Patent Publication Number: US-11038510-B2

Title: Oscillator with time error correction

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     Not Applicable. 
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to and/or claims the benefit of the earliest available effective filing date(s) from the following listed application(s) (the “Priority Applications”), if any, listed below (e.g., claims earliest available priority dates for other than provisional patent applications or claims benefits under 35 USC § 119(e) for provisional patent applications, for any and all parent, grandparent, great-grandparent, etc. applications of the Priority Application(s)). In addition, the present application is related to the “Related Applications,” if any, listed below. 
     FIELD OF THE DISCLOSURE 
     The present invention generally relates to highly accurate time sources and relates more specifically to error corrected time source devices with low power consumption requirements. 
     BACKGROUND OF THE DISCLOSURE 
     Oscillators, clocks, and other time sources play an important role for many types of data acquisition recorders. An accurate clock is typically used as an Analog to Digital Converter (ADC) clock that digitizes analog signals from sensors. Frequently in such applications, there are no Global Positioning System (GPS) timing signals or other types of reference time signals available, and therefore a real time ADC clock accuracy correction is not possible; however, if a clock behavior is well known, a post-acquisition data resampling is possible and such a post-acquisition system and method based on ADC clock correction improves data quality. 
     Ocean bottom node recorders, as one such application example, samples seismic sensor signals, and have become increasingly popular in the field of marine seismic exploration. In this case, a data acquisition recorder is deployed at each node of the seismic node network, and there are no cables interconnecting the nodes. Hydrophones and geophones are typically installed in the data acquisition recorders as sensors for measuring seismic signals. A time source for accurately timing the seismic signal data converter is integrated into each node along with components such as a power supply or battery, a microcomputer, a memory, and other supporting electronics. 
     This type of data acquisition system has several notable characteristics. The data acquisition recorders require low power consumption and the power source is not able to be recharged during long deployments. Data acquisition often occurs in GPS denied environments, and therefore accurate timing information is not available during the deployment of the node, which could last up to several months or more. Furthermore, the operation of exploration programs that utilize such data acquisition recorders is financially cumbersome. 
     During deployment of this type of seismic node at the ocean bottom, the frequency of the time source will drift from a nominal frequency due to aging, changes in ambient temperature, pressure, acceleration, or other factors, and a time error is consequently accumulated for the seismic data sampling clock. This time error results in ambiguous sampling of seismic data and therefore causes inaccurate mapping of oil and gas reserves. Any time source frequency drift or variation lessens the accuracy of data acquisition and thus negatively impacts the quality of the seismic investigation. 
     Historically, a Temperature Compensated Crystal Oscillator (TCXO) was used for marine seismic surveys owing largely to its characteristically low power consumption; however, TCXOs have not been able to provide an acceptably low enough time error for long term deployments. Oven Controlled Crystal Oscillators (OCXO) typically consume over one watt of power and are therefore not able to sustain a long time seismic survey operation owing to energy capacity limitations and the non-rechargeable nature of the power source. 
     Emerging OCXOs with significantly lower power consumption, typically on the order of two hundred milliwatts or less, have been developed and are able to provide a significant improvement in performance with regards to reduction of time error and low power operation. Other types of time sources, such as Chip Scale Atomic Clocks (CSAC), have been developed and are able to achieve significantly reduced time error but still consume on the order of two to three times more power than that of an emerging ultra-low power OCXO and are far more expensive to manufacture. 
     U.S. Pat. No. 5,697,082 describes a self-calibrating frequency standard system. In this self-calibrating timing system, a central node with an accurately known time reference, such as satellite GPS reference time signals or a cell phone tower reference time signal, is available. U.S. Pat. No. 5,940,458 describes a method for compensating for time error of time/frequency generator using an accurately known GPS time signal. Many other timing systems described in the art are configured to perform tedious error corrections that require significantly higher power consumption. What is needed is a cost effective clock system with ultra-low power consumption, consistent drift behavior, time error correction capability, and is able to provide highly accurate time signals in GPS denied environments and for long deployment times. Such a system opens the avenue for post data acquisition resampling by accurately correcting accumulated time error of the time source in relation to an absolute time reference. 
     SUMMARY OF THE DISCLOSURE 
     The present invention provides a system and method for making time error estimations and time corrections for several types of data acquisition recorders and sensor nodes. In a preferred embodiment, the system comprises a local oscillator, a phase meter, a computer-readable storage medium, a processor, a counter circuit, and a power source, wherein the processor is configured to generate a dual-linear time-dependent time error estimation or a dual-linear temperature-dependent time error estimation, wherein the local oscillator is configured to generate a periodic signal, wherein the periodic signal comprises a first frequency signal at a first time and a second frequency signal at a second time, wherein a first reference time signal, a first reference frequency signal, a second reference time signal, and a second reference frequency signal are communicated from a reference time source to the phase meter, wherein the phase meter is configured to measure the first frequency signal, the second frequency signal, a first time error, and a second time error, wherein the counter circuit is configured to receive the periodic signal from the local oscillator and generate a first time signal at a first time, a second time signal at a second time, and one or more interval time signals at corresponding interval times. 
