Abstract:
A technique is disclosed which offers an improvement in the performance of an atom interferometric (AI) sensor, such as one that is used in an accelerometer or a gyroscope. The improvement is based on the recognition that the AI-based device, which is associated with superior low-frequency performance, can be augmented with a conventional device having a superior high-frequency performance, as well as a wider frequency response, compared with that of the AI-based device. The disclosed technique combines acceleration measurements from the AI-based device, which is characterized by transfer function G(s), with acceleration measurements from the conventional device that have been adjusted by a complementary function, 1−Ĝ(s), where Ĝ(s) is an approximation of G(s). The conventional device has a considerably wider bandwidth than that of the AI-based device, and the quasi-unity transfer function of the conventional device makes possible the 1−Ĝ(s) adjustment of the measurements provided by the conventional device.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to atom interferometric devices in general and, more particularly, to improving the performance of an atom interferometric device through complementary filtering. 
       BACKGROUND OF THE INVENTION 
       [0002]    Atom interferometric-based (AI-based) devices apply the science of coherent atom-laser interactions to make sensitive and accurate measurements of the trajectories of ensembles of atoms, in order to determine acceleration. A classical analogy for the AI-based acceleration measurement is to consider measuring the trajectory of a proof mass in an accelerating reference frame. As depicted in  FIG. 1  in the prior art, an atom-interferometric accelerometer essentially operates by replacing the relatively large proof mass with atoms. The atoms are situated in an entity known as an “atom cloud.” The atom cloud is released—that is, dropped or launched—and effectively becomes a reference point in space. During the atom cloud&#39;s free fall, a measuring laser such as a Raman laser is used to measure the accelerometer&#39;s motion relative to the atom cloud. The measuring laser measures the atoms&#39; trajectory through three successive interactions with laser beams, namely φ(t 1 ), φ(t 2 ), and φ(t 3 ), where the φ-values are indicative of atom cloud displacement and t 1 , t 2 , and t 3  are the times at which these displacements are measured. The interactions are separated by interval T R . 
         [0003]    An AI-based accelerometer is advantageous for a variety of reasons. First, it provides precise inertial measurements, as they are based on the interference of atom waves. Second, the device has no moving parts, except for the atoms, thereby providing the potential for low-cost, low-maintenance sensors. Third, the atom densities in the coherent atom cloud provide the potential for high signal-to-noise ratios. And fourth, the use of an atomic proof mass ensures that the material properties between sensor proof masses will be identical. 
         [0004]    Additionally, an atom interferometric accelerometer has the potential to exhibit superior low frequency performance over conventional accelerometers, which rely on larger proof masses to provide acceleration measurements. 
       SUMMARY OF THE INVENTION 
       [0005]    Although an atom interferometric-based (AI-based) device has an advantage in low-frequency performance over a conventional device that is based on a relatively large proof mass, an AI device also has several disadvantages. First, an AI device has a low bandwidth because of a relatively long output sample time. Second, an AI device has a low output sample rate, which can cause output harmonics and aliasing when driven, for example, by a sinusoidal acceleration input. Third, an AI device is characterized by a zero-sensitivity frequency response that comprises notches at specific frequencies as determined by one or more processing parameters of the AI device, such as the Raman interval. And fourth, the time lag of when an accelerometer output sample becomes available is relatively long and, consequently, a group delay is introduced. 
         [0006]    A technique is disclosed herein which offers an improvement in the performance of an atom interferometric (AI) sensor, such as one that is used in an accelerometer or a gyroscope, over some AI-based sensors in the prior art. The improvement is based on the recognition that the AI-based device, which is associated with superior low-frequency performance, can be augmented with a conventional device having superior high-frequency performance, as well as a wider frequency response, compared with that of the AI-based device. In accordance with the illustrative embodiment of the present invention, the disclosed technique combines acceleration measurements from the AI-based device, which is characterized by transfer function G(s), where s is a complex number, with acceleration measurements from the conventional device that have been adjusted by a complementary function, 1−Ĝ(s), where Ĝ(s) is an approximation of G(s). 
         [0007]    The complementary filtering of the illustrative embodiment provides an improvement over the prior art because the conventional device has a considerably wider bandwidth than that of the AI-based device. This quasi-unity transfer function of the conventional device makes possible the 1−Ĝ(s) adjustment of the measurements provided by the conventional device. And when combined with sampled-and-held output from the AI device, the illustrative embodiment yields approximately true acceleration, including eliminating group delay and the errors due to notches in the AI device&#39;s frequency response. 
