Abstract:
To determine the level of frequency drift of a crystal oscillator as a result of a change in the its temperature, the temperature of the crystal oscillator is sensed and used together with previously stored data that includes a multitude of drift values of the frequency of the crystal oscillator each associated with a temperature of the crystal oscillator. Optionally, upon initialization of a GPS receiver in which the crystal oscillator is disposed, an initial temperature of the crystal oscillator is measured and a PLL is set to an initial frequency in association with the initial temperature. When acquisition fails in a region, the ppm region is changed. The temperature of the crystal oscillator is periodically measured and compared with the initial temperature, and the acquisition process is reset if there is a significant change in temperature. The GPS processor enters the tracking phase when acquisition is successful.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
       [0001]    The present application claims benefit under 35 USC 119(e) of U.S. Provisional Application No. 61/303,075, filed Feb. 10, 2010, and U.S. Provisional Application No. 61/422, 329, filed Dec. 13, 2010, the contents of both of which applications are incorporated herein by reference in their entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates to a clock reference signal used in a global positioning system (GPS), and more particularly to a method and apparatus for calibrating a crystal oscillator. 
         [0003]    The GPS is a satellite-based navigation system which requires a very stable local timing reference to ensure accurate navigation. There are currently three GPS systems, namely the NAVSTAR Global Positioning System controlled by the United States Defense Department, the GLONASS system maintained by the Russian Republic, and the GALILEO system proposed by Europe. 
         [0004]    To decode these satellite signals, a GPS receiver must first acquire the signals transmitted by a minimum number of satellites. A GPS receiver required a very accurate internal frequency reference in order to lock on to the GPS signals. 
         [0005]    In general, a GPS receiver has an internal crystal oscillator that is free running when the receiver is first turned on. Acquisition will not be successful if the difference between the PLL frequency of the GPS receiver and the GPS frequency is larger than the carrier frequency offset search range in acquisition. 
         [0006]    Conventional GPS receivers typically use a temperature compensated crystal oscillator to provide a stable and accurate internal reference frequency. Such temperature compensated crystals are very stable with time and temperature and provide the GPS receiver with a short amount of time to acquire satellite signals. Conventional temperature compensated crystal oscillators have a frequency drift of ±1 PPM or “ppm” (parts per million) or less throughout the operating temperature range of the crystal. 
         [0007]    However, temperature compensated crystals are very expensive. In addition, the initial acquisition time of the satellite signals may be long. A need continues to exist for a low-cost crystal oscillator for GPS receivers. The present invention provides a technical solution to overcome the frequency shift of the uncompensated crystal oscillators and simultaneously enable a fast acquisition time. 
       BRIEF SUMMARY OF THE INVENTION 
       [0008]    A method for determining the frequency drift of a crystal oscillator in response to a change in the temperature of the crystal oscillator, includes, in part, measuring the temperature of the crystal oscillator, and using the data stored in a memory to determine the size of the frequency drift of the crystal oscillator. The data includes a multitude of drift values of the frequency of the crystal oscillator each of which corresponds to a temperature value. 
         [0009]    In one embodiment the crystal oscillator is disposed in a GPS receiver. In one embodiment the multitude of drift values of the frequency of the crystal oscillator and the corresponding multitude of temperature values are collected during a tracking phase of the GPS receiver. In one embodiment the crystal oscillator provides a reference clock to a phase-locked loop disposed in the GPS receiver. In one embodiment the phase-locked loop is a fractional phase-locked loop. 
         [0010]    In one embodiment, the method further includes, in part, applying a non-linear function to the stored data to determine the frequency drift of the crystal oscillator in response to a temperature change. In one embodiment, the method further includes, changing the center frequency offset of the clock signal applied to the PLL during an acquisition phase of the GPS receiver incrementally and in accordance with a correction factor to generate a multitude of frequency ranges one of which causes the GPS receiver to acquire a GPS satellite signal. In one embodiment, adjacent frequency ranges partially overlap one another. 