     In embodiments, the local oscillator may be a TCXO, an OCXO, a MEMS time source, a lower power atomic oscillator, a low power microwave oscillator, an optical oscillators, a g-compensated oscillator, a mechanically mounted oscillator with shock and vibration isolation, a clock system further comprising a self-embodied phase meter or time interval counter circuit, or an independent one pulse per second counter circuit. 
     In various embodiments, the first time signal is synchronized with the first reference time signal, and the first frequency signal is calibrated to a nominal reference frequency signal. In various embodiments, the system further comprises a communication port configured to facilitate communication of information between the time error correcting clock system and a receiving device, an external measurement system, or the reference time source. In various embodiments, the time-dependent time error estimation is based on the first time signal, the first frequency signal, the second time signal, and the second frequency signal. In various embodiments, the processor is further configured to generate a corrected time-tag data set based on an uncorrected time-tag data set and one of either the time-dependent time error estimation or the temperature-dependent time error estimation. 
     In various embodiments, the system further comprises a temperature sensor configured to measure temperature in proximity to the local oscillator, wherein the temperature sensor generates a first temperature signal, a second temperature signal, or one or more interval temperature signals. In a further embodiment, the temperature-dependent time error estimation is based on the first temperature signal, the second temperature signal, or one or more interval temperature signals. 
     In a preferred embodiment, the system comprises a clock subsystem, a time error determination subsystem configured to generate a dual-linear time-dependent time error estimation or a dual-linear temperature-dependent time error estimation, and a communication subsystem, wherein the clock subsystem is configured to generate a first time signal and a first frequency signal at a first time and a second time signal and a second frequency signal at a second time. The system may further comprise a microcontroller configuration subsystem, a time error determination subsystem, and a time signal reconstruction subsystem. In a further embodiment, the system comprises a temperature determination subsystem configured to acquire a first temperature signal, a second temperature signal, or one or more interval temperature signals, wherein the time error determination subsystem is further configured to generate the time-dependent time error estimation based on the first temperature signal, the second temperature signal, or one or more interval temperature signals. 
     In a preferred embodiment, the method comprises the steps of determining a first time signal and a first frequency signal, determining a second time signal and a second frequency signal, and generating a time-dependent time error estimation from the first time signal, the first frequency signal, the second time signal, and the second frequency signal. 
     In various embodiments, the method further comprises the steps of generating the first time signal and the first frequency signal at a first time, receiving a first reference time signal and a first reference frequency signal, synchronizing the first time signal with the first reference time signal, calibrating the first frequency signal with the first reference frequency signal, generating the second time signal and the second frequency signal, generating one or more interval time signals, determining the interval time signals, losing reception of the reference time source for one or more of the interval times, receiving a second reference time signal and a second reference frequency signal, determining the second reference time signal at the second time, generating an uncorrected time-tag data set from the first time signal, the second time signal, or one or more interval time signals, generating a corrected time-tag data set from the time-dependent time error estimation and the uncorrected time-tag data set, wherein the first reference time signal and the first reference frequency signal are generated by a reference time source at the first time, wherein the second reference time signal and the second reference frequency signal are generated by the reference time source at the second time, wherein the time-dependent time error estimation is also generated from the first reference time signal and the second reference time signal. 
     In various embodiments, the method further comprises the steps of determining a first temperature signal at the first time, determining a second temperature signal at the second time, determining one or more interval temperature signals at the corresponding one or more interval times, generating a temperature-dependent time error estimation from the first temperature signal, the second temperature signal, or one or more interval temperature signals, and generating a corrected time-tag data set from the uncorrected time-tag data set and a total time-dependent time error estimation that is derived from the time-dependent time error estimation and the temperature-dependent time error estimation. 
     Embodiments include one, more, or any combination of all of the features listed above. Other features and advantages of the present invention will become apparent from the following more detailed description, taken in conjunction with the accompanying figures, which illustrate, by way of example, the principles of the invention. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  illustrates a block diagram of a time error correcting clock system, in accordance with an exemplary embodiment of the present invention; 
         FIG. 1B  illustrates a block diagram of alternate embodiment of a time error correcting clock system, in accordance with an exemplary embodiment of the present invention; 
         FIG. 2A  illustrates a flow chart of one embodiment of the time error correction method consistent with embodiments of the present disclosure; 
         FIG. 2B  illustrates a flow chart of an alternative embodiment of the time error correction method consistent with embodiments of the present disclosure; 
