Abstract:
Apparatus, systems, and methods to control a plurality of gyroscopes utilizing intermediate frequencies are disclosed. The gyroscopes are configured to operate at the same pre-determined intermediate frequency. To accomplish this, the natural frequency of each gyroscope is determined, and a reference signal is added to the output signal of its respective gyroscope such that the sum of the natural frequency and the reference signal frequency equals the pre-determined intermediate frequency. The output signal from each gyroscope is transmitted to a common inertial data processor, and the inertial data processor outputs a directional signal. The directional signal includes a representation of angles from an X-axis, a Y-axis, and a Z-axis. Since each signal output by the gyroscopes has the same frequency, the loss of data is decreased and the accuracy of the data increased.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     The present invention relates generally to improvements in gyroscopes, and more particularly to, hemispherical resonator gyroscopes (HRGs).  
         [0003]     2. Description of the Related Art  
         [0004]     A hemispherical resonator gyroscope (HRG) is a vibratory sensor that includes a hemispherical resonator. Examples of HRGs can be found in U.S. Pat. Nos. 3,625,067, 3,656,354, 3,678,762, 3,719,074, 4,157,041, 4,951,508, 5,763,780, 5,801,310, 5,892,152, 5,902,930, 5,983,719, 6,065,340, 6,079,270, 6,158,282, 6,565,395, 6,619,121, and 6,883,361, each of which is hereby incorporated, in its entirety, by reference.  
         [0005]     A main component of each HRG is a quartz high Q resonator. This resonator is driven into oscillation by application of electrostatic forcers that are synchronized to the individual natural frequency of the resonator. Since each individual resonator includes its own individual natural frequency, the frequency is often referred to as “4.xx kHz”, which is approximately 4.1 kHz for a 30 millimeter diameter resonator. For example, a first resonator may include a natural frequency of 4.07 kHz, while a second resonator includes a natural frequency of 4.13 kHz.  
         [0006]     The electrostatic forcers cause the resonator to flex in an elliptical mode of oscillation. A set of readout electrodes arranged around the resonator are used to sense the amplitude, location, and motion of the elliptical mode standing wave pattern (the flex wave) resulting from such oscillation. If the HRG is rotated, the angle of rotation can be determined from processing a signal output by amplifiers attached to the readout electrodes (i.e., by observing changes in the position of the flex wave or actions necessary to prevent changes in the position of the flex wave).  
         [0007]      FIG. 1  illustrates an HRG  100  partitioned into four functional segments: a sensor segment  110 , a control drive segment  120 , a readout segment  130 , and a signal processing segment  140 . Sensor segment  110  includes a hemispherical resonator  1110 , a plurality of drive electrodes  1120 , and a plurality of readout electrodes  1130 . The plurality of drive electrodes  1120  includes a set of amplitude control drive electrodes  1122 , a set of quadrature control drive electrodes  1124 , and a set of rate control drive electrodes  1126 . The plurality of readout electrodes  1130  includes a set of X-axis readout electrodes  1132 , and a set of Y-axis readout electrodes  1134 .  
         [0008]     Control drive segment  120  is in communication with sensor segment  110  to provide an amplitude control drive signal  1210  to the set of amplitude control drive electrodes  1122 , a quadrature control drive signal  1220  to the set of quadrature control drive electrodes  1124 , and a rate control drive signal  1230  to the set of rate control drive electrodes  1126 . Sensor segment  110  is also in communication readout segment  130  and provides an X readout signal  1310  from X readout electrodes  1132 , and a Y readout signal  1320  from Y readout electrodes  1134  to readout segment  130 . Readout segment  130  is in communication with signal processing segment  140  to provide signal processing segment  140  with X readout signal  1310  and Y readout signal  1320 . X readout signal  1310  is derived from signals provided by X readout electrodes  1132 , and Y readout signal  1320  is derived from signals provided by Y readout electrodes  1134 . X readout signal  1310  and Y readout signal  1320  are utilized by processing segment  140  to provide an inertial angle output signal  150 . X readout signal  1310  and Y readout signal  1320  are also used in processing segment  140  to provide amplitude drive signal  1210 , quadrature control drive signal  1220 , and rate control drive signal  1230  to control drive unit  120 .  
