Abstract:
A resonator fiber optic gyroscope includes a first light source configured to generate a light signal. A resonator element is configured to generate an optical signal based on the light signal. A photodetector is configured to generate a first electrical signal based on the optical signal. The first electrical signal includes an oscillating signal, a direct-current (DC) signal, an even-harmonic signal including components at even harmonics of the oscillating signal, and an odd-harmonic signal including components at odd harmonics of the oscillating signal. A filtering element is configured to attenuate the DC signal, at least one even-harmonic component, and an odd-harmonic component to produce a second electrical signal. An amplifier is configured to amplify the second electrical signal. An analog-to-digital converter (ADC) is configured to digitize the amplified second electrical signal.

Description:
PRIORITY CLAIM 
     This application claims priority to U.S. Provisional Application No. 61/158,734 filed on Mar. 9, 2009 entitled “METHOD FOR SIGNAL CONDITION TO PROVIDE OPTIMUM GAIN AND NOISE REDUCTION FOR RESONATOR FIBER OPTIC GYROSCOPES,” which is herein incorporated by reference in its entirety. 
    
    
     STATEMENT OF GOVERNMENT INTEREST 
     This invention was made with Government support under Contract No. N00014-06-C-00001 awarded by the Office of Naval Research. The Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     The resonator fiber optic gyroscope (RFOG) has the potential of meeting the needs of many navigation and rotation sensing markets and creating new markets because of its capability of high performance in a small size, at low power and low cost.  FIG. 1  illustrates a conventional RFOG  10  consisting of a clockwise (CW) laser  12 , a counter-clockwise (CCW) laser  14 , a fiber optic resonator  16  and electronic circuits (“electronics”) providing at least resonator-coupling and resonance-tracking (or resonance-detection) functionality. The CW laser  12  inputs light into the resonator  16  and a CW photodetector  18  detects the CW output of the resonator. 
     The electronics downstream of the CW photodetector  18 , which include a CW modulation generator  20 , a CW demodulator  22 , a CW accumulator  24 , and a summing element  26 , control the CW laser frequency to a resonance frequency of the resonator  16 . The resonance frequency is detected by modulating the laser frequency at f 1  using the CW modulation generator  20  and then demodulating the output of the CW photodetector  18  at f 1  using the CW demodulator  22 . At the resonance frequency, the CW photodetector  18  signal at f 1  passes through zero amplitude. The CW accumulator  24  controls the laser frequency via the CW laser driver  38  to the resonance frequency by adjusting the laser frequency until the output of the CW demodulator  22  is zero. The modulation at f 1  is electronically summed with the CW integrator  24  output by the summing element  26 . With regard to the similarly configured CCW path of the RFOG  10 , the CCW laser  14  is controlled to the CCW resonance frequency in a similar manner, except it is common that the modulation frequency f 2  is different than f 1  to eliminate errors that arise when light from one direction of propagation in the resonator  16  inadvertently couples into the other direction. 
     In order to achieve high performance, the RFOG electronics must be capable of digitizing and detecting a very small signal from the resonator  16  and at specific frequency in the presence of a very large unwanted (e.g., harmonic) signal. The required resolution cannot be obtained with conventional analog-to-digital converters (ADCs) alone, and therefore some type of filter, to remove the unwanted signal to allow additional gain of the rotation signal so that conventional ADCs can be used, would be desirable. Ideally, such a filter removes the unwanted signal without removing noise that is required for ADC bit interpolation. 
     SUMMARY OF THE INVENTION 
     In an embodiment, a resonator fiber optic gyroscope includes a first light source configured to generate a light signal. A resonator element is configured to generate an optical signal based on the light signal. A photodetector is configured to generate a first electrical signal based on the optical signal. The first electrical signal includes an oscillating signal, a direct-current (DC) signal, an even-harmonic signal including components at even harmonics of the oscillating signal, and an odd-harmonic signal including components at odd harmonics of the oscillating signal. A filtering element is configured to attenuate the DC signal, at least one even-harmonic component, and an odd-harmonic component to produce a second electrical signal. An amplifier is configured to amplify the second electrical signal. An analog-to-digital converter (ADC) is configured to digitize the amplified second electrical signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Preferred and alternative embodiments of the present invention are described in detail below with reference to the following drawings. 
         FIG. 1  illustrates a conventional RFOG; 
         FIG. 2  illustrates an RFOG according to an embodiment of the invention; 
         FIG. 3  illustrates a transfer function provided by filtering elements according to an embodiment of the invention; and 
         FIG. 4  illustrates components of the RFOG of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     An embodiment provides an optimum accommodation of signal rejection and passing noise for ADC bit interpolation by splitting a gyro signal into two paths, applying a filter in a first path that is optimized for unwanted signal rejection and a filter in a second path that is optimized for passing only noise necessary for good ADC bit interpolation, then recombining the two paths before ADC processing. 
