illustrated without a top cover. Disk drive  110  includes a storage disk  112  that is rotated by a spindle motor  114 . Spindle motor  114  is mounted on a base plate  116 . An actuator arm assembly  118  is also mounted on base plate  116 , and has a slider  120  mounted on a flexure arm  122  with a read head  127  and a write head  129 . Flexure arm  122  is attached to an actuator arm  124  that rotates about a bearing assembly  126 . Voice coil motor  128  moves slider  120  relative to storage disk  112 , thereby positioning read and write heads  127  and  129  over the desired concentric data storage track disposed on the surface  112 A of storage disk  112 . Spindle motor  114 , the read and write heads  127  and  129 , and voice coil motor  128  are coupled to electronic circuits  130 , which are mounted on a printed circuit board  132 . The electronic circuits  130  include a read channel, a microprocessor-based controller, and random access memory (RAM). For clarity of description, disk drive  110  is illustrated with a single storage disk  112  and actuator arm assembly  118 . Disk drive  110 , however, may also include multiple storage disks  112  and multiple actuator arm assemblies  118 . In addition, each side of disk  112  may have an associated read and write heads  127  and  129 . The invention described herein is equally applicable to devices wherein the individual heads are configured to move separately some small distance relative to the actuator using dual-stage actuation. 
       FIG. 4  illustrates storage disk  112  with data organized in a typical manner after servo wedges  244  have been written on storage disk  112  by either a media writer or by disk drive  110  itself via self servo-write (SSW). Storage disk  112  includes data storage tracks  242  located in data sectors  246  for storing data. Data storage tracks  242  are positionally defined by servo information written in servo wedges  244 . Each of data storage tracks  242  is schematically illustrated as a centerline, but in practice occupies a finite width about a corresponding centerline. Substantially radially aligned servo wedges  244  are shown crossing data storage tracks  242  and have servo sectors containing servo information. The servo information consists of a preamble field used to synchronize the timing of the read channel and to adjust the signal amplitude, a Gray code area used to determine track number and provide coarse position of read and write heads  127  and  129 , and servo bursts used to determine the fine position of read and write heads  127  and  129  relative to a specific data storage track  242 . The servo bursts contained in servo wedges  244  may be substantially similar in configuration to servo burst patterns  100 ,  150  in  FIG. 1 . Alternatively, the magnetic indicia making up the servo bursts in servo wedges  244  may be configured according to other servo patterns commonly known in the art. In practice, servo wedges  244  may be somewhat curved, for example, configured in a shallow spiral pattern. Further, the actual number of data storage tracks  242  and servo wedges  244  included on storage disk  112  is typically considerably larger than illustrated in  FIG. 2 . For example, storage disk  112  may include hundreds of thousands of data storage tracks  242  and hundreds of servo wedges  244 . As noted above, servo wedges  244  are written on storage disk  112  by either a media writer or by disk drive  110  itself via an SSW process. In either case, due to fluctuations in writing head position that occur during the process of writing servo wedges  244 , the majority of data storage tracks  242  vary slightly from the nominal track pitch for disk drive  110 , resulting in track squeeze for some of these tracks. 
     When disk drive  110  is in operation, actuator arm assembly  118  sweeps an arc between an inner diameter (ID) and an outer diameter (OD) of storage disk  112 . Actuator arm assembly  118  accelerates in one angular direction when current is passed through the voice coil of voice coil motor  128  and accelerates in an opposite direction when the current is reversed, allowing for control of the position of actuator arm assembly  118  and the attached read and write heads  127  and  129  with respect to storage disk  112 . Voice coil motor  128  is coupled with a servo system known in the art that uses positioning data read from storage disk  112  by the read head  127  to determine the position of the read and write heads  127  and  129  over data storage tracks  242 . The servo system determines an appropriate current to drive through the voice coil of voice coil motor  128 , and drives said current using a current driver and associated circuitry. 
     Embodiments of the invention provide a method for servo burst-decoding demodulation in a disk drive that accommodates track pitch variation by using a either a target-based blending scheme, a position-based blending scheme, or a weighted combination of both to determine the position of a transducer head, e.g., read head  127  or write head  129 . The particular scheme that is used to determine the position of the transducer head depends on the current track position of read head  127  relative to the current target position for read head  127 . 