         [0011]    In one embodiment, the method further includes changing at least one of the drift values of the frequency of the crystal oscillator and its corresponding temperature during a second tracking phase. In one embodiment, the method further includes increasing the number of drift values of the frequency of the crystal oscillator and the number corresponding temperature values during a second tracking phase. 
         [0012]    A device in accordance with one embodiment of the present invention includes, in part, a crystal oscillator; a temperature sensor adapted to sense the temperature of the crystal oscillator, a memory adapted to store a multitude of drift values of the frequency of the crystal oscillator and a multitude of corresponding temperature values, and a processor adapted to receive a temperature sensed by the temperature sensor and use the multitude of drift values of the frequency of the crystal oscillator and the multitude of corresponding temperature values to determine the frequency drift of the crystal oscillator caused by the oscillator&#39;s temperature. 
         [0013]    In one embodiment, the device is a GPS receiver. In one embodiment, the multitude of drift values of the frequency of the crystal oscillator and the corresponding multitude of values of the temperature are collected during a tracking phase of the GPS receiver. In one embodiment, the GPS receiver includes a phase-locked loop that receives a reference clock signal generated by the crystal oscillator. In one embodiment, the phase-locked loop is a fractional phase-locked loop. 
         [0014]    In one embodiment, the processor is adapted to apply a non-linear function to the data stored in the memory to determine the frequency drift of the crystal oscillator at any given temperature. In one embodiment, the processor is further adapted to change the center frequency offset of the reference clock signal, applied to the PLL during an acquisition phase of the GPS receiver, incrementally and in accordance with a correction factor to generate a multitude of frequency ranges one of which ranges enables the GPS receiver to acquire the GPS satellite signal. In one embodiment, adjacent frequency ranges partially overlap one another. 
         [0015]    In one embodiment, the processor is further adapted to change at least one of the drift values of the frequency of the crystal oscillator and its corresponding temperature value stored in the memory during a tracking phase. In one embodiment, the processor is further adapted to increase the number of drift values of the frequency of the crystal oscillator and the number of corresponding temperature values during a tracking phase. 
         [0016]    Embodiment of the present invention provide methods for temperature compensation of an uncompensated crystal oscillator. The method includes starting an acquisition phase upon the initialization of the crystal oscillator and entering a tracking phase once the acquisition phase is completed. The acquisition phase includes measuring the initial temperature of the crystal oscillator, and setting an initial frequency of the phase locked loop in association with the initial temperature. If the difference between the current temperature and the temperature measured before going to sleep is high, acquisition search range of carrier frequency offset will be widened. The method further includes measuring the current temperature of the crystal oscillator periodically after waiting for a time period and comparing the periodically measured temperature with the initial temperature. If the difference between the two temperatures is greater than a threshold value, the acquisition process will be reset. 
         [0017]    In another embodiment, the acquisition phase is completed if the correlation between the received GPS signal and the stored PRN code corresponding to a satellite is high; and the receiver enters then the tracking phase. 
         [0018]    In an embodiment, the tracking phase includes recording an estimated ppm of the crystal in association with the currently measured temperature and constructing a set of ppm values as a function of the currently measured temperatures. 
         [0019]    Embodiments of the present invention also include a device for frequency acquisition having a PLL coupled with a crystal oscillator. The device further includes a temperature sensor for measuring a temperature at the proximity of the crystal oscillator. Additionally, the device includes a controller that can characterize the stability of the crystal frequency relative to the temperature taken at the proximity of the crystal oscillator. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]      FIG. 1  is a simplified block diagram of a GPS receiver, in accordance with one embodiment of the present invention. 
           [0021]      FIG. 2  is a simplified block diagram of a fractional-N phase-locked loop used in the receiver of  FIG. 1 , in accordance with one embodiment of the present invention. 
           [0022]      FIG. 3A  is a plot representing a typical frequency change of a commercial crystal oscillator as the ambient temperature changes. 
           [0023]      FIG. 3B  shows the plot of  FIG. 3A  partitioned into a number of frequency regions used to acquire a GPS signal, in accordance with one embodiment of the present invention. 
