Patent Description:
Quartz oscillators are used in many different devices, systems and applications that require a stable frequency reference including computers, communications, radio-location, and navigation, by way of example. Quartz oscillators typically provide the requisite frequency stability and can be a more cost-effective alternative as compared to atomic, rubidium and other frequency references.

A key performance metric for oscillators is frequency stability in the presence of environmentally-induced effects, some of which can lead to significant performance degradation in devices and systems that incorporate oscillators. For example, frequency stability is a critical design parameter for oscillators used in navigation systems in which accuracy is of paramount importance. Navigation systems are susceptible to degraded performance as a result of environmental conditions and, as such, any compromise in the quality and performance of the oscillators used as frequency references can have detrimental effects on the accuracy of the navigation systems. Expectations for product performance continue to rise, which in turn has resulted in system specifications with increasing performance requirements on individual components, such as oscillators.

Various factors can negatively affect the frequency stability of a quartz oscillator, with such effects typically manifested as undesirable frequency shifts. For example, such frequency shifts may be caused by conditions such as: temperature changes (e.g., changes in ambient temperature and/or heat transfer effects on elements within the oscillator); humidity; pressure; changes in supply voltage or load; the presence of external electromagnetic fields; or the aging of components.

Oscillators are also known to be very sensitive to accelerations resulting from shock, rotation, vibrations, movements and inclinations. Such conditions can be particularly problematic for applications that require high-precision oscillators, such as navigation systems. For example, navigation systems are now used extensively in the operation of heavy equipment and machinery for construction and agricultural applications (e.g., "moving machines"). For example, operating equipment may include an on-board navigation receiver to facilitate precision-guided excavation, road repair, crop harvesting or any number of other tasks. Given the nature of the service conditions in these applications, shock and vibration-induced effects can detrimentally affect the precision of navigation receivers that utilize quartz oscillators. For example, during operation, a navigation receiver installed on a moving machine may be subjected to disturbances such as shaking during movement, as well as jolts, shocks or vibrations from the actions of the working assemblies on the machines. Although various techniques may be employed in equipment and systems to mitigate or correct for these effects, better test and measurement methods are still needed prior to placing such equipment into service.

Ensuring quartz oscillators meet the necessary standards of performance requires accurate and reliable testing and verification techniques to measure frequency and vibrational stability, and in particular, an oscillator's sensitivity to acceleration. The estimate of the stability of a quartz oscillator in response to acceleration effects is referred to as g-sensitivity, which is defined as the relative change in the output frequency of an oscillator at an acceleration of one g applied to an oscillator, where g is the acceleration of gravity on the surface of the earth at sea level (approximately equal to <NUM>/s<NUM>).

The g-sensitivity of an oscillator can be measured during the manufacturing process of an oscillator and various, well-known techniques have been used by oscillator manufacturers for this purpose. However, testing and verification procedures become more complicated once oscillators are integrated onto circuit boards and further integrated into systems such as navigation receivers and the like. For example, measuring g-sensitivity of a quartz oscillator that is mounted on a circuit board, but which is not inside an equipment housing, introduces thermal effects that can affect g-sensitivity estimates. Furthermore, quartz oscillators are mass-produced, giving rise to quality control concerns given the wide range of performance requirements and operating conditions in which these devices are employed. As might be expected, those who make or use navigation systems for commercial and industrial applications, which are subject to more extreme vibrational and other environmental conditions, cannot necessarily rely on testing that is performed by oscillator device manufacturers who are serving the broad spectrum of device applications.