       FIG. 5  is a graph illustrating an exemplary embodiment of a hybrid curve  501  (solid line) that represents the measured position (ordinate) of read head  127  as a function of the physical position (abscissa) of read head  127 , as determined according to a hybrid burst-decoding demodulation scheme.  FIG. 5  also includes a position-based blending scheme curve  502  (dashed line) and a target-based blending scheme curve  503  (dashed line), from which hybrid curve  501  is derived. Position-based blending scheme curve  502  depicts the measured position of read head  127  as a function of the physical position of read head  127 , as determined by a position-based blending demodulation scheme. Target-based blending scheme curve  503  depicts the measured position of read head  127  as a function of the physical position of read head  127 , as determined by a target-based blending demodulation scheme. As shown, hybrid curve  501 , position-based blending scheme curve  502 , and target-based blending scheme curve  503  each represent the measured position of read head  127  as a continuous function of physical position, so that no discontinuity occurs as read head travels between the 0 track position and the ½ track position. 
     According to embodiments of the invention, hybrid curve  501  is derived from position-based blending scheme curve  502  and target-based blending scheme curve  503 . Specifically, when read head  127  is relatively close to the target position, the target-based blending scheme is used to decode servo bursts and calculate the exact head position, as indicated by the portion of hybrid curve  501  that is coincident with target-based blending scheme curve  503 . When read head  127  is relatively far from the target position, the position-based blending scheme is used to decode servo bursts and calculate head position, as indicated by the portion of hybrid curve  501  that is coincident with position-based blending scheme curve  502 . When read head  127  is an intermediate distance from the target position, a weighted combination of the target-based and position-based blending schemes is used, as indicated by segment  505  of hybrid curve  501 . In the embodiment illustrated in  FIG. 5 , the target position for hybrid curve  501  is the 0 track position. The target-based blending scheme is used whenever read head  127  is positioned less than or equal to a first displacement limit  520  from the target position, which in  FIG. 5  is ⅛ of a nominal track width. Similarly, the position-based blending scheme is used whenever read head  127  is positioned greater than or equal to a second displacement limit  530  from the target position, which in  FIG. 5  is ¼ of a nominal track width. A weighted combination of the position-based blending scheme and the target-based blending scheme is used whenever read head  127  is positioned greater than first displacement limit  520  and less that second displacement limit  530  from the target position. Of course, different values than ⅛ track and ¼ track for first displacement limit  520  and second displacement limit  530 , respectively, may be used in some embodiments of the invention. The weighting of the position-based blending scheme and the target-based blending scheme may be linear or of a higher order. 
     The position-based blending scheme used to generate position-based blending scheme curve  502  may be a conventional seamless burst-decoding demodulation scheme commonly known in the art in which is constructed to ensure that the measured and actual positions of read head  127  are exactly equal when read head  127  is at the 0, ¼, and ½ track locations. Thus an endpoint  551  of position-based blending scheme curve  502  is fixed at the actual ½ track location, which will vary from the nominal ½ track location for squeezed tracks. Similarly, an endpoint  552  of position-based blending scheme curve  502  is fixed at the 0 track location, and a middle point  553  is fixed at the actual ¼ track location. As with the actual ½ track location, the actual ¼ track location will vary from the nominal ¼ track location for squeezed tracks. It is noted that this variance in the location of endpoint  551  and middle point  553  from the nominal ½ track and ¼ track locations, respectively, is what causes the slope of position-based blending scheme curve  502  to vary for squeezed tracks, resulting in servo loop gain changes and potentially servo loop instability. However, embodiments of the invention contemplate using such a position-based blending scheme only when read head  127  is positioned relatively far from the target position, and therefore when the servo loop is performing a seek operation. In such an operation, instability caused by changes in servo loop gain is not likely to occur. 
     According to embodiments of the invention, a hybrid curve is used to determine the measured position of read head  127  when read head  127  is being controlled by the servo loop of disk drive  110  to a single, specific target position. For example, in  FIG. 5 , hybrid curve  501  is used to determine the measured position of read head  127  when read head  127  has a target position of 0. For each different target position for read head  127 , a unique hybrid curve is used. 
     A number of seamless burst-decoding demodulation schemes are known in the art and are suitable for use as the position-based blending scheme for constructing position-based blending scheme curve  502 . Three seamless burst-decoding demodulation schemes are now provided, although other demodulation schemes known in the art may also be used in some embodiments of the invention. A first seamless burst-decoding demodulation scheme is described by Equations 1A and 1B. Equation 1A defines the position of read head  127  in region AB, i.e., when the actual position of read head  127  is between the 0 track location and the ¼ track location. Equation 1B defines the position of read head  127  in region CD, i.e., when the actual position of read head  127  is between the ¼ track location and the ½ track location. 
     