           [0024]      FIG. 3C  shows the symmetry of the plot shown in  FIG. 3A . 
           [0025]      FIG. 4  is a flowchart of steps used to acquire a GPS signal, in accordance with one embodiment of the present invention. 
           [0026]      FIG. 5  is a flow chart of steps used during a GPS tracking mode, in accordance with one embodiment of the present invention. 
           [0027]      FIG. 6  is a plot of frequency change as a function of temperature for a number of different cuts of commercially available crystal. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0028]      FIG. 1  is a simplified block diagram of a GPS receiver  100 , in accordance with one embodiment of the present invention. Receiver  100  is shown as including an antenna  102  that receives the GPS signal and delivers it to mixer  110 . Mixer  110  is adapted to downconvert the frequency of the received GPS signal using the clock signal OSC supplied by phase-locked loop (PLL)  120 . The output signal of mixer  110  is supplied to GPS processor  180  for further processing. The reference clock signal F_crystal is supplied to PLL  120  by crystal oscillator  130 . The oscillating frequency of signal F_crystal may vary in different embodiments. In one example, crystal oscillator  130  may have a nominal frequency of 16.368327 MHz. Crystal oscillator  130  is not compensated over its operating temperature range. GPS receiver  100  is shown as including a temperature sensor  140  positioned in proximity of crystal oscillator  130  and adapted to sense the temperature of crystal oscillator  130  and supply the sensed temperature to controller  150 . Controller  150  has access to data stored in memory  160  that characterizes the frequency drift of crystal oscillator  130  as a function of temperature. Controller  150  may communicate with an external host processor (not shown) through interface  170 . Controller  150  may contain multiple configuration and control registers (not shown) for configuring and controlling PLL  120  and other blocks of GPS receiver  100 . Controller  150  may also include a timer  155  for keeping track of the time period during which GPS processor  180  is in an acquisition mode. 
         [0029]      FIG. 2  is a simplified block diagram of one embodiment of fractional-N phase locked loop  120  of  FIG. 1 . Phase locked loop  120  maintains a fixed relationship between the phase and frequency of the signal it receives, namely signal F_crystal, and those of the signal it generates, namely signal FB. PLL  120  is shown as including, in part, a phase/frequency detector  180 , a charge pump  182 , a loop filter  184 , and a voltage controlled oscillator (VCO)  186  which generates the clock signal CLK at its output terminal. Divider  188  divides the frequency of signal CLK to generate signal FB. 
         [0030]    Fractional-N PLL  120  enables the use of a reference frequency higher than the frequency step size required from the PLL. Phase/frequency detector  180  receives signals REF and Clk, and in response, generates signals UP and DN that correspond to the difference between the phases of the signals F-crystal and FB. Charge pump  182  receives signals UP and DN and in response varies the current I 1  which it supplies to loop filter  184 . Loop filter  184  stores the charge supplied by current I 1  as voltage V 1  and then delivers voltage V 1  to VCO  186 . 
         [0031]    If signal F_crystal leads signal CLK in phase—indicating that the VCO is running relatively slowly—the duration of pulse signal UP increases while the duration of pulse signal DN decreases, thereby causing charge pump  182  to increase its net output current I 1  until VCO  186  achieves an oscillation frequency at which signal FB is frequency-locked and phase-locked with signal F_crystal. If, on the other hand, signal F_crystal lags signal FB in phase—indicating that the VCO is running relatively fast—the duration of pulse signal UP decreases while the duration of pulse signal DN increases—thereby causing VCO  186  achieve an oscillation frequency at which signal FB is frequency-locked and phase-locked with signal F_crystal. Signal FB is considered to be locked to signal F_crystal if its frequency is within a predetermined frequency range of signal F_crystal. Signal FB is considered to be out-of-lock with signal F_crystal if its frequency is outside the predetermined frequency range of signal F_crystal. The frequency of signal Clk may be substantially equal to the frequency of the received GPS signal or may be a multiple thereof. 
