Abstract:
The invention relates to the field of gun-launched guidance systems and to a navigation system based on inertial sensors mounted in a spinning projectile using at least one rotation sensing device with input components perpendicular to the spinning body&#39;s longitudinal axis, and an appertaining method for upfinding. The phase of the sinusoidal angular rate as detected by a phase-locked loop or correlator is used to determine the local vertical orientation. This invention may be used to align the inertial navigation system in spinning projectiles in ballistic trajectories, which can include artillery shells, satellites or underwater torpedoes.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     The invention relates to the field of gun-launched guidance systems and to a navigation system based on inertial sensors mounted in a spinning projectile using at least one rotation sensing device with input components perpendicular to the spinning body&#39;s longitudinal axis, or at least one acceleration sensing device with input components along the spinning body&#39;s longitudinal axis.  
         [0002]     A projectile in flight follows a trajectory defined by an interaction of gravity, aerodynamics, and mechanical forces due to spin, shape and possible steering fins. The projectile&#39;s flight phases can be described in terms of a pre-launch phase, launch phase, and ballistic phase.  
         [0003]     In the pre-launch phase, before launch of the projectile (e.g., an artillery shell), enough navigation information is available to perform a pre-launch alignment of the on-board inertial navigation system. The launch phase is characterized by high-G forces that occur during launch. During the launch phase, most navigation systems will not be able to navigate due to these high-G forces, and it is necessary to perform a post-launch alignment of the inertial system, as described below.  
         [0004]     After the launch phase, i.e., at the start of the ballistic phase, the navigation system has to be aligned before it can navigate. At launch, parameters such as elevation angle, muzzle velocity, heading and spin rate are known to an extent needed for a coarse alignment of the navigation system. The roll angle (the angle about the projectile&#39;s longitudinal axis, or axis roughly in parallel with its direction of travel) of the projectile is however not known. Due to the projectile&#39;s spin, the roll angle is also rapidly changing. The roll angle must therefore be established to a degree that the coarse alignment accuracy provides a sufficient initialization for a successful subsequent fine alignment phase. This process of estimating the roll angle in a spinning projectile is referred to as ‘Upfinding’.  
         [0005]     During the ballistic phase of the trajectory, the pitch angle of the shell will decrease at a small angular rate. When the shell spins, the pitch rate can be observed in an axis perpendicular to the spin axis as a sinusoidal rate, where the maximum and minimums occur when that axis is in the horizontal plane, see  FIG. 1 . The phase of the sinusoidal rate in an axis perpendicular to the projectile&#39;s spin axis can therefore be used to indicate the shell&#39;s roll angle. An accelerometer with its input axis co-aligned with the shell&#39;s spin axis and mounted off center in the shell will pick up a sinusoidal Coriolis acceleration due to the interaction of its velocity vector around the shell&#39;s center and the change in the shell&#39;s pitch rate. The phase of the sinusoidal Coriolis acceleration can also be used to indicate the shell&#39;s roll angle.  
         [0006]     Inertial sensors that are used to determine positional and orientation parameters, including the time derivatives of these parameters, generally exceed their operational ranges during the high-g shock at launch.  
         [0007]     In an existing solution to the upfinding problem, a pitch- (or yaw-angle gyroscope is positioned in the shell to detect rotation in an axis perpendicular to the spin axis. The pitch-angle gyroscope detects the change in the shell&#39;s pitch angle as the shell travels in a ballistic trajectory. As the shell spins around its longitudinal axis, the gyroscope in the perpendicular axis picks up the shell&#39;s pitch rate as a sine wave. The phase of this sine wave is directly related to the shell&#39;s roll angle and can be used to estimate the roll angle. In particular, as the input axis of the gyroscope points upward or downward, the detected rotation is approximately zero; when the axis of the gyroscope is horizontal, the gyroscope senses maximum positive or negative pitch rate.  
         [0008]     Alternately, an accelerometer with its input axis along the shell&#39;s longitudinal axis can use the Coriolis acceleration to estimate the shell&#39;s roll angle. The measured Coriolis acceleration will also exhibit a sine wave related to the shell&#39;s roll angle.  
         [0009]     The existing solutions to the upfinding problem are described, e.g., in Lucia, D. J., “Estimation of the Local Vertical State for a Guided Munition Shell with an Embedded GPS/Micro-Mechanical Inertial Navigation System”, MIT Masters of Science Thesis, May 1995 (“Lucia”), and Gustafson, D. E., Lucia, D. J. “Autonomous Local Vertical Determination for Guided Artillery Shells”, Autonomous Local Vertical Determination for Guided Artillery Shells, D. Gustafson, Draper Laboratory; D. Lucia, Falcon AFB, pp213-221 52nd Annual Meeting Proceedings “Navigational Technology for the Third Millennium” Jun. 19-21, 1996, Royal Sonesta Hotel, Cambridge, Mass. (“Gustafson &amp; Lucia”).  