         [0009]     Control of HRG  100 , and detection of any rotation of HRG  100  are provided by X readout signal  1310  and Y readout signal  1320 . Each electrode of X readout electrodes  1132  and Y readout electrodes  1134  provides an electrode readout signal (S ER ) to readout segment  130 . S ER  is related to a bias voltage (V b ) and to the amplitude (A) of the flex wave, where the relationship can be described using equation (E1) below. In equation (E1), V b  is the bias voltage applied to hemispherical resonator  1110  (which in some instances is metal clad so that its surface is electrically conductive), ω R  (≈4.1 kHz) is the natural frequency of hemispherical resonator  1110  of sensor segment  110 , A is the amplitude of the flex wave over X readout electrodes  1132  and Y readout electrodes  1134 , φ is a phase offset, and K r  is a proportionality constant. 
 
 S   ER   =K   r   *V   b [1 −A *Cos((ω R   t +φ)]  (E1) 
 
         [0010]     To operate HRG  100 , three types of control forces are applied to hemispherical resonator  1110 . These forces correspond to amplitude drive signal  1210 , quadrature control drive signal  1220 , and rate control drive signal  1230  provided by control drive segment  120 .  
         [0011]     Amplitude drive signal  1210  is used to provide amplitude control of the flex wave and to keep hemispherical resonator  1110  oscillating at or near its natural (resonant) frequency.  
         [0012]     Quadrature control drive signal  1220  is used to suppress mass and stiffness variations around hemispherical resonator  1110 , and rate control drive signal  1230  is used to position the flex wave.  
         [0013]     The force applied to hemispherical resonator  1110  by each of the plurality of drive electrodes  1120  is proportional to a direct current (DC) bias voltage V b  maintained on hemispherical resonator  1110 . In the case of rate control drive signal  1230  (represented in equation (E2) as K d ), the maximum rate that can be applied to the position of the flex wave is a function of the amplitude of the flex wave as shown by equation (E2): 
 
 S   RCD   =K   d   *V   b   *A *Sin(ω R   t +φ)]  (E2). 
 
         [0014]     As such, increasing the bias voltage V b  will increase the magnitude of the electrostatic force applied to hemispherical resonator  1110  by each of the plurality of drive electrodes  1120  (i.e., by amplitude drive signal  1210 , quadrature control drive signal  1220 , and/or rate control drive signal  1230 ).  
         [0015]     Hemispherical resonator  1110  is a high Q oscillator, the Q being, in some instances, approximately 10*10 6 . To control the flex wave of the oscillating hemispherical resonator  1110 , all forces applied via the plurality drive electrodes  1120  must be precisely synchronized and phase locked to the natural frequency (ω R ) of hemispherical resonator  1110 . In current HRG  100  devices, during normal operation the various signals all have a frequency at least approximately equal to the natural frequency ω R  of hemispherical resonator  1110 . Phase locking is achieved through the use of a phase locked loop  1410  provided by signal processing segment  140 . Phase locked loop  1410  tracks the natural frequency ω R  of hemispherical resonator  1110  via X readout signal  1310  and Y readout signal  1320  to provide a reference signal for amplitude control loop  1420 , quadrature control loop  1430 , and rate control loop  1440  to ensure amplitude drive signal  1210 , quadrature control drive signal  1220 , and rate control drive signal  1230 , respectively, have the same frequency as hemispherical resonator  1110 .  
         [0016]      FIG. 2  is a block diagram of a system  200  including two HRG devices (e.g., HRG  210  and HRG  260 ). Here, HRG  210  includes it own natural frequency (ω R1 ) (e.g., 4.1 kHz).  
         [0017]     As such, any signal (e.g., readout signal  215 ) output by HRG  210  would include frequency ω R1 . Readout signal  215  is filtered by a bandpass filter  220  and transmitted to data processor  230 . Any signal representing an angle (Δθ 1 ) output by HRG  210  would include frequency ω R1 . Moreover, any signal (e.g., a local oscillator signal) received by HRG  210  would likewise include frequency ω R1  since the frequency of each signal in HRG  210  is controlled by phase locked loop  240 . In other words, the frequency (ω LO1 ) of the local oscillator signal is the same as the natural frequency (ω R1 ) of HRG  210  (i.e., ω LO1 =ω R1 ).  