         [0032]    Divider  188  may include a dual-mode divide-by-N and divide-by-(N+1) integer divider. Divider  188  is adapted to perform a fractional division operation so as to enable VCO  186  to have any frequency resolution. The frequency of the output signal Clk of VCO  186  may be determined by the following expression: 
         [0000]        F ( Clk )= F _crystal*( N+F/K ) 
         [0000]    where N, F, and K are integers, with N representing the integer part, and F and K representing the fractional part of the division. 
         [0033]    By dividing (K−F) cycles by N and F cycles by (N+1), the resulting frequency is then (K−F)*N+F*(N+1) within K cycles, thus a fractional (F/K) frequency value can be obtained. In one embodiment, the frequency of crystal signal F crystal is 16.368 MHz, and K is 22 bits. Accordingly, in such embodiments, the fractional-N PLL  120  may produce a frequency resolution of about 4 Hz. In another embodiment, the frequency of crystal signal is 26 MHz. 
         [0034]    The fractional-N PLL includes a full adder  190  that receives the integer count N and a sigma-delta modulator  192  that is coupled to full adder  190 . The sigma-delta modulator  192  generates a fine (fractional) value for the PLL. 
         [0035]    The fractional-N PLL  120 , in accordance with the present invention, further provides the advantage of low frequency jitter. As the dual-modulus divider  188  changes state from a divide-by-N to a divide-by-(N+1), a jump in the phase difference at the output of PFD  180  can be caused. This phase jump is periodic and appears as discrete frequency spurs. Sigma-delta modulator  192  is adapted to randomize this periodicity to inhibit the formation of the discrete spurs. 
         [0036]    The PLL  120  is further shown as including a lock detector  196  that receives signals Up and DN from PFD  180  to assert the lock signal LK when the PLL is in lock. In one embodiment, lock detector  196  asserts the lock signal CLK when the signals UP and DOWN have the same logic state. 
         [0037]      FIG. 3A  is a plot representing a typical frequency change (Δf/f) of a commercial crystal oscillator as the ambient temperature changes.  FIG. 3B  shows the plot of  FIG. 3A  partitioned into multiple overlapping regions. These regions are used during the acquisition phase, in accordance with one embodiment of the present invention and as described below. Within each part per million (ppm) region, the frequency change is considered to be lying within the acquisition carrier offset search range of GPS processor  180 . In such embodiments, the frequency measurement data at some temperature points can be obtained and stored in a memory of GPS processor  180  when it is in tracking mode. A filtering algorithm can be utilized to reduce measurement noise. The number of data points can be chosen by considering the trade-off between the memory size and the complexity of frequency estimation. 
         [0038]    During an acquisition phase, the frequency estimation at any given temperature can be obtained (i) directly from stored data; (ii) by linear interpolation/extrapolation of stored data using an algorithm, such as the least square algorithm, and/or (iii) by utilizing odd or even symmetry of frequency curve of the crystal oscillator about the temperature T 0  given ppm vs. temperature is a third order polynomial as in  FIG. 3C . 
         [0039]    For example, the frequency measurement can be stored for every 2 degree. If the operating temperature range is between −30° C. and 85° C.,  61  frequency measurement data (at − 35 ° C., − 33 ° C., − 26 ° C., . . . , 90° C.) are stored in the memory (e.g., a non-volatile memory such as flash). Frequency data storage at temperature T 1  can be initialized (i.e. stored the first time) with frequency measurement from the GPS device if the measured temperature is between T 1 -1° C. and T 1 +1° C. Stored frequency data at temperature T 2  can be updated with frequency measurement from the GPS device using an IIR (infinite impulse response) filter if the measured temperature is between T 2 -0.5° C. and T 2 +0.5° C. 