         [0008]    The illustrative embodiment features an atom-interferometric accelerometer and a conventional accelerometer being used concurrently to measure acceleration. However, it will be clear to those skilled in the art, after reading this specification, how to make and use alternative embodiments in which measurements from another type of first accelerometer that features superior low-frequency performance can be complementary-filtered with measurements from another type of second accelerometer that features superior high-frequency performance and a wider frequency band than the first accelerometer. Also, it will be clear to those skilled in the art, after reading this specification, how to make and use alternative embodiments in which devices other than accelerometers are utilized, such as gyroscopes. 
         [0009]    The illustrative embodiment of the present invention comprises a method comprising: sensing an acceleration at a first accelerometer and a second accelerometer, resulting in first measurement made by the first accelerometer and a second measurement made by the second accelerometer, the first measurement being affected by a transfer function that characterizes the first accelerometer; adjusting the second measurement with an approximation of the transfer function, resulting in an adjusted measurement; and generating a filtered acceleration measurement, based on i) the first measurement and ii) the adjusted measurement. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  depicts the operations of an atom interferometric accelerometer in the prior art. 
           [0011]      FIG. 2  depicts acceleration measuring system  200  in accordance with the illustrative embodiment of the present invention. 
           [0012]      FIG. 3  depicts a signal-processing model of atom interferometric accelerometer  201 , which is part of system  200 . 
           [0013]      FIG. 4  depicts a signal-processing model of complementary filter  203 , which is part of system  200 . 
           [0014]      FIG. 5  depicts a flowchart of the main tasks performed by system  200 , in accordance with the illustrative embodiment of the present invention. 
           [0015]      FIG. 6  depicts a flowchart of the salient subtasks associated with task  501  of  FIG. 5 . 
           [0016]      FIG. 7  depicts a flowchart of the salient subtasks associated with task  502  of  FIG. 5 . 
           [0017]      FIG. 8  depicts a flowchart of the salient subtasks associated with task  503  of  FIG. 5 . 
       
    
    
     DETAILED DESCRIPTION 
       [0018]      FIG. 2  depicts acceleration measuring system  200  in accordance with the illustrative embodiment of the present invention. System  200  comprises atom interferometric accelerometer  201 , conventional accelerometer  202 , and complementary filter  203 , interconnected as shown. Although accelerometers are featured in the illustrative embodiment, it will be clear to those skilled in the art, after reading this specification, how to make and use alternative embodiments in which devices other than accelerometers are utilized, such as gyroscopes. 
         [0019]    Atom interferometric (AI) accelerometer  201  is a device that senses acceleration events through the use of atom interferometry, as is known in the art, and provides measurements of the sensed events. To do so, a measuring laser measures the trajectory of atoms in an atom cloud through three successive interactions with laser beams, as depicted in  FIG. 1 , in which the depicted φ-values are effectively indicative of atom cloud displacement and t 1 , t 2 , and t 3  are the times at which the displacements are measured. The interactions are separated by an interval T R , which is also referred to as the Raman interval. The specific time at which the sensing of the acceleration by the atomic interferometer sensor is valid corresponds to the time of the middle interaction of the laser with the atom cloud (i.e., the second of the three Raman pulses). Accelerometer  201  makes available the acceleration measurement at an output time that is equal to the valid sensing time plus a delay T OD . Delay T OD , which is also referred to as “group delay,” corresponds to the time difference between the output time and the valid sensing time. Each new acceleration measurement is provided by accelerometer  201  to complementary filter  203 , at a sample interval T S . In general, T S &gt;T OD &gt;T R . These time-related parameters are further described below and with respect to  FIG. 3 , which depicts a signal-processing model of accelerometer  201 . 
         [0020]    In accordance with the illustrative embodiment, T S , T OD , and T R  are equal to 10 seconds, 1.0 seconds, and 0.1 seconds, respectively. It will be clear to those who are skilled in the art, after reading this specification, how to make and use alternative embodiments in which one or more of T S , T OD , and T R  can be equal to different values than those used in the illustrative embodiment. Furthermore, although the illustrative embodiment utilizes three Raman pulses per acceleration measurement with the same value for T R  between each pulse, it will be clear to those who are skilled in the art, after reading this specification, how to make and use alternative embodiments in which the number of pulses is greater than three or the interval between adjacent pulses is different across the pulse pairs, or both. 
         [0021]    It will be clear to those skilled in the art how to make and use AI accelerometer  201 . 