         [0010]     U.S. Pat. No. 5,886,257 describes an apparatus and a method for making an autonomous local vertical determination for a ballistic body using recursive Kalman filtering to determine the roll angle (local vertical direction).  
         [0011]     U.S. Pat. No. 5,372,334 describes the use of a retroreflector mounted on the projectile to implement an improved local vertical reference determination.  
         [0012]     U.S. Pat. No. 6,163,021 describes a navigation system for spinning projectiles utilizing a magnetic spin sensor and a GPS/INS Kalman filter.  
         [0013]     An article by Bar-Itzack, I. Y., Reiner, J. and Naroditsky, M., titled “New Inertial Azimuth Finder Apparatus”, AIAA Journal of Guidance, Control and Dynamics, Vol. 24, No 2, March-April 2001, pp 206-213 cites Israeli Patent 129654, filed Apr. 28, 1999, titled “Method and Apparatus for Determining the Geographical Heading of a Body,” that discusses finding a geographical north of a body. All of these references are herein incorporated by reference.  
         [0014]     While these references disclose various ways of finding a solution to the upfinding problem, none of them disclose an optimized system utilizing a phase-locked-loop (PLL) or a correlator or the enhancement from complementary filtering the roll angle with roll rate.  
       SUMMARY OF THE INVENTION  
       [0015]     The objective of the invention is to provide a solution to the upfinding problem in spinning projectiles by using a PLL or correlator mechanism that can be enhanced with a complementary filter. The new upfinding solutions according to the invention are simple and work in a general environment by using either accelerometers or gyros in the upfinding process under appropriate conditions.  
         [0016]     The phase of the sinusoidal signal from an inertial sensor as detected by a phase-locked loop or a correlator is used to determine the local vertical orientation. This invention may be used to align the inertial navigation system in spinning projectiles in ballistic trajectories, which can include, among other things, artillery shells, satellites and underwater torpedoes.  
         [0017]     A navigation system may be mounted in a spinning body using at least one angular sensing device measuring an angular rate perpendicular to the body&#39;s spin axis or Coriolis acceleration off-center along the body&#39;s spin axis. The measurements from the inertial sensing device exhibit a sine-wave pattern, where the sine wave&#39;s phase angle is in synchronization with the spinning body&#39;s roll angle, which relates to the local vertical. A PLL or correlator may then be used to track the phase of the sinusoidal wave. 
     
    
     DESCRIPTION OF THE DRAWINGS  
       [0018]     The invention is explained in greater detail below and references the following drawings.  
         [0019]      FIG. 1A  is a pictorial diagram of a projectile illustrating rotational aspects;  
         [0020]      FIG. 1B  is a diagram illustrating the various rotational axes in a three-dimensional system;  
         [0021]      FIG. 2  is a pictorial diagram illustrating motion components of the accelerometer located on the projectile;  
         [0022]      FIG. 3  is a block diagram illustrating the overall architecture of an upfinding system including the use of a complementary filter;  
         [0023]      FIG. 4  is a block diagram showing the inputs, outputs, and feedback mechanisms for the PLL circuit and illustrating one implementation of a phase detector;  
         [0024]      FIG. 5  is a block diagram for the circuit of  FIG. 4  utilizing a correlator instead of a PLL as a roll angle detector; and  
         [0025]     FIGS.  6 A-D are graphs showing the correlation of measurement signals. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0000]     Upfinding System  
         [0026]     Various preferred embodiments of the invention are described below for solving the upfinding problem using inertial sensors. As background,  FIG. 1A  illustrates a projectile  10  that has been launched on a ballistic trajectory and has some degree of rotation in the three axes (pitch, roll and yaw) illustrated in  FIG. 1B .  
         [0027]      FIG. 2  illustrates the projectile center line and the longitudinal axis about which it rotates ω spin , as well as the location of an inertial sensor  40  and the lateral access illustrating the pitch of the projectile ω pitchover .  
         [0028]     As shown in  FIG. 4 , one embodiment of the invention utilizes a Costas loop PLL as a phase detector  30  in combination with, optionally, a complementary filter  70  ( FIG. 3 ) to detect the phase of the sinusoidal rate/acceleration signal identifying the roll angle based on the inertial sensor  40  (gyro or accelerometer) information.  