         [0040]    Stored frequency data are used for frequency estimation during acquisition phase. A linear extrapolation scheme may be used to estimate the frequency for temperatures for which no data is stored. For example, assume that the frequency data at temperature T 3 , for which no measured data is available, is required. Accordingly, frequency estimation can be performed by using linear interpolation if frequency measurement data are stored for any two temperatures T 4  and T 5  which satisfies T 4 &lt;T 3 &lt;T 5 . A simple linear interpolation can be computed as: 
         [0000]      ppm_out=( y 2− y 1)*(measured temperature− x 1)/( x 2 −x 1)+ y 1;
 
         [0000]    where y 1 =ppm_stored 1 , y 2 =ppm_stored 2 ,
 
x 1 =temperature corresponding to ppm stored 1 , and
 
x 2 =temperature corresponding to ppm_stored 2 .
 
         [0041]    If all the temperatures for which stored data exist are either larger or smaller than the desired temperature T 3 , a linear extrapolation may be used. Alternatively, more data points can be obtained by making use of the fact that a frequency change vs. the temperature curve is typically odd-symmetrical about room temperature or even-symmetrical about room temperature. As is well known, there are different kinds of quartz plates determined by different cut angles to quartz bars such as AT, BT, CT, DT, SL, and the like. Different types of quartz cuts show different available elastic, piezoelectric, and dielectric properties. For the most popular AT-cut crystals, the frequency change vs. the temperature curve is substantially odd-symmetrical. For CT, BT, NT, XY, DT, SL cut crystals, the frequency change vs. the temperature curve is substantially even-symmetrical.  FIG. 4  shows the ppm change in frequency as a function of temperature for a number of cut crystals. 
         [0042]    An example of linear extrapolation with a least square algorithm can be expressed as for 3 data points (N=3): 
         [0000]        A=x 1 +x 2 +x 3; 
         [0000]        B=x 1̂2+ x 2̂2+ x 3̂2;
 
         [0000]        C=x 1× y 1 +x 2 ×y 2+ x 3× y 3;
 
         [0000]        D=y 1 +y 2 +y 3; 
         [0000]    for 4 data points (N=4): 
         [0000]        A=x 1 +x 2 +x 3 +x 4; 
         [0000]        B=x 1̂2+ x 2̂2+ x 3̂2+ x 4̂2;
 
         [0000]        C=x 1 ×y 1 +x 2 ×y 2+ x 3× y 3 +x 4 ×y 4;
 
         [0000]        D=y 1 +y 2 +y 3 +y 4; 
         [0000]    for 5 data points (N=5): 
         [0000]        A=x 1 +x 2 +x 3 +x 4 +x 5; 
         [0000]        B=x 1̂2 +x 2̂2+ x 3̂2+ x 4̂2+ x 5̂2;
 
         [0000]        C=x 1 ×y 1 +x 2 ×y 2 +x 3 ×y 3 +x 4 ×y 4 +x 5 ×y 5; 
         [0000]        D=y 1 +y 2 +y 3 +y 4 +y 5; 
         [0000]        a= ( N×C−A×D )/( B×N−Â 2) 
         [0000]        b= ( B×D−A×C )/( B×N−Â 2) 
         [0000]    where (xi, yi) are data points for linear curve fitting, N is number of data points, and a and b are resulting coefficients from least square algorithm (yi=[a]x[xi]+b), where x represents the multiplication operation and i is an integer index. 
         [0043]    If valid ppm data exists for temperatures that are smaller and larger than a desired temperature, then linear interpolation can then be applied to estimate the frequency at the desired temperature. Using odd or even symmetry and then applying linear interpolation improves estimation accuracy compared to linear extrapolation. If a frequency curve has odd symmetry with respect to (T 0 , F 0 ), and (T 0 +[T 0 −T 3 ], F 1 ) can be obtained from stored data or linear interpolation, then the frequency at T 3  can be estimated with the equation F 0 +[F 0 −F 1 ] as shown in  FIG. 3C . In another embodiment, a polynomial function can be designed to best fit the frequency change curve. 
         [0044]      FIG. 3C  is a graph showing the odd symmetry of frequency change in ppm vs. temperature for estimating the ppm value associated with a temperature range. The frequency change in ppm vs. temperature range is substantially odd-symmetric with respect to an inflection point (T 0 , F 0 ). Typically, T 0  is around the room temperature of 25° C. 