       FIG. 2  illustrates an RFOG  200  according to an embodiment of the invention. Elements of the RFOG  200  illustrated in  FIG. 2  (as well as  FIG. 4 ) similar or identical to those elements illustrated in  FIG. 1  are designated with like reference numerals. For ease of illustration, the following discussion is presented, at least primarily, in the context of the CW path and its constituent elements illustrated in  FIG. 2 . It is to be understood that the same or similar principles apply equally to the CCW path illustrated in  FIG. 2 . 
     For an ideal resonator, the difference in the CW and CCW resonance frequencies is proportional to rotation rate of the RFOG. To achieve full performance potential, the resonance frequencies must be determined with high precision. The RFOG employs a modulation/demodulation technique, employing, for example, the generator  20  and demodulator  22 , to determine the resonance frequencies. 
     To provide a signal that is indicative of a deviation from the resonance frequency, the frequency of the CW and CCW lasers  12 ,  14  are modulated. The frequency modulation sweeps the laser frequency relative to the resonance frequency. The resulting output of the resonator CW and CCW preamps (photodetectors  18 ,  28  that convert resonator output light intensity to an electrical signal) depends on where the average laser frequency lies relative to the resonance frequency. If the average laser frequency deviates from the resonance frequency, then a signal at the modulation frequency is present. The sign or phase of the signal depends on which direction the average laser frequency deviates from the resonance frequency. When the average laser frequency is exactly on resonance, then the amplitude of the signal at the modulation frequency, and odd harmonics thereof, is zero. Therefore the resonance frequency is detected by detecting a null of the signal at the modulation frequency. 
     A synchronous demodulator is typically used to detect the resonator output signal at the modulation frequency. Synchronous demodulation provides significant rejection of other signals and noise that does not occur at the modulation frequency. A synchronous demodulator is also sensitive to the phase of the demodulator input signal and thus provides an output that has a sign that indicates the direction that the average laser frequency deviates from the resonance frequency. Synchronous demodulation can be performed by an analog mixer; however this may result in large sensing errors due to imperfections of the analog mixer. For example, even if there is no signal at the modulation frequency going into the analog mixer, the output of the mixer may have some offset due to imperfections. The offset will translate to a gyro rate bias error. Significant performance improvements can be realized by using a digital demodulator, which does not have offset errors like the analog mixer. 
     To employ a digital demodulator the resonator signal from the preamp must be digitized by an analog-to-digital converter (ADC)  36 . Typically an anti-aliasing (AA) filter  32  is placed in-front of the ADC to reduce the effects of signal and noise aliasing, which is accomplished by providing signal attenuation at and above the ADC sample frequency. 
     A servo may be used to maintain the average laser frequency at the resonator resonance frequency. The servo controls the laser frequency to the resonance frequency such that the demodulator output is held at zero. A servo can consist of an analog integrator, but like the analog demodulator, an analog mixer has imperfections that can lead to rotation sensing errors. An example is an effective integrator input voltage offset, which will cause the integrator to move the average laser frequency slightly off resonance to generate a demodulator output that cancels out the integrator input offset. To improve gyro performance, a digital approximation of an integrator (e.g., accumulator  24 ) can be employed. The output of the accumulator  24  can be converted back to analog by a digital-to-analog converter (DAC)  34  before being sent to the laser frequency control circuit  38 . The DAC  34  output may also be summed with the modulation generator  20  output, which provides modulation of the laser frequency. 
     Digitizing the preamp signal may introduce quantization noise associated with the ADC  36 . The ADC quantization noise will result in higher angle random walk (ARW), which is a key performance parameter of the gyro. The impact that ADC quantization noise has on ARW depends on the signal gain before the ADC  36 . A higher signal gain reduces the impact on ARW. With enough signal gain, the quantization noise impact on ARW can be made insignificant. However, without changes to the configuration of the RFOG shown in  FIG. 1 , the amount of signal gain is limited by the direct-current (DC) preamp  18  output due to the time-average light intensity at the resonator  16  output, and the even harmonic signal that results from modulating over the resonance peak. Typically, to reduce quantization noise impact on ARW to required levels, an additional 20 dB to 30 dB of signal gain may be required over the limit imposed by DC preamp output due to the average light intensity and the even harmonic signal. Thus, it is desirable to reduce the DC and even-harmonic signals to allow additional gain before signal processing by the ADC  36 . 
     Table 1 shows results from a calculation of the ratio of specific even harmonic amplitude to the second harmonic amplitude of the even harmonic signal. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Harmonic # 
                 Ratio with SH (dB) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 2 
                 0.0 
               
               
                   
                 4 
                 −15.5 
               
               
                   
                 6 
                 −31.1 
               
               
                   