         FIG. 3  illustrates an actual time error curve of an example local oscillator over a long-term time deployment, a linear frequency drift error estimation based on the example local oscillator, and a conventional two point linear time drift approximation, in accordance with an exemplary embodiment of the present invention; 
         FIG. 4  illustrates a first residual time error curve and a linear time drift error estimation for the example illustrated in  FIG. 3 , in accordance with an exemplary embodiment of the present invention; and 
         FIG. 5  illustrates a conventional two point approximation residual time error curve and a dual-linear time drift error residual curve, in accordance with an exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following detailed description provides numerous details for a thorough understanding of various embodiments and an enabling description for these embodiments. One skilled in the relevant art will recognize that the present invention may be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, operations or functions are not shown or described in detail to avoid unnecessarily obscuring the description of the embodiments. 
     The described features, operations, functions, or characteristics may be combined in any suitable manner in one or more embodiments. It will also be readily understood that the order of the steps or actions of the methods described in connection with the embodiments disclosed herein may be changed, as would be apparent to those skilled in the art. Thus, any order in the drawings or detailed description is for illustrative purposes only and is not meant to imply a required order unless specified to require an order. 
       FIG. 1A  illustrates a block diagram of a time error correcting clock system  100 , in accordance with an exemplary embodiment of the present invention. The system  100  may comprise a local oscillator  10 , a power source  12 , a processor  13 , a computer-readable storage medium  14 , a phase meter  15 , a counter circuit  16 , a temperature sensor  18 , and a communication port  20 . The local oscillator  10  may be any periodic device capable of tracking the passage of time or generating a periodic signal. A variety of local oscillators  10  are contemplated, including, but not limited to, a TCXO, an OCXO, a microelectromechanical systems (MEMS) time source, a lower power atomic oscillator, a low power microwave oscillator, an optical oscillator, or a clock system further comprising a self-embodied phase meter or time interval counter circuit, an independent one pulse per second counter circuit, or an external measurement system  19 . It is further contemplated that other types of time sources may be used as a local oscillator  10  without loss of performance in regards to time error estimations and corrections. Examples of periodic signals generated by the local oscillator  10  include, but are not limited to, sinusoidal wave signals, square wave signals, triangle wave signals, and sawtooth wave signals. In embodiments, the local oscillator  10  may be a g-compensated oscillator or an oscillator that is mechanically mounted onto the system  100  in a manner that substantially isolates the local oscillator  10  from shock and vibration. 
     In various embodiments, the first time generally refers to a time just prior to the beginning of deployment of the system  100 , and the second time generally refers to a time soon after deployment of the system  100  has ended. An interval time generally refers to a time between the first time and the second time. The reference time source  11  is any device capable of tracking the passage of time or generating a periodic signal, and which is presumed to be more accurate than the local oscillator  10  and counter circuit  16 . The first reference frequency signal  42  and second reference frequency signal  43  are representations of frequency indicated by the reference time source  11  at the first time and at the second time, respectively, and which are standards used to measure the frequency signals  41 ,  44  of the periodic signal generated by the local oscillator  10 . The system  100  is capable of detecting availability of and receiving information from the reference time source  11  and can measure the time error and frequency error between the reference time source  11  and the local oscillator  10  and counter circuit  16  at both the first time and the second time; however, the system  100  typically has no access to any external reference time source at interval times between the first time and the second time and therefore cannot measure time error or frequency error at interval times between the first time and the second time. 
     At the first time, the first time signal  31  may be synchronized with the first reference time signal  32 , thus setting the first time signal  31  to be substantially equal to the first reference time signal  32 . Likewise at the first time, the first frequency signal  41  may be calibrated with the first reference frequency signal  42 , thus setting the first frequency signal  41  to be substantially equal to a nominal reference frequency signal having a predetermined frequency value. 
     The power source  12  stores or generates power and delivers the power, typically on the order of hundreds of milliwatts or less, to the various components and subsystems of the system  100 . The power source  12  is generally a battery; however, it is contemplated that other types of power sources may be suitable without loss of performance while operating the system  100 . 
     The processor  13  may be configured to receive any of the signals  31 ,  32 ,  33 ,  34 ,  35 ,  41 ,  42 ,  43 ,  44 ,  51 ,  53 , and  54 , and perform any of the algorithms or calculations as required by the software modules  201 ,  220 ,  240 ,  260 , and  290 . The processor  13  may be further configured to transmit the results of the algorithms or calculations to the receiving device  21  via the communication port  20  or to the computer-readable storage medium  14 . The processor  13  may be embodied as a general purpose integrated circuit, an application specific integrated circuit, a field-programmable gate array or equivalent, a low-power microprocessor, and/or other programmable logic devices. 