         [0045]    In accordance with one embodiment of the present invention, the ppm range of the crystal oscillator&#39;s frequency is partitioned into multiple regions, as shown in  FIG. 3B . Upon initialization of the crystal oscillator, the initial temperature of the crystal oscillator is measured and receiver  100  applies a correction to the PLL based on a first region that is associated with the measured initial temperature. For correction, frequency ppm vs. temperature curve which is formed during a tracking phase is utilized. While the PLL is in the acquisition phase, the current temperature of the crystal oscillator is periodically measured and compared with the initial temperature. If the difference between the currently measured temperature and the initial temperature obtained at the beginning of the acquisition exceeds a threshold value, GPS processor  180  (or controller  150 ) resets the acquisition, sets the current temperature as the initial temperature and widens the acquisition carrier offset search range (if the carrier offset search range has not reached the maximum allowed search range), so as to cause the crystal temperature to be measured again after a certain time period. This process continues until the acquisition phase is successful. In one embodiment, the acquisition phase is terminated when the PLL operates within an acceptable frequency range of the received GPS signal frequency. In another embodiment, the acquisition phase is terminated after the elapse of a certain time period corresponding to a timeout. 
         [0046]    Upon completion of a successful acquisition, GPS receiver  100  enters a tracking phase during which the frequency change ppm vs. temperature will be updated and maintained. The maintenance of the frequency change in ppm vs. temperature can be performed using a look-up table, a polynomial curve, or multiple affine functions. The tracking phase is validated by making sure that tracking loops are in lock and there is a valid pseudo range/ position/ velocity/time fix. In one embodiment, the tracking phase is validated when the GPS receiver  100  obtains a suitable correlation between the received GPS signal and a spreading code corresponding to a satellite. After the tracking operation is validated, the difference between a nominal frequency of crystal and its true frequency value in association with the measured temperature is stored. The stored data is used to compensate for the frequency drift of the crystal oscillator over temperature. 
         [0047]      FIG. 4  is a flowchart  300  of actions taken to acquire a GPS signal in accordance with one embodiment of the present invention. Prior to this acquisition, the ppm change in the frequency of the oscillator as a function of temperature is obtained during a tracking and stored in the receiver&#39;s memory. After starting the carrier acquisition phase  310 , the initial temperature, shown by parameter temp_init, of the crystal oscillator is measured  315 . The initial temperature temp_init is compared  320  with the temperature of the crystal oscillator recorded before the receiver in which the oscillator is disposed enters the sleep mode; this temperature is shown as temp_sleep. If the difference (temp_init-temp_sleep) is detected  320  as being larger than a threshold value, the acquisition carrier offset search range is increased if the carrier offset search range has not reached a maximum value. Thereafter, a ppm correction corresponding to the initial temperature is estimated  330  and used to adjust the frequency of the PLL used in the receiver. The ppm estimate in frequency is obtained using the frequency-temperature data collected during a tracking phase, as explained above. If the difference (temp_init-temp_sleep) is not detected  320  as being larger than the threshold value, the frequency of the PLL is adjusted  330  in accordance with the ppm estimate of the frequency in accordance with the initial value of the temperature. After the elapse  335  of a certain time period, the current temperature is measured  340  again. 
         [0048]    Subsequently the initial temperature at  315  is compared  340  with the current temperature temp_current. If the difference between the current temperature and the initial temperature is detected  345  as being greater than a threshold value, the acquisition process will be reset  350 , the value of the initial temperature temp_init is set to the current temperature, and the acquisition carrier offset search range is widened if the carrier offset search range has not reached the maximum allowed value. The process moves to step  330 . If the difference between the current temperature and the initial temperature is detected  345  as being less than or equal to the threshold value, then a determination is made  360  about whether a request for the ppm region range has been received. If the ppm region range request has been received  360 , the ppm correction required for the new ppm region range is applied  365  to the PLL. If the ppm region range request has not been received  360 , the process moves to step  335 . 