         [0018]     The operation of HRG  260  is similar to the operation of HRG  210 . However, due to the nature of HRGs, the natural frequency (ω R2 ) of HRG  260  is different from (ω R1 ). For example, ω R2  may be 4.03 kHz. In other words, ω LO1 =ω R1  and ω LO2 =ω R2 , wherein ω LO1  and ω R1  include a different frequency from ω LO2  and ω R2  such that the signals representing angles Δθ 1  and Δθ 2  have different frequencies.  
         [0019]     Thus, previous systems are complex from a hardware, firmware, and software point of view since each HRG has its own individual natural frequency. Since each HRG has its own individual natural frequency, synchronizing the output signals (e.g., ω R1 =4.11 kHz and ω R2 =4.07 kHz) from a plurality of HRG devices requires electronics incorporating a set of complex algorithms and computations. Often, the complex algorithms and computations omit important components from one or more signals from the HRG devices since estimating and/or rounding occurs in the algorithms and computations. As such, the resulting signals are not as accurate as they otherwise could be. Notably, these systems become even more complex when each HRG also includes it own accelerometer (not shown) to measure the speed of change in direction for its associated HRG. Thus, there is a need for systems and methods to synchronize output signals from a plurality of HRG devices in a less complex and more accurate manner.  
       SUMMARY OF THE INVENTION  
       [0020]     The present invention accomplishes the above goal for two or more gyroscopes in communication with one another. By its nature, each gyroscope outputs a signal at its own individual natural frequency (ω R ). For a hemispherical resonator gyroscope (HRG), the natural frequency is about 4.1 kHz for a 30 millimeter diameter resonator. However, the techniques of the present invention are equally applicable to resonate bodies having other natural frequencies.  
         [0021]     Each HRG also includes an associated phase locked loop in communication with the HRG. A reference signal including a reference frequency (ω LO ) from each phase locked loop is added to the output signal of its associated HRG by a signal mixer to form an intermediate frequency IF signal including a (ω LO −ω R ) component and a (ω LO +ω R ) component.  
         [0022]     Each HRG&#39;s natural frequency is measured and the frequency ω LO  is determined by adding ω R  to a pre-determined operating frequency. In one exemplary embodiment, the pre-determined operating frequency is 8.0 kilohertz (kHz). Thus, for example, if the natural frequency of an HRG is 4.06 kHz and the pre-determined operating frequency is 8.0 kHz, ω LO  will be 12.06 kHz (i.e., 4.06 kHz+8.0 kHz).  
         [0023]     The ω LO +ω R ) component is filtered by a bandpass filter such that the IF signal substantially only includes the (ω LO −ω R ) component, or the pre-determined operating frequency. Each IF signal is transmitted to a common inertial data processor and compared to one another by the inertial data processor to determine a direction for the system. In one embodiment, the system includes three HRG devices such that an x-coordinate, a y-coordinate, and z-coordinate can be determined by the inertial data processor. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0024]     Additional aspects of the present invention will become evident upon reviewing the embodiments described in the specification and the claims taken in conjunction with the accompanying figures, wherein like numerals designate like elements, and wherein:  
         [0025]      FIG. 1  is a block diagram of a prior art hemispherical resonator gyroscope (HRG);  
         [0026]      FIG. 2  is a block diagram of a signal flow for a prior art system including two HRG devices;  
         [0027]      FIG. 3  is a block diagram of an HRG in accordance with an exemplary embodiment of the present invention;  
         [0028]      FIG. 4  is a block diagram of an exemplary embodiment of a system including two or more HRG devices utilizing intermediate frequency (IF) signals;  
         [0029]      FIG. 5  is a block diagram of one exemplary embodiment of a system including three HRG devices for determining an x-coordinate, a y-coordinate, and a z-coordinate of an apparatus utilizing IF signals; and  
         [0030]      FIG. 6  is a flow diagram of one exemplary embodiment of a method to control a system including two or more gyroscopes utilizing IF signals. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0031]     Reference will now be made to various exemplary embodiments of the invention, which are illustrated in the accompanying figures. While the invention is described with reference to these exemplary embodiments, these embodiments do not limit the invention. On the contrary, the invention is intended to cover alternatives, modifications, and equivalents which may be included within the spirit and scope of the invention as defined by the appended claims.  