     The computer-readable storage medium  14  may be configured to store numerical values for or other information related to any of the signals  31 ,  32 ,  33 ,  34 ,  35 ,  41 ,  42 ,  43 ,  44 ,  51 ,  53  and  54 . The computer-readable storage medium  14  may be configured to store any of the software modules  201 ,  220 ,  240 ,  260 , and  290 , as well as estimations, calculated results, time-tag data sets  212  and  262 , or other information associated with the software modules, such as predetermined models or characteristic parameters. Many types of computer-readable storage medium  14  are suitable for the system  100  to operate efficiently, including, but not limited to, Flash memory, RAM, and EEPROM. The computer-readable storage medium  14  may be integrated into or embedded within the processor  13 . 
     The phase meter  15  may be configured to measure the relative phases between the first time signal  31  and the first reference time signal  32  as well as the relative phases between the second time signal  33  and the second reference time signal  34 . The phase meter  15  may be further configured to measure the relative frequency between the first frequency signal  41  and the first reference frequency signal  42  as well as the relative frequency between the second frequency signal  44  and the second reference frequency signal  43 . In various embodiments, the phase meter  15  may be a self-embedded phase meter, an external time interval counter circuit, or an external measurement system  19 , any one of which is configured to timestamp a one pulse per second time signal or to measure a frequency signal. The counter circuit  16  receives the periodic signal from the local oscillator  10  and generates time signals  31 ,  33 , and  35  in a desired format, such as seconds from an initial time or the date and time of measurements. The communication port  20  may facilitate communication of information between the system  100  and external devices  11 ,  19 , and  21  as well as enable a user to make various measurements within the system  100  at any time. The external measurement system  19  may be used to make measurements of the frequency signals  41 ,  44 . 
     The temperature sensor  18  may be configured to determine temperature in proximity to the local oscillator  10  at any time before, after, or during deployment of the system  100 . In various embodiments, the temperature sensor  18  may be a thermistor, thermocouple, a resistance temperature detector, semiconductor junctions, or other forms of temperature sensors. 
     The sensor  17  may be configured to determine sensor data in proximity to the local oscillator  10  or sensor data being externally directed towards the local oscillator  10 . Examples of sensors  17  include, but are not limited to, pressure sensors, acceleration sensors, position sensors, gyroscopes, inertial sensors, geophones, sensors used for ocean bottom seismic nodes (OBSN), underwater autonomous vehicles (UAV), land seismic exploration devices, and sensors used in other GPS denied environment or low power applications. 
     The software modules  201 ,  220 ,  240 ,  260 , and  290  tangibly embody program, functions, and/or instructions that the processor  13  to perform operations, tasks or actions as described herein. Suitable software, as applicable, may be readily provided by those of skill in the pertinent art(s) using the teachings presented herein and appropriate programming languages and tools, such as Java, Pascal, Python, C++, C, database languages, SDKs, firmware, microcode, and/or other languages and tools. Representative data may refer to tabulated data, graphical data, or functional relationships. 
     The microcontroller configuration module  201  may comprise a set of computer instructions or computer executable code for configuring the processor  13  using time signals from the local oscillator  10 . The microcontroller configuration module  201  may comprise a set of computer instructions or computer executable code for monitoring, controlling, signal processing, and automating various components within the system  100  or for protecting monitored components within the system  100 . The microcontroller configuration module  201  may comprise a set of computer instructions or computer executable code for zeroing, resetting, or otherwise setting any time signals measured by the phase meter  15  or the counter circuit  16  to desired values or converting any time signal units to desired units, such as seconds, minutes, days, years, or specific dates and specific times. The microcontroller configuration module  201  may comprise representative data of an uncorrected time-tag data set  212 , wherein the uncorrected time-tag data set  212  comprises representative data of the first time signal  31 , the second time signal  33 , or one or more interval time signals  35  received from the phase meter  15  or counter circuit  16 . 
     The temperature determination module  220  may comprise representative data of the first temperature signal  51 , the second temperature signal  53 , and one or more interval temperature signals  54  received from the temperature sensor  18 . The temperature determination module  220  may comprise a set of computer instructions or computer executable code for converting temperature signals  51 ,  53 , or  54  received from the temperature sensor  18  into appropriate units of temperature using a predetermined model or a manufacturer&#39;s datasheet. 
     The time error determination module  240  may comprise a set of computer instructions or computer executable code for calculating relative phases of time signals measured by the phase meter  15 . Relative phases between the periodic signal generated by the local oscillator  10  and reference time signals  32 ,  34  generated respectively by the reference time source  11  at the first time and at the second time represent time errors and may be calculated using a variety of suitable techniques, which may include, but are not limited to, a coarse measurement, a fine measurement, a single-point or multipoint self-calibration measurement, or a combination of measurements for a continuous one second measurement range without glitches. The time error determination module  240  may comprise a set of computer instructions or computer executable code for calculating a first time error, denoted as δT 1 , by using Equation 1, where T 1  and t 1  represent the first time signal  31  and the first reference time signal  32 , respectively. The time error determination module  240  may comprise a set of computer instructions or computer executable code for calculating a second time error, denoted as δT 2 , by using Equation 2, where T 2  and t 2  represent the second time signal  33  and the second reference time signal  34 , respectively.
 