         [0049]    Referring to flowchart  300  and  FIG. 3B  concurrently, at  335 ,  340 ,  345 ,  360  and  365  of flowchart  300  attempt is made to acquire the GPS signal for a known time period. If the acquisition is unsuccessful, the acquisition carrier offset search range is changed. For example, assume that the acquisition is initially made at the center frequency ppm of PO with a range defined by (P 0 −Δ) to (P 0 +4). If the acquisition in this frequency range is successful, tracking operation may begin. If the acquisition in this frequency range is unsuccessful, the center frequency ppm is moved to P 1  (P 1  is higher than P 0 ) with a ppm frequency range defined by (P 1 −Δ) to (P 1 +4). If the acquisition in the ppm frequency range (P 1 −Δ) to (P 1 +Δ) is successful, tracking operation may begin. If the acquisition in the ppm frequency range (P 1 −Δ) to (P 1 +Δ) is unsuccessful, the center frequency ppm is moved to P 2  with a ppm frequency range defined by (P 2 −Δ) to (P 2 +Δ). If the acquisition in the ppm frequency range (P 2 −Δ) to (P 2 +Δ) is successful, tracking operation may begin. If the acquisition in the ppm frequency range (P 2 −Δ) to (P 2 +Δ) is unsuccessful, the center frequency ppm is moved to P 3  with a ppm frequency range defined by (P 3 −Δ) to (P 3 +Δ). In some embodiments (P 2 −P 0 ) is the same as (P 0 −P 1 ). In other embodiments, (P 2 −P 0 ) is different from (P 0 −P 1 ). This process continues, until the GPS signal is successfully acquired. 
         [0050]    In another embodiment, the acquisition phase may be considered as completed when the correlation between the received GPS signal and the stored PRN code corresponding to a satellite is high. Then the acquisition phase is switched to the tracking phase. The tracking phase is considered as validated when the carrier offset tracking and the code phase tracking loops are in lock and a valid pseudo range/position/velocity/time fix is obtained. 
         [0051]      FIG. 5  is a flow chart  400  of actions taken during a tracking operation, in accordance with one embodiment of the present invention. Tracking phase starts at  400 . During the tracking phase, the ppm frequency change estimate is known and is relatively more accurate. Accordingly, at  420 , the ppm frequency changes are estimated and the corresponding temperatures are sensed and recorded. The ppm frequency changes and the temperature corresponding to each ppm frequency change are stored in a table residing in the receiver&#39;s local memory for future temperature compensation. The new data added to the memory may be used to generate or update the function that establishes the relationship between the ppm frequency change and temperature. Such a function may be presented as multiple affine functions (e.g., ppm=slope×temperature change+offset), or a polynomial equation. Next, the rate of temperature change is determined at  430 . Based on the calculated rate of temperature change during the tracking process or temperature change during the device sleep mode or the signal strength, the bandwidth of the code phase tracking loop filter, the bandwidth of the carrier tracking loop filter, and the bandwidth of the lowpass filter may be adjusted at  440 . Next, the center frequency offset during the acquisition phase is updated  460 . If at  460 , the tracked ppm is available, in one embodiment, the acquisition center frequency offset is set to (ppm×1575.42 MHz). If at  460 , the tracked ppm is not available, the acquisition center frequency offset is set either to (approximate ppm×1575.42 MHz) or to the average of (carrier offset frequency—estimated Doppler frequency). The tracking process restarts at  420  after waiting  450  a certain time interval. In another embodiment of the present invention, a curve of the frequency change vs. the associated temperature change can be updated. 
         [0052]    While the advantages and embodiments of the present invention have been depicted and described, there are many more possible embodiments, applications and advantages without deviating from the spirit of the inventive ideas described herein. It will be apparent to those skilled in the art that many modifications and variations in construction and widely differing embodiments and applications of the present invention will suggest themselves without departing from the spirit and scope of the invention.