fig1 a and 1 b are schematic representations of the well - bore guidance system , according to some embodiments of the invention . in particular , fig1 a and 1 b show a rotary steerable tool 1 connected to a drill bit 3 , according to some embodiments of the invention . like features are referenced with like numerals . the rotary steerable tool comprises an inertial measurement unit ( imu ) 4 , a flexible shaft 5 and an outer housing 6 . the imu may provide measurements of acceleration and angular rate about three orthogonal acceleration axes 7 and three orthogonal gyro axes 8 respectively . a computer ( not shown ) may calculate on the basis of these measurements , the direction , i . e . inclination and azimuthal deviation , and / or the position of the imu . the computer may also calculate the velocity of the imu . given that the spatial relationship between the imu and the drill bit is known , the calculations of spatial position and velocity may be extrapolated to provide a measure of drill bit direction , position and velocity . the tool face deflection angle may also be calculated . the imu and computer together form an inertial measurement system . this system may be configured either as an attitude and heading reference system to provide directional survey data , or as a full inertial navigation system ( ins ) in order to provide both directional and positional survey data . the direction and / or position of the drill bit may be calculated with respect to a pre - determined reference frame . in addition , the computer may be provided with depth / well bore hole path length information . in full inertial navigation mode , depth information may be used to obtain accurate co - ordinate position data . by combining the inertial system data with independent depth measurements , it is possible to bound the growth of inertial system error propagation . in fig1 b , the imu is positioned in the rotating shaft 9 at the up - hole end of the rotary steerable drilling tool . in fig1 a , the imu is positioned in the outer housing of the rotary steerable drilling tool ; the non - or slowly - rotating section . fig4 shows how steering commands are generated in a down - hole closed loop control system , according to some embodiments of the invention . in particular , fig4 shows the down - hole closed loop control system 10 , according to some embodiments of the invention . initial surface input data 11 , which comprise start co - ordinates and planned bore - hole trajectory , may be input into target position means 12 together with continuous measured bore path length updates 13 ( surface to rotary steerable system ). the target position means may generate target direction and / or position information as a function of bore hole path length . this information may then be input into a difference means 14 together with ins direction and / or position estimate information from the ins 15 . the difference between the planned direction and / or position and actual direction and / or position may then be input into well bore axes resolution means 16 . the well bore axes resolution means may then resolve the direction and / or position differences into well bore axes . this information may then be fed into steering command generation means 17 , which generates steering commands to pass to the rotary steerable tool bend unit 18 in the rotary steerable tool 19 . the rotary steerable tool may incorporate an inertial measurement unit 20 and is connected to a drill bit 21 . fig5 shows how steering commands are generated in a surface control system with possible manual intervention , according to some embodiments of the invention . fig5 shows a system in some embodiments of the invention in which the closed loop control system is located on the surface in a surface unit 22 . in fig5 , features which correspond to those shown in fig4 are referenced with like numerals . the additional features are a down hole unit 23 , a surface control unit 24 , a two - way communications link 25 , a drive unit 26 and operator interface 27 . the provision of the closed loop control system at the surface allows for possible operator intervention in circumstances where this is necessary . for example , if problems are encountered during the automated guidance process and a change of well - bore trajectory is required . thus by utilizing an inertial measurement system , which provides continuous and accurate information concerning the direction and / or position of the drill bit , and comparing this information with pre - planned well bore trajectory information , a closed loop control system for the automatic guidance of rotary steerable tools is achieved . in some embodiments in which only direction calculations are used , the estimated inclination and azimuth readings at a given well depth / bore hole path length may be compared with a stored profile of these quantities corresponding to the required well profile . steering commands may then be generated in proportion to the difference between these estimates . the differences between the desired and estimated inclination and azimuth may be resolved into steering tool axes , using the estimated tool face angle , to form the signals to be passed to the bend unit of the rotary steerable tool . δ x r ( d )= { circumflex over ( x )} r ( d )− x r ( d ) in some embodiments in which position calculations are used , the position estimates , which may be generated in a local vertical geographic reference frame , may be compared with the desired trajectory profile specified in the same coordinate frame , as a function of well depth . in vector form : where x r ( d )= reference trajectory position at depth d , specified in reference axes { circumflex over ( x )} r ( d )= estimated position at depth d , specified in reference axes δx r ( d ) position error depth d , specified in reference axes the differences between the estimated and desired positions may be transformed into well bore axes using the attitude estimates generated by the inertial measurement unit , to form : δ ⁢ ⁢ x w ⁡ ( d ) = [ δ ⁢ ⁢ x δ ⁢ ⁢ y δ ⁢ ⁢ z ] = c r w ⁡ ( d ) ⁢ δ ⁢ ⁢ x r ⁡ ( d ) where c r w ( d )= direction cosine matrix relating reference and well bore axes δx w ( d )= position error at depth d , specified in well bore axes δx , δy , δz = components of position error the z axis of the well bore coordinate frame ( xyz ) is coincident with the along - hole axis of the well , and the x and y axes are perpendicular to z and to each other . steering commands ( α and β ) may then be derived as a function of the lateral positional errors specified ( δx and δy ) in well bore axis : other control strategies may be adopted , rather than the simple form shown here . for example , steering signals may be derived taking into account the rates of change of the position error components . in some embodiments , the closed loop operation may include activation or reaction limits