Various methods are used to test and measure g-sensitivity in quartz oscillators. These methods are classified as either static or dynamic. In static testing, the quartz crystal is maintained in a stationary position (i.e., static position) along one axis for a predetermined period of time during which gravity acceleration affecting the crystal is not changed. The position of the crystal is then changed (e.g., typically turned <NUM>°), and the crystal is maintained in this subsequent position the same predetermined period of time as the first instance. Despite the evident simplicity, static testing has several drawbacks, one example being deficiencies in measuring and/or accounting for temperature drift of an oscillator's frequency, which can be a significant consideration for practical applications and operations. In dynamic testing, different apparatuses and test setups can be used (e.g., vibration benches, etc.) to provide the necessary accelerations while testing. Using vibration benches, for example, harmonic and random vibrations at different frequencies and strengths can be created. However, vibration benches and other dynamic test setups can be quite expensive and may require rigorous control of specific conditions for the setup and conduct of tests
Further prior art is disclosed in the following documents. <NPL>, discloses an investigation of the influence of the oscillator quality on carrier phase tracking performance. Particularly, the effects of acceleration sensitivity (or g-sensitivity) of the oscillator are examined in the context of pedestrian navigation. A method to compensate for the oscillator's g-sensitivity, using information from Inertial Measurement Unit is proposed and tested. In the method the oscillator is mounted inside a rectangular parallelepiped box, and three axes are marked arbitrarily. Intermediate frequency samples are logged for a period of <NUM> seconds, during which time, the oscillator is rotated through each of its three axes, resting momentarily when each axis is aligned with the vertical. The algorithm is validated using a high quality Inertial Measurement Unit and, subsequently, the relative performance of a MEMS grade sensor is assessed. <NPL> discloses three topics on acceleration sensitivity of quartz crystal oscillators. The topics include the effects of sinusoidal and random vibration, phase noise and integrated phase jitter; the vector nature of quartz resonator sensitivity; the theoretical description of the cause of the acceleration sensitivity of quartz resonators; techniques for the measurement of acceleration sensitivity; and the effect of frequency multiplication on acceleration effect. <NPL>, discloses results from laboratory and flight test experiments. Laboratory tests were conducted to characterize oscillator performance under varying gravity and magnetic field conditions. Three Rubidium oscillators were flown on Ohio University's DC-<NUM> research aircraft. The oscillators were mounted in three different locations in different ways, including vibration isolation and hard mounting to the floor of the aircraft. Each of the oscillators was connected to a GPS receiver for error characterization. The frequency stability performance is profiled against the flight dynamics based on a navigation-grade inertial navigation system. The goal of this document is to characterize the in-flight performance of Rb oscillators and to determine the feasibility of deriving frequency error corrections based on aircraft orientation and dynamics.

An improved testing method is needed to measure g-sensitivity of quartz oscillators that are incorporated in high-precision systems, such as navigation receivers, which operate in environments that are subjected to vibrational effects and other mechanical forces. Embodiments described herein include a method and system for measuring the g-sensitivity of quartz oscillators in a manner that overcomes the issues and challenges of conventional test methods.

A method according to the independent claim <NUM>, for estimating the g-sensitivity of a quartz oscillator comprises rotating the quartz oscillator successively around each of a plurality of axes constituting a full-rank system, measuring a frequency of the quartz oscillator at a predetermined rate as a function of time as the quartz oscillator is rotated, wherein the predetermined rate has a value of approximately greater than or equal to <NUM>, and estimating an integral g-sensitivity vector, while the quartz oscillator is rotated, using a data fitting and estimation model, e.g., a Least Square Method (LSM) in one example, using the plurality of frequency measurements obtained while the quartz oscillator was in rotation around the three orthogonal axes.

The plurality of axes in the full-rank system comprises three orthogonal axes including an x-axis, a y-axis and a z-axis. In the embodiments, rotations around the x-axis, y-axis, z-axis are performed at a substantially constant angular velocity.

According to an aspect, the frequency of the quartz oscillator is measured to derive a frequency estimate used to obtain a relative deviation of the frequency of the quartz oscillator, relative to its nominal frequency, as it is rotated around the three orthogonal axes, wherein the relative deviation is represented in parts per billion (ppb) units.

According to one aspect, the constant angular velocity can be a value in the range of approximately <NUM> to <NUM> turn per second and the predetermined rate of measuring frequency is a value of approximately greater than or equal to <NUM>.

In one embodiment, to facilitate the estimate of the integral g-sensitivity vector, frequency measurements from rotation of the quartz oscillator are represented as a function of relative frequency deviations, angular velocity, time-dependent terms representing thermal frequency variations, and projections of orthogonal harmonic components of the oscillator's frequency onto respective planes that are orthogonal to the respective axes of rotation.