δ T   1 =( T   1   −t   1 )   Equation 1
 
δ T   2 =( T   2   −t   2 )   Equation 2
 
     If the local oscillator  10  and counter circuit  16  are synchronized with the reference time source  11  at the first time, then the first time signal  31  is substantially equal to the first reference time signal  32 ; furthermore, if the frequency of the local oscillator  10  is calibrated at the first time, then the first frequency signal  41 , denoted as f 1 , is set substantially equal to a nominal reference frequency signal, denoted as f 0 , and therefore any of the equations f 1 =f 0 , T 1 =t 1 , and δT 1 =0. 
     The time error determination module  240  may comprise a set of computer instructions or computer executable code for calculating a time-dependent time error estimation, denoted as δT(T), by using Equation 3, which is a dual-linear estimation that takes into account the sum of a linear frequency drift time error estimation and a linear time drift time error estimation, where T represents interval time signals measured by the local oscillator  10  and is constrained to T 1 ≤T≤T 2 . Equation 3 is able to achieve highly accurate interval time error estimations δT(T) that are used by the time signal reconstruction module  260  to generate a corrected time-tag data set  262  having values of T−δT(T) at one or more interval times.
 
δ T ( T )=( f   2   −f   1 )*( T−T   1 ) 2 /[2 *f   0 *( T   2   −T   1 )]+( T−T   1 )*[δ T   2   −δT   1 −( T   2   −T   1 )*( f   2   −f   1 )/(2* f   0 )]/( T   2   −T   1 )   Equation 3
 
     In various embodiments, the temperature in proximity to the local oscillator  10  at the first time or at the second time, denoted respectively by K 1  and K 2  and measured in units of kelvin or centigrade, may have significantly different values. In this case, the time error determination module  240  may comprise a set of computer instructions or computer executable code for calculating a total time error estimation by using Equation 4, which provides an estimation for the frequency drift rate of the local oscillator  10  and therefore provides a more accurate linear frequency drift time error estimation by normalizing f 1  and f 2  to f 1 (K) and f 2 (K) at any convenient temperature K, with the available temperature characteristic of the local oscillator  10 .
 
δ T ( T )=[( f   2 ( K )− f   1 ( K )]*( T−T   1 ) 2 /[2 *f   0 *( T   2   −T   1 )]+( T−T   1 )*{δ T   2   −δT   1 −( T   2   −T   1 )*[ f   2 ( K )− f   1 ( K )]/(2 *f   0 )}/( T   2   −T   1 )   Equation 4
 
     The time error determination module  240  may comprise a set of computer instructions or computer executable code for determining and computing a total time error estimation at the first time, at the second time, at any interval time between the first time and the second time, at a time prior to the first time, or at a time after the second time. The temperatures K 1  and K 2 , may differ significantly from the temperature in proximity to the local oscillator  10  at one or more interval times during deployment, denoted by K D . As a result of this possible temperature difference, a total time error estimation that takes into consideration the frequency drift of the local oscillator  10  at various temperatures may further improve the accuracy of error estimation and corrections made by the clock system  100 . 
     In various embodiments, the time error determination module  240  may comprise a set of computer instructions or computer executable code for determining a temperature-dependent time error estimation from temperature characteristics based on testing performed on a representative local oscillator  10 , from storage data for temperature characteristics of local oscillator  10 , or predetermined model for the drift behavior of the local oscillator  10  as a function of temperature, or from measurements taken by the temperature sensor  18  and the local oscillator  10  during operation of the system  100 . In various embodiments, the temperature-dependent time error estimation, denoted as δT TCD , may be calculated by Equation 5, where the temperature-dependent frequency f(K) has been well characterized.
 