       
         
           
             
               
                 
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     A second seamless burst-decoding demodulation scheme is described by Equation 2: 
     
       
         
           
             
               
                 
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     A third seamless burst-decoding demodulation scheme is described by Equations 3A and 3B: 
     
       
         
           
             
               
                 
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     The target-based blending scheme used to generate target-based blending scheme curve  503  is a seamless demodulation scheme similar to the position-based burst-decoding demodulation schemes described in equations 3A and 3B, but with one notable difference. Specifically, target-based blending scheme curve  503  is generated with a fixed shape, and therefore does not change with track squeeze. This is in contrast to position-based blending schemes, in which the shape of a curve representing the measured position of read head  127  is a function of physical position changes shape based on how much track squeeze is present (see, for example, curve  202  in  FIG. 2  and position-based blending scheme curve  502  in  FIG. 5 ). In one embodiment, the fixed shape of target-based blending scheme curve  503  is based on a position-based burst-decoding demodulation scheme for a track having nominal track pitch. Thus, in such an embodiment, for a target position set at the 0 track position, target-based blending scheme curve  503  is constructed to begin at the 0 track location, pass through the nominal ¼ track location, and end at the nominal ½ track location. It is noted that for target positions other than the 0 track position, target-based blending scheme curve  503  will not pass through the nominal positions of the 0, ¼, and ½ track locations, as illustrated below in  FIG. 6 , but will still have the same shape as a curve constructed for a target position set at the 0 track position. Further, the shape of target-based blending scheme curve  503  is the same for squeezed tracks as it is for tracks having nominal track pitch. Another property of target-based blending scheme curve  503  is that said curve is fixed at the target position for read head  127 , so that the target position is set equal to the corresponding actual position for that track rather than the corresponding nominal position. For example, for a target position at the ¼ track position for a squeezed track, target-based blending scheme curve  503  is positioned so that a measured position of ¼ track corresponds to the actual (squeezed) ¼ track position, rather than the nominal ¼ track position. This property is illustrated in  FIG. 6 . 
       FIG. 6  is a graph  600  depicting three curves  601 ,  602 , and  603  constructed using a target-based blending scheme for a squeezed track, according to embodiments of the invention. For clarity, curves for only three target positions are illustrated in  FIG. 6 , but in practice a different curve is constructed for each target position of read head  127 . Curve  601  is positioned for a target position at the 0 track position, curve  602  is positioned for a target position at the ¼ track position, and curve  603  is positioned for a target position at the ½ track position. Curve  601  is a continuous curve and, because it is selected for a target position at the 0 track position, passes through the nominal 0 track, ¼ track, and ½ track positions. It is noted that in this way, curve  601  is substantially similar to target-based blending scheme curve  503  in  FIG. 5 . Curves  602  and  603  are constructed with the same shape as curve  601 , but are translated to different locations in graph  600  so that the target position is aligned with the corresponding actual position for the track and not with the corresponding nominal position for the track. Thus, for a squeezed track, curve  602  is positioned in graph  600  so that the target position of ¼ track is aligned with the actual ¼ track location  610  of the squeezed track and not the nominal ¼ track location  611 . Similarly, curve  603  is positioned in graph  600  so that the target position of ½ track is aligned with the actual ½ track location  612  of the squeezed track and not the nominal ½ track location  613 . Consequently, when using curves  601 ,  602 ,  603 , the measured position of read head  127 , i.e., the ordinate of graph  600 , equals the target position when read head  127  is aligned with the corresponding actual position rather than with the nominal position. For example, given a target position for read head  127  of ¼ track, curve  602  is used to determine the measured position of read head  127  as a function of the physical position of read head  127 . As shown in  FIG. 6 , curve  602  is positioned in graph  600  so that the measured position of read head  127  equals the target position of ¼ track when read head  127  is aligned with the ¼ track position  610  of the squeezed track rather than with the nominal ¼ track position. 
     Because each of curves  601 ,  602 ,  603  have identical shapes by definition, there is no change is slope between curves  601 ,  602 ,  603  regardless of track squeeze, thereby avoiding unwanted servo gain variation due to track squeeze. In addition, because the hybrid burst-decoding demodulation scheme described above in conjunction with  FIG. 5  only uses the portion of curves  601 ,  602 ,  603  proximate the target position, i.e., the portions within first displacement limit  520  of the target position, the large position error associated with using such fixed-shape curves is also avoided. 
       FIG. 7  is a flow chart that summarizes, in a stepwise fashion, a method  700  of determining the position of a transducer head of a hard disk drive, according to embodiments of the invention. Method  700  is described in terms of a disk drive substantially similar to disk drive  110  in  FIG. 3 . However, other disk drives may also benefit from the use of method  700 . The commands for carrying out steps  701 - 705  may reside in the disk drive control algorithm and/or as values stored in the electronic circuits of the disk drive or on the storage disk itself. 
     In step  701 , position information is collected from burst pairs on a recording medium. The position information is read by read head  127  as it passes over the burst pairs, e.g., an AB burst pair and a CD burst pair. The raw position of read head  127  is computed based on the position information from each burst pair. In one embodiment, raw position is computed in step  701  using Equations 4A, 4B: 
     