In another embodiment, according to the independent claim <NUM>, a system is provided that includes a test adapter unit configured to receive the quartz oscillator for testing, wherein the test adapter unit is configured to rotate the quartz oscillator and wherein the test adapter unit is configured to measure a frequency of the quartz oscillator at a predetermined rate as a function of time during rotation of the quartz oscillator, wherein the predetermined rate has a value of approximately greater than or equal to <NUM>; and a processor, for executing computer program instructions stored in a memory, to perform operations for estimating the g-sensitivity of a quartz oscillator. The operations include rotating the quartz oscillator, in cooperation with the test adapter unit configured to receive the quartz oscillator for testing, at a substantially constant angular velocity successively around each of three orthogonal axes, measuring a frequency of the quartz oscillator at a predetermined rate as a function of time during the rotating of the quartz oscillator, and estimating an integral g-sensitivity vector, during the rotating of the quartz oscillator, using a data fitting and estimation model and a plurality of frequency measurements obtained from the measuring of the frequency of the quartz oscillator.

According to another aspect, the relative deviation of the frequency of the quartz oscillator can measured when the quartz oscillator is fixed in position on a Global Navigation Satellite System (GNSS) receiver board, taking into account a derivative offset variable, based on clock offset and drift rate relative to GNSS system time.

Various illustrative embodiments will now be described more fully with reference to the accompanying drawings in which some of the illustrative embodiments are shown. It should be understood, however, that there is no intent to limit illustrative embodiments to the particular forms disclosed, but on the contrary, illustrative embodiments are intended to cover all modifications falling within the scope of the claims. Like numbers refer to like elements throughout the description of the figures. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of illustrative embodiments.

An improved testing method is needed to measure g-sensitivity of quartz oscillators that are incorporated in high-precision systems, such as navigation receivers, which operate in environments that are subjected to vibrational effects and other mechanical forces. Embodiments described herein include a method and system for measuring the g-sensitivity of quartz oscillators in a manner that overcomes the issues and challenges of conventional test methods.

As described, the estimate of the stability of a quartz oscillator in response to acceleration effects is referred to as g-sensitivity, which is defined as the relative change in the output frequency of an oscillator at an acceleration of one g (<NUM>) applied to an oscillator, where g is the acceleration of gravity on the surface of the earth at sea level (approximately equal to <NUM>/s<NUM>). Generally, for different oscillator types, relative frequency shifts depend on their configuration and can range from <NUM>-<NUM> to <NUM>-<NUM>. It is often expressed in terms of ppb/g (parts per billion/g). A unit of ppb/g corresponds to a change in relative frequency by <NUM>-<NUM> at an acceleration equal to <NUM>. G-sensitivity is represented as a vector because it depends on both its value (magnitude) and the direction of acceleration.

A measure of g-sensitivity shows the sensitivity of the quartz oscillator to acceleration along a plurality of axes in a full-rank system, such as three orthogonal axes (e.g., x-axis, y-axis, z-axis), the direction of which can be determined in different ways. For example, manufacturers of quartz oscillators normally measure g-sensitivity by directing axes x, y and z along the quartz crystal axes. However, this method is not practical for measuring g-sensitivity of a quartz oscillator that has already been incorporated inside a housing of a device "hiding" its axes. It is thus more practical to test and measure g-sensitivity by orienting the axes relative to the geometrical features of the assembling board onto which the quartz oscillator is installed. In this manner, one can more readily ascertain along which axis the board exhibits the greatest amount of vibration sensitivity, the least amount, and so on.

<FIG> shows the projections of g-sensitivity vector P on axes x, y and z. As shown, the absolute value of the g-sensitivity vector P is normally directed at an angle to the axes and therefore does not coincide with a normal to an axis. The value of g-sensitivity vector P can be calculated based on orthogonal components Px, Py and Pz as follows: <MAT> <MAT> <MAT>.

If the value and orientation angle of the quartz oscillator are known relative to a device comprising a quartz oscillator (e.g., a navigation receiver), wherein the device is fixed to a source of vibration (e.g., tractor, bulldozer, etc.), then the direction of most intense vibrations can predict the effect of the acting accelerations.

A further description of static and dynamic testing of g-sensitivity in quartz oscillators will now be provided.

