an advantage of the invention is a marked reduction in the size requirement of each servo wedge compared with prior art servo systems . some experiments indicate that reductions from 5 to 10 times are possible . the system also maintains the size advantage while simultaneously reducing the native phase - error and frequency requirements of the servowriter . the invention is more efficient than prior art methods because it uses a single integrated servo field with multiple functions . the invention is an improvement over the prior art methods that are essentially only workable as pes fields , with perhaps 1 bit of stm or track - id , and then only using a particular sequence type ( one of the pseudo - noise ( pn ) or pseudorandom sequences ). the present invention allows a solution that includes multiple effective track - id ( tid ) bits and a full sequence set instead of a single antipodally - used sequence of the prior art . the concepts of the invention will be described in four major sections . embodiments of the basic sequences and sequence sets used in the invention will be described first . the sequence sets and the corresponding set of filters essentially specify the servo track mark ( stm ) function . second , methods will be described for arranging such sequence sets on the disk in such a way that digital positional information ( such as track or sector id ) and pes may be encoded . third , methods are described for distributing and coalescing digital location information across multiple servo wedges . finally , detection and signal processing aspects of the invention are discussed . a basic building block of the invention is the design of an underlying sequence set from which the integrated servo fields are built . the arrangement of the sequences in the servo wedges encodes desired digital location information such as the track and sector number while also supplying an analog pes for fractional track positioning . fig1 is a block diagram illustrating an information storage system ( disk drive ) 110 according to an embodiment of the invention . the disk drive includes data recording disk 15 , actuator arm 113 , and read head 112 that are arranged in conventional manner . a write head ( not shown ) will also be included in the same package with the read head . the servo system 90 , read / write electronics 114 , interface electronics 115 , controller electronics 116 , microprocessor 117 , and ram 118 . the basic system components are generally according to the prior art except as described herein . a disk drive can include multiple disks stacked on a hub that is rotated by a disk motor , with a separate heads for each surface of each disk . the term servo wedge 120 will be used to mean the contiguous set of integrated servo fields extending from id to od on the disk . as in the prior art , a disk 15 according to the invention will typically have multiple servo wedges 120 arranged radially across the disk , but only two are shown . fig1 a is an illustration of an embodiment of integrated servo fields 11 on a disk 15 according to the invention . only a small portion of two data tracks are shown . many thousands of tracks typically appear on a disk in an hdd . the width of the data tracks is the width of the data that is written by the heads ( not shown ) in the hdd . the effective reading width of the head may be slightly less than the writing width . only four sequences ( a - d ) are shown in this illustration , but a practical embodiment will include a larger number of sequences as will be described below . in this embodiment the width of the encoded sequences a - d is one half of the data track width . the sequences a - d are preferably written by a servowriter as a part of the manufacturing process . the width of the sequences a - d is equivalent to the servo track pitch . the effective reading width of the read head in this example is , therefore , approximately equal to or slightly less than the combined width of 2 encoded sequences . the read signal will , therefore , necessarily include contributions from at least two encoded sequences . the sequences are selected and arranged on the disk to facilitate decoding of adjacent sequence contributions in the read signal . an integrated servo field for track n is composed of encoded sequences a and b , which are members of a selected sequence set . similarly integrated servo field for track n + 1 is composed of encoded sequences c and d , which are also members of the selected sequence set . fig1 b is an illustration of an alternative embodiment of integrated servo fields 11 t on a disk 15 according to the invention . in this embodiment the width of the encoded sequences a - d is equal to the data track width . sequences a and b for track n are written in tandem with sequence b being offset by one - half the width of a data track . fig1 c is an illustration of an embodiment of an extended sequence 12 that can be used in either of the embodiments described above . extended sequence 12 consists of a sequence 13 of bits b 0 through b i which are determined by the