                 8 
                 −46.6 
               
               
                   
                 10 
                 −62.2 
               
               
                   
                   
               
             
          
         
       
     
     Without additional filtering of the signal, the 2nd harmonic component of the even harmonic signal dominates and is what limits the additional gain. To obtain an additional gain of 30 dB, the even harmonic signal amplitude should be reduced by approximately 30 dB. The table shows that if only the 2nd harmonic is eliminated (such as using a notch filter with a notch frequency at the 2nd harmonic frequency, as discussed in greater detail below herein), then the 4th harmonic will limit the additional gain to about 15 dB. To obtain an additional gain of 30 dB, the Table 1 shows that at least the 2nd and 4th harmonics must be removed. Since the 6th harmonic is −31 dB down from the second, there is little design margin if 30 dB of additional gain is required; therefore, even rejection of the 6th harmonic is desirable. 
     Setting the cutoff frequency of the AA filter  32  with an appropriate roll-off just above the modulation frequency can achieve the desired rejection of the even harmonic signals. However, by doing so, another important criteria associated with the ADC may not be met; to meet performance requirements the required detection level of the resonator output signal at the modulation frequency is typically much less than the bit resolution of available ADCs. For an ideal case, if the average resonator signal is between two adjacent bits of the ADC, then a non-zero resonator signal will not be detected until its amplitude is large enough to be detected by either bit. This can lead to a deadband in the gyro rotation-sensing transfer function, or additional rotation sensing noise. 
     To overcome the resolution limitation of ADCs, a method known as noise dithering and over-sampling may be employed. With sufficient noise amplitude, adjacent ADC bits are always toggled even if the signal is in-between bits. The bit toggling provides a signal at the ADC  36  output that has an average duty cycle depending on the amplitude of the signal that lies between bits. The signal can be digitally reconstructed by averaging the ADC  36  output. To accurately reconstruct the signal with averaging, the ADC sample frequency must be greater than the frequency of the averaged samples, which in turn must be greater than the frequency of the signal to be reconstructed. Typically, in fiber optic gyros, the, ADC sampling frequency is at least 100 times greater than the signal frequency. It has been shown in the literature that to obtain accurate reconstruction of the ADC input signal, the total root mean square (RMS) amplitude of the ADC input noise should be at least ⅓ of the least significant bit (LSB) of the ADC. If the RMS noise amplitude is less than ⅓ LSB, then the noise dithering may not eliminate deadband in the gyro rotation sensing transfer function, or additional rotation sensing noise due to finite ADC resolution. 
     In practice, the resonator  16  signal has some wide-band noise due to many noise sources, such as photon shot noise. The wide-band noise can be used to provide a dither signal to the ADC  36 . To provide enough noise at the ADC  36  to meet the ⅓ LSB criteria, the noise bandwidth from the preamp  18  to the ADC  36  may be approximately 1 MHz. A typical modulation frequency for an RFOG ranges from 20 kHz to about 200 kHz. If the cut-off frequency of the AA filter  32  is set to just above the modulation frequency, then the AA filter will limit the noise bandwidth to much less than required, and therefore there will not be enough noise at the ADC  36  input for bit interpolation. Thus, it is desirable to reject at least the 2nd, 4th and 6th harmonics of the even harmonic signal while providing enough noise amplitude at the ADC input. 
     Referring to  FIG. 2 , an embodiment includes respective filtering elements  210 ,  220  and amplifiers  230 ,  240  employed in the CW and CCW paths of the RFOG  200 . In an embodiment, the filtering elements  210 ,  220  may include a notch filter, or a series of notch filters, that reject an even-harmonic component of the even-harmonic signal. For example, one notch filter may be set to reject the 2nd harmonic, another notch filter for the 4th harmonic, another notch filter for the 6th harmonic, etc. This approach can provide the desired attenuation of the even-harmonic signal to allow the desired additional gain provided by amplifiers  230 ,  240  without saturating the electronics of the RFOG  200 . However, the notch filters may pass noise at the odd harmonics of the signal. Noise at these frequencies can increase ARW if a square-wave digital demodulator is employed. A square-wave demodulator is commonly used in FOG signal processing because of its simplicity requiring very few digital gates in the digital processor chip. 
     A square-wave demodulator is not only sensitive to a signal at the modulation/demodulation frequency, but also odd harmonics of the modulation frequency. The square-wave demodulator sensitivity to an odd harmonic is inversely proportional to the harmonic number n. Equation 1 shows how noise at the modulation odd harmonics contributes to the total gyro ARW: 
     
       
         
           
             
               
                 
                   
                     A 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     W 
                   
                   = 
                   
                     k 
                     ⁢ 
                     
                       
                         S 
                         in 
                       
                     
                     ⁢ 
                     
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             0 
                           
                           
                             n 
                             = 
                             
                               n 
                               max 
                             
                           
                         