       
         
           
             
               
                 
                   
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                   ( 
                   
                     4 
                      
                     A 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     Q 
                     1 
                   
                   = 
                   
                     
                       C 
                       - 
                       D 
                     
                     
                       A 
                       + 
                       B 
                       + 
                       C 
                       + 
                       D 
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                      
                     B 
                   
                   ) 
                 
               
             
           
         
       
     
     In some embodiments, Equations 5A and 5B may be used to compute linearized positions using the raw positions computed using Equations 4A, 4B: 
         N=ƒ   lin ( N   1 )  (5A)
 
         Q=ƒ   lin ( Q   1 )  (5B)
 
     In step  702 , a preliminary position of read head  127  is computed using a position-based blending scheme using Equations 6A, 6B to calculate the measured position. Alternatively, other methods may be used to estimate the position of read head  127 . For example, the measured position computed in step  702  using a target-based blending scheme may be used. 
     
       
         
           
             
               
                 
                   
                     y 
                     pos 
                   
                   = 
                   
                     
                       
                         b 
                         pos 
                       
                        
                       N 
                     
                     + 
                     
                       
                         ( 
                         
                           0.5 
                           - 
                           
                             b 
                             pos 
                           
                         
                         ) 
                       
                        
                       Q 
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     A 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     b 
                     pos 
                   
                   = 
                   
                     
                       min 
                        
                       
                         ( 
                         
                           
                              
                             N 
                              
                           
                           , 
                           
                              
                             Q 
                              
                           
                         
                         ) 
                       