         [0032]     In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the present invention. However, it will be understood by one of ordinary skill in the art that the present invention is capable of being practiced without these specific details. In other instances, well known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily obscure the important aspects of the present invention.  
         [0033]     Embodiments of the present invention provide systems and methods including a plurality of gyroscopes operating at substantially the same intermediate frequency. Since each gyroscope is operating at the same frequency, a common inertial data processor can be utilized to process signals from the gyroscopes without substantially losing data and more accurately than current systems. Moreover, the invention allows a system to be manufactured and/or repaired cheaper than current systems incorporating a plurality of gyroscopes.  
         [0034]      FIG. 3  is a block diagram of a gyroscope  300  in accordance with an exemplary embodiment of the present invention. Gyroscope  300  may be any hardware and/or software suitably configured to produce a signal to indicate a direction gyroscope  300  is oriented. As such, gyroscope  300  may be any gyroscope known in the art or developed in the future. In accordance with one exemplary embodiment of the invention, gyroscope  300  is a hemispherical resonator gyroscope (HRG) manufactured by Northrop Grumman Corporation of Los Angeles, Calif. As such, gyroscope  300  may be similar to HRG  100  discussed above with reference to  FIG. 1 .  
         [0035]     In one exemplary embodiment of the invention, gyroscope  300  includes a readout section  330 , similar to readout section  130  discussed above, to produce a readout signal  315  similar to X readout signal  1310  and/or Y readout signal  1320  discussed above. Readout signal  315  includes a natural frequency (ω R ) of gyroscope  300 . As discussed above, ω R  is the individual operating frequency of gyroscope  300  and includes a frequency of approximately 4.1 kilohertz (kHz). However, gyroscopes with other natural operating frequencies are contemplated by the invention.  
         [0036]     Readout section  330  is in communication with a mixer  318 , wherein readout section  330  is also configured to transmit readout signal  315  to mixer  318 . Mixer  318  may be any hardware and/or software suitably configured to combine two or more signals. As such, mixer  318  may be any mixer known in the art or developed in the future. In accordance with one exemplary embodiment of the invention, mixer  318  is configured to combine readout signal  315  with a reference signal with a pre-determined reference frequency (ω LO ) to form an intermediate frequency (IF) signal having a (ω LO −ω R ) component and a (ω LO +ω R ) component. The reference signal is received from a phase locked loop (discussed below) and ω LO  is determined by adding ω R  to a desired operating frequency.  
         [0037]     For example, if the desired operating frequency is 8.0 kHz and ω R  is 4.15 kHz, ω LO  is 12.15 kHz (i.e., 8.0 kHz+4.15 kHz). Thus, in this example, when readout signal  315  is combined with the reference signal, the IF signal includes a frequency (ω IF1 ) having a 16.3 kHz component (ω LO +ω R ) and an 8.0 kHz component (ω LO −ω R ).  
         [0038]     In accordance with one embodiment, mixer  318  is in communication with a bandpass filter  322 , wherein bandpass filter  322  may be any hardware and/or software suitably configured to allow components of a signal having a pre-determined frequency to pass through. As such, bandpass filter  322  may be any bandpass filter known in the art or developed in the future. In accordance with one exemplary embodiment of the invention, bandpass filter  322  is configured to receive the IF signal and allow substantially only the (ω LO −ω R ) component to pass through. In other words, the high frequency component (ω LO +ω R ) is filtered from the IF signal. Thus, in the example above, the IF signal includes a frequency (ω IF1 ′) of 8.0 kHz after passing through bandpass filter  322 .  
         [0039]     Bandpass filter  322  is in communication with a phase locked loop  340 , wherein phase locked loop  340  is any hardware and/or software suitably configured to receive the IF signal and maintain a constant phase angle (i.e., lock) on the frequency of the IF signal. As such, phase locked loop  340  may be any phase locked loop known in the art or developed in the future. In accordance with one exemplary embodiment of the invention, phase locked loop  340  produces the reference signal including the frequency ω LO  discussed above. Furthermore, phase locked loop  340  is in communication with mixer  318  and a signal inverter  343 , and provides the reference signal to mixer  318  and signal inverter  343 .  