method which will be described in detail below . also shown are optional leading and trailing redundant bits 13 l , 13 t which are duplicates of b i and b 0 respectively . thus , leading redundant bits 13 l is a duplicate of b i which is the last bit in sequence 13 . trailing redundant bits 13 t is a duplicate of b 0 which is the first bit in sequence 13 . the alternative embodiment , which represents a cyclic extension of the sequence 13 , will be called an extended sequence . the additional redundant bits improve the detectability of the sequence due to special sequence properties described below . although particular preferred embodiments described below apply several constraints to the sequence set which are particularly useful for hdd applications , other embodiments of the invention need not include these constraints . for hdd applications the constraints adopted for the described embodiments are : 1 . each sequence in the sequence set must be writeable or otherwise storable in magnetic media . bipolar binary (+ 1 , − 1 ) sequences match this constraint for conventional recording . unipolar binary ( 1 , 0 ) sequences are appropriate for dc - magnet servowriting systems currently under consideration for bit - patterned recording ( bpr ) or discrete track recording ( dtr ). there is no fundamental reason why the sequences have to be binary , so they could in principle be made ternary or even real - valued . for example , embodiments can include ternary (+ 1 , 0 , − 1 ) sequences , from a combination of the binary and unipolar options . the particular embodiments and examples described herein use the bipolar binary constraint . 2 . each sequence in the set should be reasonably dc - free as recorded on the disk ; i . e ., extreme sequences of bits should be avoided . preferably each sequence should sum to approximately zero . this property reduces sensitivity , in the matched filter detection banks in the read channel hardware , to low - frequency problems in perpendicular magnetic recording system or ac coupling poles , and eliminates static dc offset problems in the arm electronics ( ae ) and channel electronics . 3 . as laid out on the disk , adjacent sequences ( in the cross - track direction ) are selected to be orthogonal , that is , their dot product is zero . this means that the analysis matched filters corresponding to these sequences do not interfere with each other . this allows desired sequence to be separated out from other sequences present in the read signal using the filters in the read channel hardware . an important distinction between this constraint and that of standard orthogonal sequence sets is that only those sequences which are adjacent on the disk must be necessarily mutually orthogonal , i . e . the sequence set can contain members that are not mutually orthogonal . the combination of constraints ( 1 ) and ( 3 ) means that exactly one half of the sequence components ( bits ) change from track to track , which limits the pes - dominating cross - track transition noise . finally , the combination of ( 2 ) and ( 3 ) means that second - order head nonlinearities do not affect the analysis filter outputs . 4 . adjacent sequences on the disk are constrained to be orthogonal under cyclic extension and time shifts up to a selected parameter which will be called “ tau .” this property will be called the plesiosynchronous property . plesiosynchronous will be used as synonymous with “ loosely synchronous ” and plesiosynchronous sequence sets are “ zero correlation zone ” sequence sets . this property provides insensitivity to phase error in the servo - writing process , improves the autocorrelation properties of each sequence for stm purposes , and is useful as a signal processing check in the detection electronics . those skilled in the art will note that obvious changes to these constraint details may lead to other types of sequence sets which are within the scope of this invention . once the number of bits in a sequence is selected , application of the 4 constraints listed above generates a novel family of sequence sets , which can be found in a straightforward way by exhaustive computer search . four of the simplest such sets ( enclosed in parentheses ) with a length of 8 bits are shown in fig2 . these sequences are not strictly dc - free , but each sequence has at least 2 bits of opposite sign so that the sequences sum to a max of +/− 4 . fig2 shows the four binary , mutually plesiosynchronous sequence sets of length 8 with tau = 1 . in the special case of the sequence sets of fig2 , all sequences in the set are mutually orthogonal , and remain orthogonal under a cyclic shift of 1 unit . each sequence is shifted one unit with respect to all other sequences . an antipodal sequence is obtained by inverting each of the bit values in the sequence . because the antipodal sequences of each set are usable , there are a total of 8 sequences available for use in the integrated servo field in this example . this point will be discussed in more detail below . the constraint that a sequence and its negative ( antipodal sequence ) cannot be adjacent in a servo wedge on the disk avoids null - signal conditions which are not appropriate for positive stm detection . antipodal sequences are permissible and commonly - used in pes - only applications such as one - step pes and null - phase pes . the resulting adjacency constraints , in addition to any plesiosynchronous constraints arising from the 3rd sequence set in fig2 as an example , are shown in table 1 . the 4 sequences 21 , 22 , 23 , 24 of the third sequence set in fig2 are listed as sequence numbers 1 through 4 respectively , and their 4 corresponding antipodal sequences are represented with “^” symbols . the presence of “*” in the cells means that the two sequences may be adjacent on the disk . no sequence is orthogonal to itself or its antipodal sequence , but otherwise in this example all sequences are orthogonal to each other and can be adjacent on the disk . fig3 shows a more complex example of computer - generated sequence sets , in which not all of the sequences in the set are mutually plesiosynchronous . in fig3 there are 6 sequence sets ( a ′- f ′) of 9 exactly dc - free length 12 sequences . those sequences which are plesiosynchronous have parameter tau = 1 . this set of sequences illustrates the more general case in which the size of the sequence set can be increased by allowing non - orthogonal sequences to be part of the set . the advantage of orthogonal sequences is maintained by arranging the order that sequences appear on the disk so that adjacent sequences ( in the cross - track direction ) on the disk are , in fact , orthogonal . this constraint can be implemented because the sequences are predetermined and are fixed once written on the disk , which is not the case for general communications . the sequence set c ′ in fig3 has the interesting property that the palindrome of each sequence in the set is also in the set ( within a sign ). the phrase “ palindromic set ” will be used to describe this property . servo patterns based on palindromic sets can be decoded even if all patterns are reversed , using the same basic read channel electronics hardware . such a property is useful in bpm manufacture of a and b sides of the disk using the same master . ( see , for example , u . s . published application 20080266701 ). the plesiosynchronous properties of the 9 sequences in set c ′ of fig3 are shown in the graph in fig4 and labeled as 1 through 9 with 1 being the first sequence in set c ′ of fig3 and 9 the last one . the vertices represent the sequence , and the presence or absence of edges denotes the presence or absence of the plesiosynchronous property between the corresponding sequences . table 2 describes the sequence relationships for the sequences of fig4 with antipodal sequences which are listed using “^” symbols . the information in table 2 is the equivalent of a graph . a complete graph is a graph in which all vertices are connected to all other vertices by edges . there are 4 complete subgraphs of 4 sequences ( e . g ., sequences 1 , 2 , 4 , and 5 ) which can be used in the same manner as the length 8 sequence sets of fig2 . the sequences are the vertices of the graph . the edges , connecting the vertices , of the graph specify which sequences may be adjacent on the disk . however , these distinct sequence sets are connected to each other , providing new degrees of freedom and more complex disk pattern configurations than would be allowed with the 4 sets used independently . the minimum possible length of sequences ( in a set of order 4 ) to be strictly dc - free is 12 . all such sets are listed in fig3 . the exposition thus far illustrates the tradeoffs between the number of sequences available for use , and the complexity ( that is , the length ) of the sequences . table 3 shows that the tradeoff also involves the plesiosynchronous parameter , tau . table 3 shows the maximum order m of fully mutually plesiosynchronous sets as a function of the sequence length l and parameter tau . specific embodiments for the pattern of sequences as laid out on the disk to encode track - id data and pes will now be described . examples of the restrictions on which sequences can be adjacent have been noted above . with little loss of generality , we may consider the case in which order in which patterns appear on the disk , from track to track , is a periodic pattern of period t . such a cyclic pattern can be drawn on a graph as a closed path which may repeat vertices , but not edges . such a path will be called a “ cycle .” if an admissible cycle , for example , is 1 - 2 - 3 - 4 - 1 - 2 - 3 - 4 - 1 - 2 - 3 - 4 etc . and the head signal can be determined to be composed of sequences 2 and 3 of some relative amplitude , then the head must be located in the unique point in the cycle which is along the edge joining the vertices ( corresponding to the sequences ) 2 and 3 . fractional track information ( that is , the pes ) is determined by the relative amplitude of the two sequences in the signal from the read head ( sensor ). for example , if the two amplitudes are the same , then the head is situated halfway on the edge between vertices 2 and 3 on that cycle . generalizing from this example , if the head &# 39 ; s reading width is exactly equal to the servo track pitch ( one half of the data track width ), we may determine ( except at a finite number of singular points on the cycle ) both the integral and the fractional location of the head , modulo with length of the cycle t . the fractional error signal ( the pes ) will be discussed further below . it is advantageous to maximize the cycle length t , which has the effect of increasing the number of effective track or sector id bits in a single measurement . this problem is equivalent to the well - known problem of finding an eulerian cycle on the graph , that is , a cycle which uses every edge exactly once . by the euler cycle theorem , it is possible to show that there always exists a cycle of length 2 * n *( n − 1 ) for a complete graph of n sequences and n antipodal sequences . for example , where n = 4 , there is a length 24 cycle . the effective number of track or sector bits which can be achieved with a complete set of n sequences is approximately 1 + 2 log 2 ( n ). in the case where 3 sequences exist in the read signal , the graph does not encompass all constraints which need to be applied to the physical system . in particular , the 1st and 3rd of 3 adjacent sequences cannot be antipodal . this extra constraint is typically quite weak ; for example , it is easy to show that length 24 eulerian cycles exist on the graph which obey this additional constraint . similar considerations apply to more complex examples , such as systems based on mixed sequence sets such as those depicted in fig4 . there exist 80 - length eulerian cycles on this graph , yielding approximately 6 . 4 effective digital bits available for track or sector id . a complete - graph sequence set of order 7 is required to exceed this number of effective bits . such sequence sets exist ( as shown in table 3 ), however , those sequences are longer and / or more complex . the pes for fractional track positioning of the head in embodiments of the invention is obtained from signal amplitudes from two or more sequences . in the embodiment of fig1 a , the head &# 39 ; s reading width is larger than the ( cross track ) width of a sequence written on the disk but smaller than twice the width of a sequence . in this case , depending on the relative location of the read head and the written track edges , the read head signal always contains a nominally - linear combination of two or three sequences from adjacent tracks . the fractional part of the track number ( that is , the pes ) is proportional to (| v1 |−| v2 |)/(| v1 |+| v2 |), where v1 and v2 are the signal amplitudes read from adjacent sequences and the absolute values are necessary because antipodal versions of the sequences may be present . if the head &# 39 ; s reading width is positioned over 3 sequences , and the middle sequence amplitude is v2 , then the pes is proportional to (| v1 |−| v3 |)/(| v1 |+| v2 |+| v3 |). alternative pes calculations are possible . if the head is over two sequences , then location detection defaults to the algorithm outlined above . in either case , the two or three amplitudes fully determine the location on the cycle . alternative embodiments can use multiple fields in a single wedge . an example of a dual - field system is illustrated in fig1 b . in this example , the sequences in the two fields are each as wide as the data track width but are written in tandem sequence along the tracks ( down - track direction ), which extend horizontally in the figure . in this embodiment the second sequence field ( sequences b & amp ; d on the right ) are positioned one half of a data track width offset ( out of phase ) with the corresponding sequences a & amp ; c ( with respect to the cross track direction ). as an example , assume that the read head reading width is approximately equal to the data track width and the disk is rotating under the read head from right to left . if the head is centered over track n + 1 , the read path passes directly over the sequence c field on the left and then straddles sequences b & amp ; d on the right . in this type of embodiment , there will be either 1 or 2 sequences under the head at one time . if the head reads one sequence in the first field , for example , then the head typically can read two adjacent sequences in the second field . similarly if the head is aligned with respect to the boundaries so that only one sequence in the second field is read , then two sequences can be read from the first field . this one half data track offset arrangement mimics the standard quad - burst pes arrangement of the prior art sufficiently to allow standard pes calculations to work in the case when two adjacent fields are read . when the head is not centered on either field , the head might read two adjacent sequences in each field . this embodiment is easily configurable to mimic the characteristics of prior art pes systems because the amplitude of the signal read for adjacent