                     
                     
                       
                          
                         N 
                          
                       
                       + 
                       
                          
                         Q 
                          
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     B 
                   
                   ) 
                 
               
             
           
         
       
     
     In step  703 , a preliminary PES of read head  127  is determined. In a preferred embodiment, the measured position computed in step  702  using the position-based blending scheme, i.e., Equations 6A, 6B, is compared to the target position of read head  127 . 
     In step  704 , the preliminary PES is compared to first displacement limit  520  and second displacement limit  530  to select what algorithm is used to calculate the final measured position of read head  127 . When the preliminary PES of read head  127  is determined to be less than or equal to first displacement limit  520  from the target position, the final measured position of read head  127  is equal to a measured position determined using Equations 7A, 7B, which is a target-based blending scheme: 
         y   t arg   =b   t arg   N +(0.5− b   t arg ) Q   (7A)
 
         b   t arg =min( x   t arg ,0.5− x   t arg )  (7B)
 
     When the preliminary position of read head  127  is determined to be greater than or equal to second displacement limit  530  from the target position, the final measured position of read head  127  is equal to the measured position determined in step  702  using Equations 6A, 6B, which is a position-based blending scheme. When the preliminary position of read head  127  is determined to be less than second displacement limit  530  from the target position and greater than first displacement limit  520  from the target position, the final measured position of read head  127  is determined by Equation 8, which is a weighted combination of the target-based blending scheme described by Equations 7A, 7B and the position-based blending scheme described by Equations 6A, 6B: 
         y=w*y   pos +(1.0− w )* y   t arg   (8)
 
     where w is a typical weighting function, that may be a function of the preliminary PES calculated in step  703 , first displacement limit  520 , and second displacement limit  530 . A typical weighting function is: 
     
       
         
           
             
               
                 
                   w 
                   = 
                   
                     
                       
                          
                         
                           e 
                           pre 
                         
                          
                       
                       - 
                       
                          
                         
                           L 
                           
                             t 
                              
                             
                                 
                             
                              
                             arg 
                           
                         
                          
                       
                     
                     
                       
                         L 
                         pos 
                       
                       - 
                       
                         L 
                         
                           t 
                            
                           
                               
                           
                            
                           arg 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     where e pre  is the prelimnary PES, L targ  is the first displacement limit and L pos  is the second displacement limit. 
     In steps  705 A- 705 C, the final measured position of head  127  is computed using the algorithm determined in step  704 . In step  705 A, the final measured position of read head  127  is determined using Equations 7A, 7B, which is a target-based blending scheme. In step  705 C, the final measured position of read head  127  is determined using Equations 6A, 6B, which is a position-based blending scheme. And in step  705 B, the final measured position of read head  127  is determined by Equation 8, which is a weighted combination of the target-based blending scheme described by Equations 7A, 7B and the position-based blending scheme described by Equations 6A, 6B. 
     In step  706 , the final PES of head  127  is computed using the final measured position for head  127  determined in one of steps  705 A,  705 B, and  705 C. 
     Method  700  is described herein for write operations by disk drive  110 . However, method  700  may also be used beneficially for read operations, according to embodiments of the invention. For read operations, a micro-jog value may be used to determine the position of write head  129  once the position of read head  127  is computed. Such a micro-jog value may be provided by consulting a conventional micro-jog calibration curve. 
       FIG. 8  is a graph  801  of servo loop gain in a disk drive using a conventional position-based demodulation scheme.  FIG. 9  is a graph  901  of servo loop gain across the sectors of a substantially similar disk drive using a hybrid demodulation scheme, according to embodiments of the invention. As shown, loop gain variation is significantly reduced in graph  901 . 
     In sum, embodiments of the invention have the significant advantage of avoiding PES chatter associated with stitched servo-burst demodulation schemes when demodulating position information from a storage disk. In addition, embodiments of the invention avoid the gain variation and related servo loop instability associated with seamless servo-burst demodulation schemes. 
     While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.