         [0040]     Signal inverter  343  may be any hardware and/or software suitably configured to combine two or more signals. As such, signal inverter  343  may be any signal inverter known in the art or developed in the future. In accordance with one exemplary embodiment, signal inverter  343  is configured to receive the reference signal having frequency ω LO  from phase locked loop  340  and receive a second IF signal with a frequency ω IF2  from a source (not shown), wherein ω IF2  includes a frequency (ω LO +ω R ). Furthermore, signal inverter  343  is configured to combine the reference signal with the second IF signal to form a drive signal  345  and transmit drive signal  345  to a control drive segment  320  similar to control drive segment  120  discussed above.  
         [0041]     Notably, when signal inverter  343  combines the reference signal with the second IF signal, drive signal  345  includes a frequency (ω R ) (i.e., ω LO +ω R −ω LO ). Thus, drive signal  345  will include the natural frequency of gyroscope  300 .  
         [0042]      FIG. 4  is a block diagram of an exemplary embodiment of a system  400  including a gyroscope  500  and a gyroscope  600  and utilizing IF signals. Gyroscope  500  includes a readout section  530 , a mixer  518 , a bandpass filter  522 , a phase locked loop  540 , and a signal inverter  543  configured similar to readout section  330 , mixer  318 , bandpass filter  322 , a phase locked loop  340 , and signal inverter  343  discussed above, respectively.  
         [0043]     Furthermore, gyroscope  600  includes a readout section  630 , a mixer  618 , a bandpass filter  622 , a phase locked loop  640 , and a signal inverter  643  configured similar to readout section  330 , mixer  318 , bandpass filter  322 , a phase locked loop  340 , and signal inverter  343  discussed above, respectively. Since gyroscopes typically operate at their own individual natural frequencies, gyroscope  500  and gyroscope  600  have natural frequencies different from one another. Thus, ω R1  and ω R2  are different frequencies.  
         [0044]     In accordance with one exemplary embodiment of the invention, system  400  is configured to operate in the range of about 100 Hz to about 100 kHz. In another embodiment, system  400  is configured to operate at approximately 8.0 kHz. As such, since ω R1  and ω R2  are different frequencies, phase locked loops  540  and  640  are configured to produce reference signals including frequencies (e.g., ω LO1  and ω LO2 ) different from one another. For example, if ω R1  is 4.18 kHz and ω R2  is 4.09 kHz, ω LO1  will be 12.18 kHz (8.0 kHz+4.18 kHz) and ω LO2  will be 12.09 kHz (8.0 kHz+4.09 kHz). Thus, the frequency (ω IF1 ) of the IF signal in gyroscope  500  will include an 8.0 kHz component (i.e., 12.18 kHz−4.18 kHz) and a 16.36 kHz component (i.e., 12.18 kHz+4.18 kHz), and the frequency (ω IF2 ) of the IF signal in gyroscope  600  will include an 8.0 kHz component (i.e., 12.09 kHz−4.09 kHz) and a 16.18 kHz component (i.e., 12.09 kHz+4.09 kHz).  
         [0045]     Furthermore, when the IF signal in gyroscope  500  and the IF signal in gyroscope  600  pass through bandpass filter  522  and bandpass filter  622 , respectively, the high frequency component (ω LO +ω R ) of each signal is filtered such that each resulting IF signal includes a frequency (ω IF1 ′) of approximately 8.0 kHz. Each respective IF signal is transmitted to a respective data processor (i.e., data processors  533  and  633 ) and, thus, gyroscopes  500  and  600  each output an 8.0 kHz IF signal.  
         [0046]     In accordance with one exemplary embodiment of the invention, gyroscopes  500  and  600  are in communication with a common inertial data processor  433 . Inertial data processor  433  may be any hardware and/or software suitably configured to receive an IF signal from two or more gyroscopes and output a directional signal representing one or more angles (e.g., Δθ 1  and Δθ 2 ). As such, inertial data processor  433  may be any processor known in the art or developed in the future capable of performing the above functions.  