field tells the servo system where the head is in relation to center of the data track in the same way that the amplitude of the signals read from quad - burst pes do . it is clear from the discussion above , that the number of sequences required to span an entire drive in a single period t can be very large , because the number of tracks on each disk in an hdd is currently in the many hundreds of thousands . an efficient method to increase the effective number of track or sector bits is to distribute the required information into multiple fields . it is possible to share information between multiple fields in a servo wedge , or to share information fields in multiple servo wedges ( or both ). in this section , two examples of these techniques are given . in the first example , single fields are used in each wedge and track - id information is distributed across 4 adjacent wedges . alternatively the 4 fields could be included in a each wedge with a significant increase in the area taken up by sequences . in this example only track - id information will be shown , but sector - id information can be added using the same concepts . the 4 consecutive wedge distribution system is appropriate when the head &# 39 ; s reading width is known to be sufficiently larger than the servo track pitch ( typically one - half the width of a data track ). in this embodiment the full track - id is recovered by reading 4 consecutive fields and uniquely mapping the sequences from the 4 fields to the expected track - id . in this embodiment a chinese remainder theorem ( crt ) mapping is used , but other mappings can be used to transform a set of sequences read in one or more servo wedges into a track - id . for example , a table lookup method could map an ordered set of sequences into a track - id , sector id or other desired information . fig5 illustrates the arrangement of a cycle of 64 sequences m64 in a first servo wedge 71 of the set of four wedges . each sequences is one half the width of the data track ; thus there are two sequences per track . fig6 illustrates the set of four servo wedges 71 , 72 , 73 , 74 . in this illustration ( which is not drawn to scale ) only selected servo fields are shown and the data which would be recorded between the servo fields is not shown . multiple tracks are represented in the cross - track direction which is vertical in the figure . the disk patterns in fig6 are repeated from id to od . for servo wedge 71 a cycle of 64 sequences m64 repeats in the cross track direction . for servo wedge 72 a cycle of 63 sequences m63 is repeated . for servo wedge 73 a cycle of 61 sequences m61 is repeated . for servo wedge 74 a cycle of 59 sequences m59 is repeated . a set of 4 cycles m64 , m63 , m61 , m59 is shown in fig7 which are based on the length 12 sequences in sequence set c ′ of fig3 and their antipodal sequences which are represented by the “ a ” symbol . there are a total of 18 allowed sequences . these cycles have the property that any 3 adjacent sequences are mutually different and plesiosynchronous . a chinese remainder theorem ( crt ) mapping is used which guarantees uniqueness and is implemented by means of the set of 4 cycles shown in fig7 , each of differing periods t = 64 , 63 , 61 and 59 ( corresponding to m64 , m63 , m61 , m59 ) which are relatively prime to each other . the resulting system identifies the integral portion of the track - id ( modulo ti ), with i = 1 , 2 , 3 , 4 , and by the uniqueness part of the chinese remainder theorem ( crt ), recovers the entire track - id modulo 64 * 63 * 61 * 59 = 14511168 servo tracks , which is sufficiently large for current hdds . note that in this example two servo tracks exist for each data track . as an example , assume that the head is reading along the path 82 shown in fig6 , which is assumed to be centered on the 1st data track from the bottom of the figure . in servo wedge 71 , the head will read the 1st pair of sequences in cycle m64 , which are represented by the notation m64 ( 1 , 2 ). similarly in servo wedges 72 , 73 , 74 the head will also read the 1st pair of sequences in cycles m63 , m61 , and m59 . one conceptually simple implementation could use a table to translate the four pairs of sequences into a track number , but calculations as described above may be preferable . for comparison when the head is reading along the path 83 shown in fig6 , it is assumed to be centered on the 33rd data track from the bottom of the figure . in servo wedge 71 , the head will the 1st pair of sequences in cycle m64 , which are again m64 ( 1 , 2 ). but in servo wedge 72 the head will read the 2nd and 3rd sequences in cycles m63 = m63 ( 2 , 3 ), because cycle m63 is one sequence shorter than m64 . it follows that in servo wedge 73 the head will read the sequences m61 ( 4 , 5 ), and in servo wedge 74 the head will read the sequences m59 ( 6 , 7 ). thus , the set of sequences uniquely corresponding to each track is systematically determined . a location identifier decoder that implements a method as defined above will described as using a chinese remainder