which could be specified or changed as required . this feature would inhibit the response of the control system to small measurement variations , thus suppressing mico - tortuosity in the drilled well path , the objective being to provide a smooth well path to the target location . the activation limit settings may be governed by prevailing drilling conditions and formation effects . fig2 is a block diagram of an inertial navigation system , according to some embodiments of the invention . the ins is shown here in configuration for drill bit position calculation . fig2 shows the imu 30 which comprises gyroscopes 31 and accelerometers 32 . the measurements taken by the gyroscopes concerning angular rate may be passed to an attitude computation means 33 . the attitude computation means may use the angular rate measurements and information concerning the earth &# 39 ; s rate 34 and may compute the attitude of the imu . this may be output in the form of a direction cosine matrix 35 . an acceleration output resolution means 36 may take the acceleration measurement information output from the accelerometers and the direction cosine matrix and may pass this information onto a navigation computation means 37 . the navigation computation means may then produce inertial navigation system ( ins ) velocity estimates 38 . the estimates 38 may be first fed into a coriolis correction means 39 , the output of which is added by means 40 to the input of the navigation computation means forming a first feed back loop . the ins velocity estimates may be second fed into a velocity integration means 41 which produces ins position estimates 42 . the position estimates may be first fed into a gravity computation means 43 the output of which is added by means 44 to the input of the navigation computation means forming a second feed back loop . the ins position estimates may also be used to compute the components of earth &# 39 ; s rate which are fed into the attitude computation means . finally the ins position estimates may be output from the ins to provide positional information . in order to limit , or bound , the growth of errors in the ins arising as a result of instrument biases and other errors in the sensor measurements , independent measurements of bore hole path length may be used . these measurements may be compared with estimates of the same quantities derived from the ins outputs and used to correct the ins as indicated in fig3 . alternatively , zero velocity updates may be applied at pipe connections when the down hole system is known to be stationary , to achieve a similar effect . fig3 is a block diagram showing the use of depth information in conjunction with the inertial navigation system , according to some embodiments of the invention . in particular , fig3 shows ins 50 path length estimates 51 being differenced with depth sensor 52 path length estimates 53 by difference means 54 . the ins path length estimates may be derived from the ins position estimates and may be received from the ins 50 . the depth sensor path length estimates may be derived from a depth sensor 52 and signal processor 55 . the difference between the two sets of estimates may then be passed to an error model filter 21 which may be a kalman filter . the error model filter may first apply a gain to the difference data at gain means 56 . the output of the gain means may be fed into an ins error model means 57 , the output of which may be fed into a measurement model means 58 and a resent control means 59 . the output of the measurement model means may be taken away from the difference data which is initially input into the error mode filter and the resultant signal may be input into the gain means . the output of the resent control means may be input into the ins error model and the ins itself . thus the ins is able to output a corrected estimate of borehole trajectory 60 . as described above , the imu provides measurements of acceleration and angular rate about three orthogonal axes . this is typically achieved using three single axis accelerometers and three single axis gyroscopes , the axes of which are mutually orthogonal . alternatively , the three single axis gyroscopes may be replaced by two dual - axis gyroscopes . while it is often the case that the sensitive axes of the inertial sensors are configured to be perpendicular to one another , this is not essential , and a so - called skewed sensor configuration may be adopted . provided the sensitive axis of one of accelerometers and one of the gyroscopes does not lie in the same plane as the sensitive axes of the other two accelerometers and gyroscopes respectively , it is possible to compute the required readings about three mutually orthogonal axes . in addition to the survey data produced by the imu system described above , other survey data generated by a conventional mwd survey tool located further up the tool string may be used in correlation with the imu calculations . this data would provide additional survey checks and an increased confidence in the calculated well path position . in the description , numerous specific details such as logic implementations , opcodes , means to specify operands , resource partitioning / sharing / duplication implementations , types and interrelationships of system components , and logic partitioning / integration choices are set forth in order to provide a more thorough understanding of the present invention . it will be appreciated , however , by one skilled in the art that embodiments of the invention may be practiced without such specific details . those of ordinary skill in the art , with the included descriptions will be able to implement appropriate functionality without undue experimentation . references in the specification to “ one embodiment ”, “ an embodiment ”, “ an example embodiment ”, etc ., indicate that the embodiment described may include a particular feature , structure , or characteristic , but every embodiment may not necessarily include the particular feature , structure , or characteristic . moreover , such phrases are not necessarily referring to the same embodiment . further , when a particular feature , structure , or characteristic is described in connection with an embodiment , it is submitted that it is within the knowledge of one skilled in the art to affect such feature , structure , or characteristic in connection with other embodiments whether or not explicitly described . in view of the wide variety of permutations to the embodiments described herein , this detailed description is intended to be illustrative only , and should not be taken as limiting the scope of the invention . what is claimed as the invention , therefore , is all such modifications as may come within the scope and spirit of the following claims and equivalents thereto . therefore , the specification and drawings are to be regarded in an illustrative rather than a restrictive sense .