         [0047]     In addition, gyroscopes  500  and  600  each include a signal inverter (i.e., signal inverters  543  and  643 , respectively) to combine the reference signal with a respective second IF signal to form a drive signal (i.e., drive signals  545  and  645 , respectively) having a frequency equal to the natural operating frequency of its respective gyroscope. In other words, drive signal  545  includes a frequency of 4.18 kHz (i.e., ω LO1 +ω R1 −ω LO1 ) and drive signal  645  includes a frequency of 4.09 kHz (i.e., ω LO2 +ω R2 −ω LO2 ) to match the natural frequencies of gyroscope  500  (i.e., ω R1 ) and gyroscope  600  (i.e., ω R2 ), respectively.  
         [0048]     Since each of gyroscopes  500  and  600  output a signal having substantially the same frequency, there is not a need for performing complex algorithms and/or calculations when interpreting the data. As such, system  400  is more reliable and accurate than previous systems. Moreover, system  400  may be assembled without needing to calibrate gyroscopes  500  and  600  since they are individual gyroscopes configured to operate at the same frequency. Thus, system  400  may be compatible with numerous different systems and/or systems manufactured by numerous different manufacturers.  
         [0049]      FIG. 5  is a block diagram of one exemplary embodiment of a system  700  including three gyroscopes (e.g., gyroscope  700 , gyroscope  800 , and gyroscope  900 ) for determining an X-coordinate, a Y-coordinate, and a Z-coordinate utilizing IF signals. Gyroscope  800  includes a readout section  830 , a mixer  818 , a bandpass filter  822 , a data processor  833 , a phase locked loop  840 , and a signal inverter  843  configured similar to readout section  330 , mixer  318 , bandpass filter  322 , data processor  333 , a phase locked loop  340 , and signal inverter  343  discussed above, respectively. Furthermore, gyroscope  900  includes a readout section  930 , a mixer  918 , a bandpass filter  922 , a data processor  933 , a phase locked loop  940 , and a signal inverter  943  configured similar to readout section  330 , mixer  318 , bandpass filter  322 , data processor  333 , a phase locked loop  340 , and signal inverter  343  discussed above, respectively. Moreover, gyroscope  1000  includes a readout section  1030 , a mixer  1018 , a bandpass filter  1022 , a data processor  1033 , a phase locked loop  1040 , and a signal inverter  1043  configured similar to readout section  330 , mixer  318 , bandpass filter  322 , data processor  333 , a phase locked loop  340 , and signal inverter  343  discussed above, respectively. As discussed above, gyroscope  800 , gyroscope  900 , and gyroscope  1000  have natural frequencies different from one another.  
         [0050]     Similar to the discussion above, ω RX , ω RY , and ω RZ  are different frequencies, and ω LOX , ω LOY , and ω LOZ  are different frequencies. However, after ω RX  is added to ω LOX  by mixer  818 , ω RY  is added to ω LOY  by mixer  918 , and ω LOZ  is added to ω LOZ  by mixer  1018  to form IF signals including a (ω LOX −ω RX ) component, a ω LOY −ω RY ) component, and a (ω LOZ −ω RZ ) component, respectively, and each IF signal is filtered by a bandpass filter (i.e. bandpass filters  822 ,  922 , and  1022 , respectively), each resulting IF signal includes the same frequency (ω IF ′). Thus, each of gyroscopes  800 ,  900 , and  1000  operate at the same frequency (e.g., 8.0 kHz).  
         [0051]     Furthermore, system  700  includes a common inertial data processor  733  similar to inertial processor  433  discussed above in communication with each of gyroscopes  800 ,  900 , and  1000 . In accordance with one exemplary embodiment of the invention, inertial data processor  433  outputs a directional signal representing an angle in one or more planes (e.g., ΔθX, Δ 74  Y, and/or ΔθZ). Notably, since each of gyroscopes  800 ,  900 , and  1000  operate at the same frequency, inertial data processor  733  is capable of processing IF signals received from each of the gyroscopes without needing to perform complex algorithms and/or computations for processing the different signals. As such, system  700  is more accurate and less likely to lose data when processing the signals from gyroscopes  800 ,  900 , and  1000  than previous systems utilizing multiple gyroscopes. Moreover, since gyroscopes  800 ,  900 , and  1000  are essentially self-contained, any of these gyroscopes can be replaced without affecting the output and performance of the other gyroscopes. Moreover, system  700  may be assembled without needing to calibrate gyroscopes  800 ,  900 , and  1000  since they are individual gyroscopes configured to operate at the same frequency. Thus, system  700  may be compatible with numerous different systems and/or systems manufactured by numerous different manufacturers.  