δ T   TCD =( T   2   −T   1 )*[ f ( K   D )− f   1 ]/ f   0    Equation 5
 
     In various embodiments wherein the clock system  100  is at a particular deployment site for an extensive period of time soon after the first time and just before the second time, a first frequency offset estimation may be included with the measured first frequency signal  41  to set the first frequency signal  41  substantially equal to a nominal reference frequency signal. 
     In various embodiments wherein the clock system  100  is at a particular deployment site for a period of time long after the first time and long before the second time, one of two error estimating techniques may be implemented for the time error estimation during transitions both at the beginning and at the end of the deployment, depending on the temperature dependent nature of the local oscillator  10 . In embodiments wherein the frequency of the local oscillator  10  is known to vary substantially linear with time due to a temperature difference, a first linear offset value, denoted by δT TC1 , and a second linear offset value, denoted by δT TC2 , may be calculated by Equation 6 and Equation 7, respectively.
 
δ T   TC1   =ΔT   1 *[ f   1 ( K   D )− f   1 ]/(2* f   0 )   Equation 6
 
δ T   TC2   =ΔT   2 *[ f   2   −f   2 ( K   D )]/(2* f   0 )   Equation 7
 
     In embodiments wherein the frequency of the local oscillator  10  is known to vary substantially similar to a step function with time due to a temperature difference, a first step offset value, denoted by δT TC3 , and a second step offset value, denoted by δT TC4 , may be calculated by Equation 8 and Equation 9, respectively.
 
δ T   TC3 =(Δ T   1 )*[ f   1 ( K   D )− f   1 ]/(f 0 )   Equation 8
 
δ T   TC4 =(Δ T   2 )*[ f   2   −f   2 ( K   D )]/( f   0 )   Equation 9
 
     In Equations 6-9, the value of ΔT 1  corresponds to the difference in time between the synchronization at the first time and the time that the system  100  reaches the deployment site, and the value of ΔT 2  corresponds to the difference in time between the time when the system  100  leaves the deployment site and the time in which the system reestablishes communication with the reference time source  11  and receives the second reference time signal  34  and second reference frequency signal  43 . 
     The time signal reconstruction module  260  may comprise a set of computer instructions or computer executable code for computing a dual-linear time error estimation by using Equation  10 . A corrected time-tag data set  262  may be generated by subtracting the computed time error estimations δT(T) from the corresponding measured values T of interval time signals  35  comprised within the uncorrected time-tag data set  212 , wherein the values of T−δT(T) in the corrected time-tag data set  262  are substantially more accurate than the values of T in the uncorrected time-tag data set  212 . In Equation 10, T p1 =T 1 +ΔT 1 , T p2 =T 2 −ΔT 2 , and T p1 ≤T≤T p2 ; furthermore, the value for δT TC  may be substantially equal to any one of the sums δT TC1 +δT TC2 , δT TC3 +δT TC4 , δT TC1 +δT TC4 , or δT TC2 +δT TC3 . In embodiments wherein the value of ΔT 1  is substantially small, then δT TC1  and δT TC3  could be removed from the value of δT TC  in Equation 10 without introducing a significant error in calculating δT(T). Likewise, in embodiments wherein the value of ΔT 2  is substantially small, then δT TC2  and δT TC4  could be removed from the value of δT TC  in Equation 10 without introducing a significant error in calculating δT(T).
 
δ T ( T )=[ f   2 ( K   D )− f   1 ( K   D )]*( T−T   p1 ) 2 /[2 *f   0 *( T   p2   −T   p1 )]+( T−T   p1 )*[ f   1 ( K   D )− f   1 ]/ f   0 +( T−T   p1 )*{δ T   2   −δT   1 −( T   p2   −T   p1 )*[ f   2 ( K   D )− f   1 ( K   D )]/(2* f   0 )−( T   p2   −T   p1 )*[ f   1 ( K   D )− f   1 ]/ f   0   −δT   TC }/( T   p2   −T   p1 )   Equation 10
 