Static Testing. One of the most common and conceptually simple static test methods is commonly referred to as the "<NUM> Tipover" test, which is essentially using changes in the earth's gravitational field to cause shifts in the oscillator frequency. The "<NUM> Tipover" name is derived from the fact that frequency change is measured as the unit under test is effectively turned upside-down. That is, the unit is turned around the horizontal axis (e.g., by <NUM> degrees) such that the scalar multiplication product of acceleration and the normal vector to the original resonator's tip changes from -<NUM> to +<NUM>, the net effect being a change (difference) of <NUM>. Therefore, the amount of measured frequency shift divided by <NUM> represents the oscillator's g-sensitivity in that axis. The procedure is then repeated for the other two axes.

As indicated, this method of static testing has a considerable disadvantage with regard to measuring or accounting for a temperature drift of oscillator's frequency, which is particularly relevant when testing quartz oscillators on assembled boards without placing them in a device housing. Thus, testing by an oscillator manufacturer does not have the same complexities as those who must test oscillators that have already been installed on assembly boards and/or integrated into devices such as navigation receivers. In these latter scenarios, an oscillator's temperature mode changes due to re-orientation of the board, resulting in a temperature frequency drift as shown in <FIG>. In particular, <FIG> is a plot showing the drift of relative frequency in ppb/g units as a function of time during the process of re-orientation of an oscillator in <NUM>° around one axis, with the relative frequency drift represented in units <MAT>, i.e., the ratio of frequency deviation to the nominal frequency of the oscillator multiplied by <NUM><NUM>. The measurements in <FIG> were taken for a typical quartz oscillator used in navigation receivers. In particular, the measurements were obtained for a quartz oscillator arranged on navigation receiver's assembly board without the housing. As shown in <FIG>, there are meander oscillations of the oscillator's frequency due to sign reversals of the gravity acceleration (g) from the re-orientation of the board by <NUM> degrees in the vertical plane. Moreover, when the assembly board is fixed, there is a temperature drift (e.g., thermal trend) from the overlaid noise component caused by oscillator frequency alternations (e.g., the so-called "flicker effect"), which reduces the accuracy of estimating the g-sensitivity of the oscillator.

Dynamic testing. Generally, dynamic testing methods obtain measurements of g-sensitivity by influencing continuously-varied accelerations on a quartz oscillator along a tested axis. As indicated, vibration benches, are commonly used to apply both sinusoidal and wide-band random vibrations to the oscillator. There are also dynamic methods that do not utilize vibration benches, where g-sensitivity is determined based on the acceleration of gravity. For example, if meander re-orientations around the axis used in the static method (see <FIG>) are replaced with rotation around the same axis (and the oscillator's axes positions are recorded), then one can estimate g-sensitivity in this axis. This method requires rotation of the oscillator around two axes at a certain speed with further indication (e.g., recordation) of the oscillator's axes positions at each time moment. <FIG> is a plot showing the relative frequency drift in ppb/g units as a function of time during the process of rotating the oscillator around one of its axes. Among other disadvantages, the device for implementing rotation in the test configuration is more complicated because of the requirement to indicate positions of axes in motion (e.g., at each time instant). In another dynamic method not requiring a vibration stand, gravity acceleration can be applied to an oscillator under test that is kept in motion according to known rotation scenarios/techniques capable of providing an observable three-dimensional model for estimating the three-dimensional g-sensitivity vector of the quartz crystal. However, these scenarios/techniques typically require expensive equipment and more complex implementations.

In view of the aforementioned shortcomings of the conventional test methods, embodiments of the invention described herein provide a test method that is capable of estimating vibration characteristics of a quartz oscillator without requiring the indication of axes positions at each time instant.

In particular, <FIG> shows a simplified flowchart depicting method <NUM> according to an illustrative embodiment for estimating the g-sensitivity of a quartz oscillator. As shown in step <NUM>, the quartz oscillator is rotated successively around each of a plurality of axes in a full-rank system. In one illustrative embodiment, the full-rank system can have a rank equal to <NUM> and comprise three orthogonal axes (e.g., x, y and z axes). In step <NUM>, the frequency of the quartz oscillator is measured at a predetermined rate as a function of time as the quartz oscillator is rotated, but without indicating axis positions at each time instant. In step <NUM>, an integral g-sensitivity vector is estimated, in one example, using a Least Square Method (LSM) according to frequency measurements obtained in rotation around the three orthogonal axes. Importantly, at the same time while the quartz oscillator is rotated around each of the axes, the projection of the frequency integral vector P to the respective plane that is orthogonal to the respective axis of rotation is estimated (see <FIG>), where vector P characterizes the g-sensitivity of the quartz oscillator.