         [0029]     Another embodiment of the invention utilizes a correlator  80  ( FIG. 5 ) as the phase detector  30  in combination with, optionally, a complementary filter  70  to detect the phase of the sinusoidal rate/acceleration signal identifying the roll angle based on inertial sensor  40 ; the choice between using pitch gyro information versus accelerometer information for the inertial sensor  40  is dependent on the application itself. The phase detector  30  estimates the phase error or equivalently the roll angle correction of the sinusoidal measurement signal  32  obtained from the inertial sensor  40 .  
         [0030]     As described below, all methods to detect the roll angle directly from the sinusoidal measurement signal show a significant sine-wave component coming from the projectile&#39;s motion motion. To dampen the error from the nutation and to smoothen the result, a complementary filter  70  using the roll rate from the roll gyro  50  may be inserted after the phase detector  30 . The complementary filter  70  may also provide a coarse estimation of the roll gyro&#39;s  50  scale factor error.  
         [0000]     Phase-Lock Loop  
         [0031]     Referring to  FIG. 4 , in an embodiment of the invention, the PLL  30  is designed as a Costas loop. For detecting the phase of the small amplitude, noisy sine wave (such as that coming from the inertial sensor  40 ), the known Costas loop is preferred over simpler formulations of a PLL due to the inherent amplitude normalization when the in-phase and out-of-phase signals are compared in the arctan function block.  
         [0032]     The inertial sensor(s)  40  generates a sinusoidal measurement signal  32  in response to rotation by the projectile. A roll gyro  50  combined with an accumulator  54  provides a coarse estimation of the roll angle. The remaining circuitry provides correction to the estimation of the roll angle.  
         [0033]     After the sinusoidal measurement signal  32  is multiplied  37 ,  37 ′ with the sine  36  and cosine  36 ′ of the estimated roll angle  34 , the resulting signals in each branch  38 ,  38 ′ are the sum of two signals, one with the frequency equal to the sum of the measurement and the accumulated roll angle, and one with the difference. The sum frequencies do not contribute to the detection of the measurement signal&#39;s phase, so they are attenuated in low-pass filters  40 ,  40 ′, one in each branch.  
         [0034]     The phase error between the measurement  32  and the estimated accumulated roll angle  34  may be computed by a four quadrant arctan function  33 . To make the loop lock on to the measurement signal  32 , the detected roll angle error correction  44  may be fed back to adjust the accumulated roll angle, using feedback control  46  that produces the roll angle correction value  48 . This permits control of the estimated roll angle  58  so that the error estimated by the arctan computation results in a zero phase error between the measurement  32  and the estimated roll angle  58 .  
         [0000]     Correlator-Based System  
         [0035]     Referring to  FIGS. 5 and 6 A-D, an alternative method to estimate the roll angle is to use a correlator  80  instead of a PLL. The principle is to correlate the sinusoidal measurement signal  32  from the inertial sensors  40  carrying the roll angle phase information ( FIG. 6A ) with a sinewave of known phase and adjust the known phase until the sine waves&#39; phase coincide. The phase and thus the roll angle is then known.  
         [0036]     Using just one correlator  80  will not tell the controller for the phase adjustment of the known sinewave in which direction to apply control. A scheme of two correlators  80  fed with sinewaves  39 ,  39 ′ that lead and lag the known phase with an equal amount is the solution used in this embodiment ( FIG. 6B ). The controller principles are then to drive the two correlator  80  outputs until they lie symmetrical around the midpoint of the correlator window, indicating that the measurement signal&#39;s phase coincides with the phase of the estimated roll angle ( FIGS. 6C , D).  
         [0037]     The total estimated roll angle  58  is made up from the accumulation of the roll gyro  50  output, representing the raw continuously increasing roll angle  52  and the corrections generated by the correlator control loop  40 .  
         [0038]     A segment or measurement window of the sinusoidal signal ( FIG. 6A ) is correlated with two phase shifted segments of a test sine-wave signal  39 ,  39 ′ with a known phase ( FIG. 6B ). The phase shift of the two segments is symmetric, i.e., + and −90 degrees. The segments of the sensor signal  32  and the test signals  39 ,  39 ′ must contain enough samples to describe at least one rotation. The cross-correlation returns two sequences ( FIGS. 6C , D) of length 2*N−1, where N is the number of samples in the measurement window.  
         [0039]     An error is calculated from the maximums of the two phase shifted correlation signals and the symmetry point of the measurement window, such that the Error=(d1−d2)/2, where: 
        d1 represents the number of samples that the +90 deg shifted test signal deviates from the symmetry point N at which the maximum should occur if the measurement signal&#39;s phase coincides with the phase of the estimated roll angle ( FIG. 6C ); and     d2 represents the number of samples that the −90 deg shifted test signal deviates from the symmetry point N at which the maximum should occur if the measurement signal&#39;s phase coincides with the phase of the estimated roll angle ( FIG. 6D ).        