     The communication module  290  may comprise a set of computer instructions or computer executable code for communicating information between components and modules within the system  100  and may further comprise a set of computer instructions or computer executable code for communicating any information within the system  100  from a reference time source  11 , to and from an external measurement system  19 , or to an external receiving device  21 . 
       FIG. 1B  illustrates a block diagram of alternate embodiment of a time error correcting clock system  100 , in accordance with an exemplary embodiment of the present invention. The system  100  may comprise a power source  12 , a clock subsystem  101 , a microcontroller configuration subsystem  110 , a temperature determination subsystem  120 , a time error determination subsystem  140 , a time signal reconstruction subsystem  150 , and a communication subsystem  190 . 
     The clock subsystem  101  may be configured to generate a first time signal  31  and a first frequency signal  41  at a first time, a second time signal  33  and a second frequency signal  44  at a second time, and one or more interval time signals  35  that may be used by the temperature determination subsystem  120 , the time error determination subsystem  140 , the time signal reconstruction subsystem  150 , and/or the communication subsystem  190 . 
     The microcontroller subsystem  110  may be configured to synchronize the processor  13  with the periodic signal from the local oscillator  10 . The microcontroller subsystem  110  may be configured to monitor, control, signal processing, and automate components within the system  100  or to protect monitored components within the system  100 . The microcontroller subsystem  110  may be configured to zero, reset, or otherwise set any time signals measured by the phase meter  15  to desired values or convert any time signal units to desired units, such as seconds, minutes, days, years, or specific dates and specific times. 
     The temperature determination subsystem  120  may be configured to acquire or provide temperature measurements that may be used by the time error determination subsystem  140  to generate a temperature-dependent time error estimation or a total time error estimation that may be used by the communication subsystem  190 . 
     The time error determination subsystem  140  may be configured to generate a time-dependent time error estimation or a total time error estimation that may be used by the time signal reconstruction subsystem  150  or the communication subsystem  190 . The time signal reconstruction subsystem  150  may be configured to generate a corrected time-tag data set  262  that may be used by the communication subsystem  190 . 
     The communication subsystem  190  may be configured to facilitate communication of any information between any of the components or subsystems  101 ,  110 ,  120 ,  140 ,  150 , or  190  in the system  100 . The communication subsystem  190  may comprise analog signal lines, digital signal lines, optical signal lines, or other communication interfaces. The communication subsystem  190  may be configured to transmit any information within the system  100  to at least one receiving device  21 . 
       FIG. 2A  illustrates a flow chart of one embodiment of the time error correction method  300  consistent with embodiments of the present disclosure.  FIG. 2B  illustrates a flow chart of an alternative embodiment of the time error correction method  300  consistent with embodiments of the present disclosure. The time error correction method  300  may comprise the steps of determining the first time signal  31  and the first frequency signal  41  ( 310 ), determining the second time signal  33  and the second frequency signal  44  ( 320 ), and generating a time-dependent time error estimation from the first time signal  31 , the first frequency signal  41 , the second time signal  33 , and the second frequency signal  44  ( 330 ). 
     The time error correction method  300  may further comprise the steps of generating the first time signal  31  and the first frequency signal  41  at the first time ( 306 ), receiving a first reference time signal  32  and a first reference frequency signal  42  ( 308 ), synchronizing the first time signal  31  with the first reference time signal  32  ( 304 ), calibrating the first frequency signal  41  with the first reference frequency signal  42  ( 305 ), generating one or more interval time signals  35  ( 312 ), receiving one or more interval time signals  35  ( 313 ), determining the interval time signals  35  ( 314 ), generating the second time signal  33  and the second frequency signal  44  at the second time ( 316 ), receiving the second reference time signal  34  and a second reference frequency signal  43  ( 318 ), generating an uncorrected time-tag data set  212  from the first time signal  31 , the second time signal  33 , or one or more interval time signals  35  ( 328 ), or generating a corrected time-tag data set  262  from the time-dependent time error estimation and the uncorrected time-tag data set  212  or the total time error estimation and the uncorrected time-tag data set  212  ( 360 ), wherein the first reference time signal  32  and the first reference frequency signal  42  are generated by the reference time source  11  at the first time, wherein the second reference time signal  34  and the second reference frequency signal  43  are generated by the reference time source  11 , wherein the time-dependent time error estimation may also be generated from the first reference time signal  32  and the second reference time signal  34 . 
     In various embodiments, the time error correction method  300  may further comprise the steps of determining a first temperature signal  51  at the first time ( 342 ), determining a second temperature signal  53  at the second time ( 344 ), determining one or more interval temperature signals  54  at the corresponding one or more interval times ( 346 ), or generating a temperature-dependent time error estimation from the first temperature signal  51 , the second temperature signal  53 , or the one or more interval temperature signals  54  ( 348 ). 
     In various embodiments, the time error correction method  300  may further comprise the steps of communicating the temperature-dependent time error estimation, the time-dependent time error estimation, or the corrected time-tag data set  262  to a receiving device  21  using a communication module  290  ( 390 ). 
       FIG. 3  illustrates an actual time error curve  410  of an example local oscillator  10  over a long-term time deployment, a linear frequency drift error estimation  420  based on the example local oscillator  10 , and a conventional two point linear time drift approximation  400 , in accordance with an exemplary embodiment of the present invention. The actual time error curve  410  is based upon laboratory data collected over an approximate sixty four day deployment for a local oscillator  10  having a nominal frequency near one hertz. The linear frequency drift error estimation  420 , denoted by δT LFD (T), is related to the difference in frequencies of the local oscillator  10  at the start of and near the end of deployment by Equation 11.
 