As will be appreciated by those skilled in the art, a non-trivial rotation scenario for rotating the quartz oscillator in prior arrangements typically requires more complex and expensive equipment. According to the embodiments herein, various rotation scenarios can be employed and are contemplated by these teachings. For example, the quartz oscillator can be rotated according to known rotation scenarios, but successively around each of a plurality of axes (e.g., linearly independent axes) that collectively form or otherwise constitute a full-rank system. In the embodiments, the quartz oscillator is rotated at a substantially constant angular velocity. In one example, the constant angular velocity can be set at a value in the range of <NUM> to <NUM> turn per second while the predetermined rate of measuring frequency is set at a value of no less than <NUM>. In another embodiment, the predetermined rate of measuring frequency may be set to be no less than <NUM>. However, these values and ranges are only meant to be illustrative and not limiting in any manner. Other values and combinations of values for constant angular velocity and/or the measuring frequency rate are contemplated by the teachings herein. For example, rotation about the axes can be at a higher angular velocity, e.g., greater than <NUM> turn per second, but other factors (e.g., centripetal acceleration, etc.) may have to be considered as will be apparent to one skilled in the art. Test equipment may also need to be modified and/or augmented to support rotation at higher angular velocities. Conversely, lower angular velocities (e.g., less than <NUM> turns per second) may be possible in some scenarios, but other factors may need to be considered as will now be described (e.g., in the context of thermal noise in one example). According to an aspect of the invention, estimating the integral frequency shift parameter (e.g., ppb/g parameter) is done taking into account the disturbing effects from thermal frequency variations. For example, the choice of a value for constant angular velocity is based on the following considerations. The spectrum of thermal noise lies within a certain finite band. The constant angular velocity must be distinguishable from the spectrum of thermal noise, e.g., it should be much higher. On the other hand, the rate of measuring frequency must distinguish rotation terms and thus should be, for example, at least <NUM> times higher than the constant angular velocity, due to the Nyquist-Shannon sampling theorem.

<FIG> is a plot showing the drift of relative frequency in successive rotations of an oscillator around axes x, y and z measured according to an illustrative embodiment of the invention. In particular, <FIG> shows the relative deviation of the oscillator's frequency (e.g., the ratio of frequency deviation to the nominal frequency multiplied by <NUM><NUM>) in rotating successively around axes x, y and z. In <FIG>, measurements up to approximately <NUM> seconds correspond with the rotation around axis x, measurements after approximately <NUM> seconds and up to approximately <NUM> seconds correspond to rotation around axis y, and measurements after approximately <NUM> seconds and up to approximately <NUM> seconds correspond to rotation around axis z.

For the operation that follows, <MAT> designates results of oscillation frequency in rotation around the x-axis, <MAT> designates results in rotation around the y-axis, and <MAT> designates results in rotation around the z-axis. The expression for <MAT> is provided below, with the expressions for <MAT> and <MAT> derived and represented in a similar manner, e.g., with appropriate substitution of the corresponding variables pertaining to the respective rotations around axes y and z (e.g., Cy or Cz instead of Cx, and so on). From the above noted frequency measurements shown in <FIG> for rotations around the x, y and z axes, the following operation can be represented, in general: <MAT> where:.

To estimate integral g-sensitivity vector P, coefficients Cx, Sx (the projections of orthogonal harmonic components from Equation set <NUM>) have to be estimated. A wide range of estimators (e.g., data fitting and estimation models/methods) can be applied to solve the problem, e.g., the Least Squares Method (LSM), Kalman filter method, neural networking methods, regression methods, or other types of non-linear or heuristic estimators. Accordingly, coefficients Cx, Sx are evaluated and their corresponding estimates Ĉx, Ŝx are provided as outputs.

The term Bx(i·T) can also be modelled in various fashions as will be appreciated by those skilled in the art. As such, the Bx(i·T) representation also has an influence on the variability of specified estimate methods.