         [0022]    Conventional accelerometer  202  is a device that senses and provides measurements of the same acceleration events as does AI accelerometer  201 , but through the use of a technique such as one that involves measuring the deflection of a much larger proof mass than an atom cloud and through non-laser means. Accelerometer  202  continually provides acceleration measurements to complementary filter  203 , as does AI accelerometer  201 . Because it is not constrained to using laser pulses, conventional accelerometer  202  is capable of providing acceleration measurements at a much higher sample rate than AI accelerometer  201  and at a much wider bandwidth. It is for this reason that the measurements from accelerometer  202 , as they are used by filter  203 , are assumed to be subject to a unity transfer function. However, as those who are skilled in the art will appreciate, in some alternative embodiments, the transfer function assumed for the measurements can be assumed to be different than unity, depending on the particular application to be optimized (e.g., seismic acceleration measurement, missile acceleration measurement, etc.). In any event, it will be clear to those skilled in the art how to make and use conventional accelerometer  202 . 
         [0023]    Complementary filter  203  is a data-processing system that receives accelerometer measurements from AI accelerometer  201  and conventional accelerometer  202 , and provides filtered accelerometer measurements in accordance with the illustrative embodiment of the present invention. Filter  203  comprises a general-purpose processor or a special-purpose processor such as a digital signal processing device, or both. Filter  203  combines acceleration measurements from AI accelerometer  201 , which is characterized by transfer function G(s), with acceleration measurements from conventional accelerometer  202  that have been adjusted by a complementary function, 1−Ĝ(s), where Ĝ(s) is an approximation of G(s). This complementary filtering is further described below and with respect to  FIG. 4 , which depicts a signal-processing model of complementary filter  203 . It will be clear to those skilled in the art, after reading this specification, how to make and use complementary filter  203 . 
         [0024]      FIG. 3  depicts a signal-processing model of atom interferometric accelerometer  201 , in accordance with the illustrative embodiment of the present invention. 
         [0025]    As described above, the signal processing of AI accelerometer  201  is characterized by transfer function G(s), which is represented by signal-processing model  300 . Model  300  comprises AI continuous model  301 , sampling model  302 , and zero-order hold model  303 , interrelated as shown. 
         [0026]    Model  301  represents the “continuous” transfer function H AI (S) of the atom interferometric sensing that is utilized. As those who are skilled in the art will appreciate, for an illustrative AI accelerometer, H AI (S) is equal to: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
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                         AI 
                       
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                   ( 
                   
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         [0000]    where T R  and T OD  are as defined earlier. For frequency response, s=jω where ω is in radians per second. 
         [0027]    Model  302  represents the sampling that occurs as part of the illustrative AI accelerometer processing, in which the sample rate is T 5  as defined earlier. 
         [0028]    Model  303  represents the zero-order hold (ZOH) function that occurs as part of the AI accelerometer processing. As those who are skilled in the art will appreciate, the transfer function of the ZOH function is equal to: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ZOH 
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         [0000]    where T S  is the sample rate as defined earlier, α=0 if the expression within the absolute value operation is greater than or equal to zero, and α=1 if the same expression within the absolute value operation is less than zero. 
         [0029]      FIG. 4  depicts a signal-processing model of complementary filter  203 , in accordance with the illustrative embodiment of the present invention. In accordance with the illustrative embodiment, the sampling for the sampling model in  FIG. 4  is synchronous with the sampling for the sample model in  FIG. 3 . 
         [0030]    As described above, the signal processing of conventional accelerometer  202  is characterized by complementary function 1−Ĝ(s), where Ĝ(s) is an approximation of G(s), and where the complementary function is represented by signal-processing model  400 . Model  400  comprises estimation function  401  of AI continuous model  301 , sampling model  402 , zero-order hold model  403 , and difference function  404 , interrelated as shown. 
         [0031]    Model  401  represents the approximation Ĥ AI (S) of continuous transfer function H AI (s), defined earlier. 
         [0032]    Model  402  represents the sampling that occurs, in which the sample rate is also equal to T S , as defined earlier. The sampling occurring at model  402  is synchronized with the sampling occurring at model  302 . 
         [0033]    Model  403  represents the zero-order hold (ZOH) function performed, in which the transfer function is also equal to ZOH(jω), as defined earlier. 
         [0034]    Difference function  404  compares i) the output measurements from conventional accelerometer  202 , to which output measurements an ideal wideband accelerometer (i.e., with a unity transfer function) is assumed to apply, to ii) those output measurements as adjusted by Ĝ(s). The transfer function Ĝ(s) represents the combined transfer functions of models  401  through  403 . 