δ T   LFD ( T )=( f   2   −f   1 )*( T−T   1 ) 2 /[2* f   0 *( T   2   −T   1 )] Equation 11
 
       FIG. 4  illustrates a first residual time error curve  430  and a linear time drift error estimation  440  for the example illustrated in  FIG. 3 , in accordance with an exemplary embodiment of the present invention. The first residual time error curve  430  was generated by subtracting the linear frequency drift error estimation  420  from the actual time error curve  410 , and the linear time drift error estimation  440  is generated by implementing Equation 12.
 
δ T   LTD ( T )=( T−T   1 )*[δ T   2   −δT   1 −( T   2   −T   1 )*( f   2   −f   1 )/(2 *f   0 )]/( T   2   −T   1 )   Equation 12
 
       FIG. 5  illustrates a conventional two point approximation residual time error curve  500  and a dual-linear time drift error residual curve  510 , in accordance with an exemplary embodiment of the present invention. The conventional two point approximation residual time error curve  500  was generated by subtracting the two point linear time approximation  400  from actual measured time error  410 . The dual-linear time drift error residual curve  510  was generated by subtracting the linear time drift error estimation  440  from the first residual time error curve  430 . The dual-linear time drift error residual curve  510  demonstrates the effectiveness and accuracy of the time error correction method  300  when implemented using embodiments described herein. 
     While particular embodiments of the invention have been described and disclosed in the present application, it is clear that any number of permutations, modifications, or embodiments may be made without departing from the spirit and the scope of this invention. Accordingly, it is not the inventor&#39;s intention to limit this invention in this application, except as by the claims. 
     Particular terminology used when describing certain features or aspects of the invention should not be taken to imply that the terminology is being redefined herein to be restricted to any specific characteristics, features, or aspects of the invention with which that terminology is associated. In general, the terms used in the claims should not be construed to limit the invention to the specific embodiments disclosed in the specification, unless the above Detailed Description section explicitly defines such terms. Accordingly, the actual scope of the invention encompasses not only the disclosed embodiments, but also all equivalent ways of practicing or implementing the invention. 
     The above detailed description of the embodiments of the invention is not intended to be exhaustive or to limit the invention to the precise embodiment or form disclosed herein or to the particular field of usage mentioned in this disclosure. While specific embodiments of, and examples for, the invention are described above for illustrative purposes, various equivalent modifications are possible within the scope of the invention, as those skilled in the relevant art will recognize. Also, the teachings of the invention provided herein can be applied to other systems, not necessarily the system described above. The elements and acts of the various embodiments described above can be combined to provide further embodiments. 
     All of the above patents and applications and other references, including any that may be listed in accompanying filing papers, are incorporated herein by reference. Aspects of the invention can be modified, if necessary, to employ the systems, functions, and concepts of the various references described above to provide yet further embodiments of the invention. 
     In general, the terms used in the claims should not be construed to limit the invention to the specific embodiments disclosed in the specification, unless the above Detailed Description section explicitly defines such terms. Accordingly, the actual scope of the invention encompasses not only the disclosed embodiments, but also all equivalent ways of practicing or implementing the invention under the claims. 
     In light of the above “Detailed Description,” Inventor may make changes to the invention. While the detailed description outlines possible embodiments of the invention and discloses the best mode contemplated, no matter how detailed the above appears in text, the invention may be practiced in a myriad of ways. Thus, implementation details may vary considerably while still being encompassed by the spirit of the invention as disclosed by the inventor. As discussed herein, specific terminology used when describing certain features or aspects of the invention should not be taken to imply that the terminology is being redefined herein to be restricted to any specific characteristics, features, or aspects of the invention with which that terminology is associated.