To estimate coefficients Cx, Sx (from Equation set <NUM>), approximate the term Bx(i·T) in the form of polynomial <MAT> where:.

So, Equation <NUM> will take the form: <MAT>.

To estimate unknown coefficients in Equation <NUM>, compose the parameter vector in the form <MAT> and estimate it (using LSM, for example) with reference to an observation vector <MAT>.

Using LSM for example, a solution for equal weights of measurements can be represented as: <MAT> where <MAT> <MAT> <MAT>.

Thereafter, only estimates of the quadrature harmonic components, e.g., Ĉx and Ŝx are used. Similarly, estimates of quadrature components Ĉy andŜy are obtained in rotation around axis y and estimates of quadrature components Ĉz and Ŝz are obtained in rotation around axis z, in a similar manner as shown above, e.g., with appropriate substitution of the corresponding variables pertaining to the respective rotations around axes y and z.

The magnitude of the integral g-sensitivity vector P is then obtained based on the calculated estimates: <MAT>.

Projection estimates of the absolute value for g-sensitivity vector P on axes x, y, z can then be calculated according to the obtained results by using the following variables for these calculations: <MAT> <MAT> <MAT>.

The magnitude of the integral g-sensitivity vector P (from Equation <NUM>) can therefore be written as: <MAT>.

As shown in <FIG>, values Ax, Ay and Az are the projections of the integral g-sensitivity vector P for the quartz oscillator <NUM> (unit under test) onto planes YZ, XZ and XY, respectively, during rotation of the quartz oscillator.

The expression for g-sensitivity vector P can be written as follows: <MAT> and <MAT>.

Knowing Ax, Ay and Az, one can express projection estimates of the g-sensitivity vector P on axes x, y and z as follows: <MAT> where: <MAT> for any real number a.

According to another aspect of the invention, signs of the projections Px,Py,Pz of the integral g-sensitivity vector P on the x-axis, y-axis and z-axis, respectively, are obtained to derive actual values of the projections Px,Py,Pz. The signs can be obtained and evaluated in a number of ways. In one example, the signs can be obtained and evaluated by conducting successive <NUM>-tipover tests for each of the x-axis, y-axis and z-axis, respectively. The signs can also be obtained and evaluated via fixation of a rotation angle during each successive rotation of the quartz oscillator around the x-axis, y-axis and z-axis, respectively. In one example, the fixation of the rotation angle can be performed at the start of each successive rotation and, in another alternative example, the fixation of the rotation angle can be performed at the end of each successive rotation.

In this manner, the values of the projections Px,Py,Pz can be derived as follows: <MAT> <MAT> <MAT> and where
SNx, SNy, SNz correspond to the signs for the respective three orthogonal axes.

According to one illustrative embodiment noted above, rotations around the x-axis, y-axis, z-axis are performed at a substantially constant angular velocity, and rotation phases are represented as: <MAT> wherein
ωrot = <NUM>π · frot is the angular velocity.

According to another embodiment, the quartz oscillator is affixed in position on a Global Navigation Satellite System (GNSS) receiver board for use in the aforementioned navigation applications. According to an aspect of the invention, the g-sensitivity of the quartz oscillator can be measured while mounted on the receiver board. In this example, all heterodyne frequencies of the GNSS receiver and time scale are generated using the frequency of the quartz oscillator. A signal from a stationary antenna is fed to the receiver and, once satellites are locked, antenna coordinates are determined. Additionally, clock offset relative to system time and its drift rate, commonly referred to as derivative offset (DO), are also determined. Relative frequency shift (relative deviation) of the oscillator (mounted on the GNSS receiver board), as it is rotated around the x-axis, y-axis and z-axis, respectively, can then be defined as: <MAT> <MAT> and<MAT>.

This inventive method and system provide a more robust, accurate and practical method for measuring g-sensitivity of quartz oscillators that are incorporated in high-precision systems, such as navigation receivers, which operate in environments that are subjected to vibrational effects and other mechanical forces.

As detailed above, the various embodiments herein can be embodied in the form of methods and a system for practicing those methods. The disclosed methods may be performed by a combination of hardware, software, firmware, middleware, and computer-readable medium (collectively "computer") installed in and/or communicatively connected to a user device.