 
         [0042]     This sample error is then converted into a phase error  44  and fed back through a feed back control  46  to produce a phase correction  48  and to drive the phase error of the test signal to zero which means to drive the two correlator  80  outputs until they lie symmetrical around the midpoint of the correlator window.  
         [0000]     Complementary Filter  
         [0043]     A projectile&#39;s motion is greatly influenced by aerodynamic forces. These forces create torques that make the spinning projectile precess and nutate. The precession and nutation motion is picked up by the pitch and yaw gyros and also in the Coriolis acceleration experienced by the longitudinal accelerometer. The result is that the phase angle determination by the PLL  30  and the correlator  80  will have the precession/nutation overlaid on the roll angle determination as a sine wave of several degrees amplitude.  
         [0044]     To dampen the effect of the precession/nutation and also smoothen the estimation of the accumulated roll angle, a complementary filter  70  may be inserted after the PLL  30  ( FIG. 4 ) or the correlator  80  ( FIG. 5 ).  FIG. 3  illustrates the use of a complementary filter  70 . The version of complementary filter  70  used in embodiments of the invention blends the estimated roll angle  58  from the PLL  30  with the roll rate  52  from the roll gyro  50 . The roll rate gyro signal  52  has better short-term behavior than the estimated roll angle  58  and is also less affected by the precession/nutation. The primary filtering function is performed by the integrator  74  that inputs the combined roll rate gyro signal  52  and the output of a transfer function H(s)  72 . The transition between relying on the short term roll rate behavior and the long term roll angle behavior is determined by the parameters of the transfer function H(s)  72 , which (in most cases) is a fixed gain.  
         [0045]     By comparing the roll rate  52  from the roll gyro  50  with the complementary filtered roll rate, it is also possible to estimate the roll gyro scale factor error.  
         [0046]     The invention shows that it is possible to estimate roll angle and other navigation states with enough accuracy to perform a coarse alignment using the methods described above. Two methods to measure roll angle information, using either gyros or accelerometers have been described.  
         [0047]     For the purposes of promoting an understanding of the principles of the invention, reference has been made to the preferred embodiments illustrated in the drawings, and specific language has been used to describe these embodiments. However, no limitation of the scope of the invention is intended by this specific language, and the invention should be construed to encompass all embodiments that would normally occur to one of ordinary skill in the art.  
         [0048]     The present invention may be described in terms of functional block components and various processing steps. Such functional blocks may be realized by any number of hardware and/or software components configured to perform the specified functions. For example, the present invention may employ various integrated circuit components, e.g., memory elements, processing elements, logic elements, look-up tables, and the like, which may carry out a variety of functions under the control of one or more microprocessors or other control devices. Similarly, where the elements of the present invention are implemented using software programming or software elements the invention may be implemented with any programming or scripting language such as C, C++, Java, assembler, or the like, with the various algorithms being implemented with any combination of data structures, objects, processes, routines or other programming elements. Furthermore, the present invention could employ any number of conventional techniques for electronics configuration, signal processing and/or control, data processing and the like.  
         [0049]     The particular implementations shown and described herein are illustrative examples of the invention and are not intended to otherwise limit the scope of the invention in any way. For the sake of brevity, conventional electronics, control systems, software development and other functional aspects of the systems (and components of the individual operating components of the systems) may not be described in detail. Furthermore, the connecting lines, or connectors shown in the various figures presented are intended to represent exemplary functional relationships and/or physical or logical couplings between the various elements. It should be noted that many alternative or additional functional relationships, physical connections or logical connections may be present in a practical device. Moreover, no item or component is essential to the practice of the invention unless the element is specifically described as “essential” or “critical”. Numerous modifications and adaptations will be readily apparent to those skilled in this art without departing from the spirit and scope of the present invention.  
       List of Reference Characters Update  
       [0000]    
       
           10  projectile  
           30  phase-locked loop (PLL); phase detector  
           32  inertial sensor signal; sinusoidal measurement signal  
           33  four-quadrant arctan function  
           34  estimated roll angle  
           35 ,  35 ′ low pass filter  
           36  sine function  
           36 ′ cosine function  
           37 ,  37 ′ multiplier  
           38 ,  38 ′ multiplied signals  
           39 ,  39 ′ sinewaves  
           40  inertial sensor; rotation sensing device (e.g., accelerometer, pitch/yaw gyro)  
           44  phase error  
           46  feedback loop control  
           48  correlator control loop phase correction  
           52  Incremental roll angle  
           54  accumulator for roll incremental angle  
           56  adder  
           58 ,  58 ′ estimated roll angle  
           60  output  
           70  complementary filter  
           72  filter transfer function  
           80 ,  80 ′ correlator; phase detector; correlator components  
          r distance from longitudinal axis to rotation sensing device