                         ⁢ 
                         
                           1 
                           
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   n 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     The ADC input noise density is S in , which is assumed to be constant over all frequencies, and n is the odd harmonic number, and k is a proportionality constant. The minimum (best) ARW is obtained if the noise at the odd harmonics is removed. An exemplary approach is to set the AA filter  32  cutoff frequency low enough to remove noise at the 3rd harmonic and above. However, the AA filter  32 , with such a low frequency cutoff, may also remove noise required for ADC bit dithering. Equation 2 shows what happens to ARW if only the lower odd harmonics are removed: 
     
       
         
           
             
               
                 
                   
                     A 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     W 
                   
                   = 
                   
                     k 
                     ⁢ 
                     
                       
                         S 
                         in 
                       
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               n_min 
                             
                             
                               n 
                               = 
                               n_max 
                             
                           
                           ⁢ 
                           
                             1 
                             
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     n 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     Where n_min is the lowest odd harmonic that is allowed to pass. Table 2 shows the fractional increase in ARW for various n_min. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 n_min 
                 Noise Factor 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 3 
                 1.109 
               
               
                   
                 5 
                 1.057 
               
               
                   
                 7 
                 1.038 
               
               
                   
                 9 
                 1.028 
               
               
                   
                 11 
                 1.022 
               
               
                   
                 13 
                 1.018 
               
               
                   
                 15 
                 1.015 
               
               
                   
                 17 
                 1.013 
               
               
                   
                 19 
                 1.011 
               
               
                   
                 21 
                 1.010 
               
               
                   
                 23 
                 1.009 
               
               
                   
                   
               
             
          
         
       
     
     For n_min=3, noise at all odd harmonics are allowed to pass to the ADC  36  and the ARW is increased by about 11%. If noise at the 3rd harmonic is removed, (n_min=5), then the ARW is increased by only about 6%. After removing noise at the 3rd through 19th harmonics, any additional removal of higher harmonics has insignificant (i.e., less than 1%) impact on ARW. Therefore, besides rejecting the 2nd, 4th and 6th harmonics of the even harmonic signal, and passing enough noise for ADC bit dithering, the filtering elements  210 ,  220  may advantageously reject noise from about the 3rd to the 19th harmonic of the modulation frequency, but can pass noise above the 19th harmonic. A transfer function provided by filtering elements  210 ,  220  according to an embodiment is shown graphically in  FIG. 3 .  FIG. 4  illustrates a configuration of filtering element  210  (as well as filtering element  220 ) according to such an embodiment. 
     In the embodiment illustrated in  FIG. 4 , the preamp  18  signal includes an oscillating signal (e.g., f or f mod ), a direct-current (DC) signal, an even-harmonic signal including a set of components at even harmonics (e.g., 2f, 4f 6f etc.) of the oscillating signal, and an odd-harmonic signal including a set of components at odd harmonics (e.g., 3f 5f 7f, etc.) of the oscillating signal. At the filtering element  210 , the preamp  18  signal is split into two paths. In one path, a Low-Frequency Bandpass Filter (BPF)  410  passes only a fundamental component (e.g., 1f) of the oscillating signal and rejects the DC signal, the even harmonic signal and noise at odd harmonics. In the other path, a High-Frequency BPF  420  passes enough noise (e.g., a subset of harmonic components above the 19 th  harmonic) for ADC  36  bit dithering, but rejects the DC signal, significant even harmonic signals (e.g., a subset of harmonic components below the 8th harmonic) and significant noise at odd harmonics (e.g., a subset of harmonic components including the 19 th  harmonic and below). The outputs of the two BPFs  410 ,  420  are summed together at a summing element, such as a summing amplifier  430 , or a summing node of the amplifier  230 . After amplification by the amplifier  230 , the filtered signal may then be digitized by ADC  36 . 
     Referring to  FIG. 3 , the gain of the filtering element  210  drops with lower frequencies below f 1  and goes to zero at DC to block any DC signal from the preamp  18 . The gain reaches a maximum between f 1  and f 2  to pass the desired signal at the modulation frequency f mod . Just above the modulation frequency f mod  at f 2 , the gain decreases with increasing frequency to provide the desired attenuation of the even harmonic signal and odd harmonic noise. To provide noise for ADC  36  bit dithering, the gain of the filtering element  210  increases again near the frequency f 3 . The bandwidth between f 3  and f 4  determines how much noise is presented to the ADC  36  for bit dithering. In an embodiment, this bandwidth may be approximately 1 MHz to provide enough noise for bit dithering. The gain drops off after f 4  to provide attenuation at the ADC sampling frequency f samp  to reduce the effects of aliasing. 
     While a preferred embodiment of the invention has been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of the preferred embodiment. Instead, the invention should be determined entirely by reference to the claims that follow.