<FIG> is a high-level block diagram of an exemplary system <NUM> for carrying out the method in accordance with the various embodiments herein. In particular, system <NUM> may include computer <NUM> (which may function as a test server) connected or otherwise coupled to a test adapter unit <NUM>, which is further connected or coupled to unit under test <NUM>. By way of example, unit under test <NUM> may be a receiver board from a navigation receiver, wherein the receiver board includes a quartz oscillator. Computer <NUM> is shown to comprise a processor <NUM> operatively coupled to a data storage device <NUM> and a memory <NUM>. Processor <NUM> controls the overall operation of computer <NUM> by executing computer program instructions that define such operations. Communications bus <NUM> facilitates the coupling and communication between the various components of computer <NUM>. The computer program instructions may be stored in data storage device <NUM>, or a non-transitory computer readable medium, and loaded into memory <NUM> when execution of the computer program instructions is desired. Thus, the steps of the disclosed method (see, <FIG> and the associated discussion herein above) can be defined by the computer program instructions stored in memory <NUM> and/or data storage device <NUM> and controlled by processor <NUM> executing the computer program instructions via a computer-readable medium. For example, the computer program instructions can be implemented as computer executable code programmed by one skilled in the art to perform the illustrative operations defined by the disclosed method. Accordingly, by executing the computer program instructions, processor <NUM> executes an algorithm defined by the disclosed method.

Processor <NUM> may include both general and special purpose microprocessors, and may be the sole processor or one of multiple processors of computer <NUM>. Processor <NUM> may comprise one or more central processing units (CPUs), for example. Processor <NUM>, data storage device <NUM> and/or memory <NUM> may include, be supplemented by, or incorporated in, one or more application-specific integrated circuits (ASICs) and/or one or more field programmable gate arrays (FPGAs).

Data storage device <NUM> and memory <NUM> each comprise a tangible non-transitory computer readable storage medium. Data storage device <NUM>, and memory <NUM>, may each include high-speed random access memory, such as dynamic random access memory (DRAM), static random access memory (SRAM), double data rate synchronous dynamic random access memory (DDR RAM), or other random access solid state memory devices, and may include non-volatile memory, such as one or more magnetic disk storage devices such as internal hard disks and removable disks, magnetooptical disk storage devices, optical disk storage devices, flash memory devices, semiconductor memory devices, such as erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM), digital versatile disc read-only memory (DVD-ROM) disks, or other non-volatile solid state storage devices.

It should be noted that for clarity of explanation, the illustrative embodiments described herein may be presented as comprising individual functional blocks or combinations of functional blocks. The functions these blocks represent may be provided through the use of either dedicated or shared hardware, including, but not limited to, hardware capable of executing software. Illustrative embodiments may comprise digital signal processor ("DSP") hardware and/or software performing the operation described herein. Thus, for example, it will be appreciated by those skilled in the art that the block diagrams herein represent conceptual views of illustrative functions, operations and/or circuitry of the principles described in the various embodiments herein. Similarly, it will be appreciated that any flowcharts, flow diagrams, state transition diagrams, pseudo code, program code and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer, machine or processor, whether or not such computer, machine or processor is explicitly shown. One skilled in the art will recognize that an implementation of an actual computer or computer system may have other structures and may contain other components as well, and that a high level representation of some of the components of such a computer is for illustrative purposes.

Claim 1:
A method (<NUM>) for estimating g-sensitivity of a quartz oscillator, comprising:
rotating (<NUM>) the quartz oscillator successively around each of a plurality of axes constituting a full-rank system, wherein the plurality of axes comprises three orthogonal axes including an x-axis, a y-axis, and a z-axis, and wherein the rotations around the x-axis, y-axis and z-axis are performed at a substantially constant angular velocity;
measuring (<NUM>) a frequency of the quartz oscillator at a predetermined rate as a function of time during the rotating (<NUM>) of the quartz oscillator; wherein the predetermined rate has a value of approximately greater than or equal to <NUM>; and
estimating (<NUM>) an integral g-sensitivity vector, during the rotating (<NUM>) of the quartz oscillator, using a data fitting and estimation model and a plurality of frequency measurements obtained from the measuring (<NUM>) of the frequency of the quartz oscillator.