         [0052]      FIG. 6  is a flow diagram of one exemplary embodiment of a method  2000  to control two or more gyroscopes utilizing IF signals. In accordance with an exemplary embodiment of the invention, method  2000  initiates by determining an operating frequency for the gyroscopes (step  2005 ). In one aspect of the invention, the operating frequency is in the range of about 100 Hz to about 100 kHz. In another aspect of the invention, the operating frequency is about 8.0 kHz.  
         [0053]     Method  2000  also includes the step of measuring the natural frequency (ω R ) of a signal output by each resonator of a plurality of gyroscopes (e.g., gyroscope  300 ,  500 ,  600 ,  800 ,  900 , or  1000 ) (step  2010 ). Once the operating frequency is determined and the natural frequency of each resonator is known, method  2000  includes the step of determining a reference frequency ω LO ) for a reference signal for each gyroscope (step  2015 ). In accordance with one exemplary embodiment of the invention, each reference frequency is determined by adding the operating frequency to the natural frequency for each respective gyroscope. For example, if the operating frequency is 8.0 kHz and the natural frequency for a particular gyroscope is 4.12 kHz, the reference frequency for that particular gyroscope is 12.12 kHz. Thus, in general terms, the reference frequency may be referred to as 12.xx kHz since the “xx” is determined by the natural frequency.  
         [0054]     After the operating frequency, the natural frequency, and the reference frequency are determined are each gyroscope, the output signal and the reference signal for each gyroscope are combined to form an IF signal including a (ω LO −ω R ) component (step  2020 ). Doing the calculation, the IF signal will include a component having a frequency of 8.0 kHz (i.e., the desired operating frequency). Thus, each gyroscope operates at substantially the same pre-determined frequency.  
         [0055]     Notably, because of the nature of gyroscopes, the natural frequency of the resonator for each gyroscope will be different. As such, the frequency of each reference signal will be different. However, once the output signal is added to the reference signal for each gyroscope, each resulting IF signal will include a component (ω LO −ω R ) having the same pre-determined operating frequency (i.e., 8.0 kHz). Thus, method  2000  includes the step of outputting a plurality IF signals with substantially the same frequency to a common inertial data processor (step  2025 ). Furthermore, method  2000  includes the common inertial data processor outputting a directional signal having the same frequency as the IF signals, wherein the directional signal represents an angle (e.g., ΔθX, ΔθY, and/or ΔθZ) from an X-plane, a Y-plane, and/or a Z-plane (step  2030 ).  
         [0056]     Notably, the above apparatus, systems, and methods may have been described as including specific frequencies. However, one skilled in the art will appreciate that each apparatus, system, and method may operate at any number of frequencies and at frequencies higher and/or lower than the specific frequencies referenced. As such, the invention is not to be limited by the disclosure of specific frequencies, examples, and embodiments.  
         [0057]     Furthermore, other advantages, benefits, and solutions to problems have been described herein with regard to specific embodiments. However, the benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as critical, required, or essential features or elements of any or all the claims or the invention. The scope of the invention is accordingly to be limited by nothing other than the appended claims, in which reference to an element in the singular is not intended to mean “one and only one” unless explicitly so stated, but rather “one or more.” All structural, chemical, and functional equivalents to the elements of the above-described exemplary embodiments that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Moreover, it is not necessary for a device or method to address each and every problem sought to be solved by the present invention, for it to be encompassed by the present claims. Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims. No claim element herein is to be construed under the provisions of 35 U.S.C. §112, sixth paragraph, unless the element is expressly recited using the phrase “means for.” As used herein, the terms “comprises”, “comprising”, or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Further, no element described herein is required for the practice of the invention unless expressly described as “essential” or “critical”.