         [0035]    The signal-processing model of complementary filter  203  further comprises adder function  405 , which combines the measurements subject to model  300  with the complementary data produced by model  400 , in accordance with the illustrative embodiment of the present invention. The resulting output from function  405  comprises filtered acceleration measurements. 
         [0036]      FIGS. 5 through 8  depict flowcharts of the salient tasks as performed by system  200 , in accordance with the illustrative embodiment of the present invention. As those who are skilled in the art will appreciate, in some alternative embodiments, only a subset of the depicted tasks is performed. In some other alternative embodiments, at least some of the tasks are performed simultaneously or in a different order from that depicted. 
         [0037]    In accordance with the illustrative embodiment, AI accelerometer  201  performs the subtasks that are associated with task  501  and with respect to  FIG. 6 , conventional accelerometer  202  performs the subtasks that are associated with task  502  and with respect to  FIG. 7 , and complementary filter  203  performs the subtasks that are associated with task  503  and with respect to  FIG. 8 . However, as those who are skilled in the art will appreciate, the performing of the tasks depicted in  FIGS. 5 through 8  can be distributed among processing elements  201 ,  202 , and  203  in a different way than described, or can involve another combination of processing elements entirely. 
         [0038]      FIG. 5  depicts a flowchart of the main tasks performed by system  200 , in accordance with the illustrative embodiment of the present invention. For pedagogical purposes, tasks  501 ,  502 , and  503  are depicted as being performed in series by system  200 . However, as those who are skilled in the art will appreciate, system  200  is able to perform two or more of the depicted tasks in parallel. 
         [0039]    At task  501 , system  200  processes an acceleration event input via AI accelerometer  201 , in well-known fashion. The processing associated with task  501  is described in detail below and with respect to  FIG. 6 . 
         [0040]    At task  502 , system  200  processes the same acceleration event input via conventional accelerometer  202 , in well-known fashion. The processing associated with task  502  is described in detail below and with respect to  FIG. 7 . 
         [0041]    At task  503 , system  200  generates filtered accelerometer measurements, based on the processing performed at tasks  501  and  502 , in accordance with the illustrative embodiment of the present invention. The processing associated with task  503  is described in detail below and with respect to  FIG. 8 . 
         [0042]    After task  503 , task execution proceeds back to task  501 , in which system  200  continues to process subsequent acceleration event inputs. For example, system  200  can process the subsequent events periodically, sporadically, or on demand. 
         [0043]      FIG. 6  depicts a flowchart of the salient subtasks associated with task  501 . At task  601 , AI accelerometer  201  senses an acceleration event in well-known fashion, resulting in a measurement that is one of multiple, intermediate samples that are independent of measurements provided by conventional accelerometer  202 . 
         [0044]    At task  602 , AI accelerometer  201  performs a zero-order hold function on the intermediate samples, in well-known fashion. The zero-order hold function results in a series of AI accelerometer output samples. 
         [0045]      FIG. 7  depicts a flowchart of the salient subtask associated with task  502 . At task  701 , conventional accelerometer  202  senses an acceleration event in well-known fashion, resulting in a raw measurement. The raw measurement is one of multiple samples provided by accelerometer  202 . 
         [0046]      FIG. 8  depicts a flowchart of the salient subtasks associated with task  503 . At task  801 , complementary filter  203  approximates a transfer function H AI (S) that is characteristic of AI accelerometer  201 , resulting in the approximation Ĥ AI (S). 
         [0047]    At task  802 , filter  203  adjusts the raw acceleration measurements produced by conventional accelerometer  202 , with the approximation of the transfer function obtained at task  801 . This results in adjusted measurements that constitute a series of intermediate samples. 
         [0048]    At task  803 , filter  203  performs a zero-order hold function, with transfer function ZOH(jω), on the intermediate samples. This results in a series of zero-order hold output samples. 
         [0049]    At task  804 , filter  203  compares one or more raw acceleration measurements received from conventional accelerometer  202  to which a unity function is applied, with one or more of the output samples provided at task  803 . The comparison, which is a difference calculation, results in a series of complementary output samples. 
         [0050]    At task  805 , filter  203  generates one or more filtered acceleration measurements based on i) the complementary output samples provided at task  804  and ii) the output samples from AI accelerometer  201 . In accordance with the illustrative embodiment, filter  203  generates the filtered measurements based on adding the complementary output samples and the AI accelerometer output samples together. 
         [0051]    It is to be understood that the disclosure teaches just one example of the illustrative embodiment and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.