solver . only track - id numbers are mentioned above , but the concepts of the invention can be extended to include sector identifiers . sector encoding can be achieved in several ways . there can be hundreds of sectors per track . one method is to use a second group of filters to decode one of the other sets of sequences shown in fig3 , for example . a given servo wedge could utilize either sequence set c ′ or sequence set d ′ to encode a sector bit of ‘ 0 ’ or ‘ 1 ’ respectively . as another alternative , sequences can be stolen from the cycle for that servo wedge . for example , one can encode the sector using the antipodal sequence of the first sequence field . a second method is to use antipodal sequences to encode the sector bit rather than utilizing the antipodal sequences to construct longer cycles . more efficiently , one can use two different graphs for the first sequence . here the key is that there is a method to encode 1 bit of information for each servo wedge that can be used for a distributed sector identifier ( regardless of distribution method ). in this embodiment , two sequences are used to generate two different stms to encode this bit . a third method introduces another stm type to encode the sector bit for a given servo wedge . prior art devices use a similar technique by utilizing two different stm patterns . however , the method by which the stm is encoded is different from the prior art . the graph type encodes the sector bit . for example , referring to fig4 , the stm1 graph could use nodes +/− 1 , +/− 2 , +/− 4 and + 5 . the stm2 graph could use nodes +/− 6 , +/− 8 , +/− 9 and − 5 . a preferred embodiment takes advantage of the orthogonality constraints of the design to detect the stm , the sequences , and the amplitude of the sequences by means of a matched filter . in a matched - filter detection system , each sequence determines both the pattern on the disk ( which in this case will be a cyclic extension of the sequence ) and the correlation filter used to detect the presence of that sequence . these sequence sets have fast algorithms to determine the multiple outputs of the analysis filter bank from the single input representing the head signal . fig8 shows an example filter bank 81 implementing a fast algorithm for a sequence set ( sequences 21 , 22 , 23 , 24 ) in fig2 in which each component of the sequence (+ 1 or − 1 ) on the disk is sampled m times , with a boxcar accumulator 82 to average the m results . the output labeled a corresponds to sequence 21 , output b corresponds to sequence 22 , output c corresponds to sequence 23 , and output d corresponds to sequence 23 , the complexity of the resulting filter bank is essentially dominated by the delay elements . there are 10 2 - input adds and 21m delays . similarly simple filter - bank implementations are possible with more - complex sequences sets of the types considered above . fig9 shows the output of the matched filter bank for the 9 - sequence version in which the head signal contains a linear combination of a maximum of two sequences , corresponding to the filter outputs graphed with lines with triangles and circles . the resulting information ( which sequences are detected , and their amplitude ) gives track or sector id information as well as pes . an example stm detection rule is : find a location with sufficient total absolute amplitude in which the amplitude of each filter output is sufficiently close to zero ( see labeled points in fig9 ) on either side of the maximum . the second constraint is helpful to reduce false stms and comes from the plesiosynchronous tau parameter . fig1 is a block diagram illustrating a servo system 90 according to an embodiment of the invention . a plurality of sequence filters 92 as described above detect the presence of the predetermined sequences in the input data stream . the input for the sequence filters 92 are analog - to - digital converter ( adc ) samples from the read channel ( not shown ) which processes the signal from the head . the stm / seq detector 94 uses the output from the sequence filters 92 and supplies signals to the location identifier decoders : tid decoder 96 and the sector decoder 97 . the pes muxing unit 95 uses the output from the sequence filters 92 as well as a signal from the stm / seq detector 94 . the hard disk controller ( hdc )/ servo processor 100 supplies an expected tid to the tid decoder 96 , which in turn supplies the actual tid to the hdc / servo processor 100 . the sector decoder 97 supplies the sector id to the hdc / servo processor 100 . the pes signal for hdc / servo processor 100 comes from the pes muxing unit 95 , which uses the output from the sequence filters 92 as well as a signal from the stm / seq detector 94 . while the invention has been illustrated with reference to the embodiments , it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the spirit and scope of the invention . accordingly , the disclosed embodiments of the invention are merely illustrative and not intended to limit the scope of the invention as specified in the appended claims .