Abstract:
A method and apparatus for estimating the changing frequency of a signal received by a satellite receiver from, illustratively, positioning system satellites is disclosed that enables a more accurate measurement of the change in frequency of that signal due to movement of the satellite receiver relative to those satellites. The system includes a PLL having a numerically controlled oscillator (NCO) and a filter of frequency estimates (FFE). In operation, an analog signal is received at the satellite receiver and the PLL tracks the changing signal frequency and outputs non-smoothed frequency estimates into the FFE. The FFE then smoothes noise in the signal to produce a more accurate smoothed frequency estimate of the input signal. Comparing multiple estimates over time allows Doppler shift of the signal frequency received by the satellite receiver to be calculated more precisely, thus resulting in more accurate satellite receiver velocity vector determinations and, hence, position measurements.

Description:
BACKGROUND OF THE INVENTION 
   This invention relates generally to satellite navigation receivers and more particularly to interference mitigation in a satellite navigation receiver. 
   Satellite navigation systems, such as GPS (USA) and GLONASS (Russia), are well known in the art and are intended for highly accurate self-positioning of users possessing special navigation receivers. A navigation receiver receives and processes radio signals transmitted by satellites located within line-of-sight distance of the receivers. The satellite signals comprise carrier signals that are modulated by pseudo-random binary codes. The receiver measures the time delay of the received signal relative to a local reference clock or oscillator. These measurements enable the receiver to determine the so-called pseudo-ranges between the receiver and the satellites. The pseudo-ranges are different from the ranges (distances) between the receiver and the satellites due to various noise sources and variations in the time scales of the satellites and receiver. If the number of satellites is large enough, then the measured pseudo-ranges can be processed to determine the user location and coordinate time scales. 
   The requirement of accurately determining user location with a high degree of precision, and the desire to improve the stability and reliability of measurements, have led to the development of differential navigation (DN). In differential navigation, the task of finding the user position, also called the Rover, is performed relative to a Base station (Base). The precise coordinates of the Base station are known and the Base station is generally stationary during measurements. Since the position of the satellites is also known, the range of the Base to each of the satellites can be determined by comparing the position of the Base with the position of each of the satellites. The Base station also has a navigation receiver which receives and processes the signals of the satellites to generate pseudo-range measurements, as discussed above, from the Base to each satellite. The Base then compares these measurements with the expected range to each of the satellites. Any difference between the pseudo-range calculated measurements and the expected range to the satellites represents an error in the pseudo-range calculations. For relatively short distances between the Rover and the Base (e.g., less than 20 km), these range errors are strongly correlated (e.g., are essentially the same for both the Rover and the Base). Therefore, by transmitting the pseudo-range error measurements made at the Base to the Rover (e.g., via wireless communication channel), the pseudo-range of each of the satellites to the Rover, as calculated at the Rover, can be also be more accurately determined based on the errors calculated at the Base. Accordingly, the location determination is improved in the differential navigation mode because the Rover is able to use the Base station pseudo-range error measurements in order to compensate for the major part of the errors in the Rover measurements. 
   Various modes of operation are possible while using differential navigation. In post-processing (PP) mode, the Rover&#39;s coordinates are determined by co-processing the Base and Rover measurements after all measurements have been completed. This allows for highly accurate location determination, albeit not in real-time, because more data is available for the location determination. In real-time processing (RTP) mode, the Rover&#39;s coordinates are determined in real time upon receipt of the Base station information received via the communication channel. 
   The location determination accuracy of differential navigation may be further improved by supplementing the pseudo-range measurements with measurements of the phases of the satellite carrier signals. If the carrier phase of the signal received from a satellite in the Base receiver is measured and compared to the carrier phase of the same satellite measured in the Rover receiver, measurement accuracy may be obtained to within several percent of the carrier&#39;s wavelength. The practical implementation of those advantages, which might otherwise be guaranteed by the measurement of the carrier phases, runs into the problem of ambiguity resolution for phase measurements. 
   The ambiguities are caused by two factors. First, the difference of distances from any satellite to the Base and Rover is usually much greater than the carrier&#39;s wavelength. Therefore, the difference in the phase delays of a carrier signal received by the Base and Rover receivers may substantially exceed one cycle. Second, it is not possible to measure the integer number of cycles from the incoming satellite signals; one can only measure the fractional part. Therefore, it is necessary to determine the integer number of cycles, which is called the “ambiguity”. More precisely, we need to determine the set of all such integer parts for all the satellites being tracked, one integer part for each satellite. One has to determine this set along with other unknown values, which include the Rover&#39;s coordinates and the variations in the time scales. 
   At a high level, the task of generating highly-accurate navigation measurements is formulated as follows: it is necessary to determine the state vector of a system, with the vector containing n Σ  unknown components. Those include three Rover coordinates (usually along Cartesian axes X, Y, Z) in a given coordinate system (sometimes time derivatives of coordinates are added too); the variations of the time scales which is caused by the phase drift of the local main reference oscillator in the receiver; and n integer unknown values associated with the ambiguities of the phase measurements of the carrier frequencies. The value of n is determined by the number of different carrier signals being processed, and accordingly coincides with the number of satellite channels actively functioning in the receiver. At least one satellite channel is used for each satellite whose broadcast signals are being received and processed by the receiver. Some satellites broadcast more than one code-modulated carrier signal, such as a GPS satellite which broadcasts a carrier in the L 1  frequency band and a carrier in the L 2  frequency band. If the receiver processes the carrier signals in both of the L 1  and L 2  bands, a so-called dual-frequency receiver, the number of satellite channels (n) increases correspondingly. Dual-frequency receivers allow for ionosphere delay correction therefore making ambiguity resolution easier. 
   Two sets of navigation parameters are measured by the Base and Rover receivers, respectively, and are used to determine the unknown state vector. Each set of parameters includes the pseudo-range of each satellite to the receiver, and the full (complete) phase of each satellite carrier signal. Each pseudo-range is obtained by measuring the time delay of a code modulation signal of the corresponding satellite. The code modulation signal is tracked by a delay-lock loop (DLL) circuit in each satellite tracking channel. The full phase of a satellite&#39;s carrier signal is tracked by a phase-lock-loop (PLL) in the corresponding satellite tracking channel. An observation vector is generated as the collection of the measured navigation parameters for specific (definite) moments of time. 
   The relationship between the state vector and the observation vector is defined by a well-known system of navigation equations. Given an observation vector, the system of equations may be solved to find the state vector if the number of equations equals or exceeds the number of unknowns in the state vector. Conventional statistical methods are used to solve the system of equations: the least squares method, the method of dynamic Kalman filtering, and various modifications of these methods. Practical implementations of these methods in digital form may vary widely. In implementing or developing such a method on a processor, one usually must find a compromise between the accuracy of the results and speed of obtaining results for a given amount of processor capability, while not exceeding a certain amount of loading on the processor. 
   Most DN receivers not only provide the Rover&#39;s coordinates, but also provide a derived vector of velocity of the Rover&#39;s movement. A simple method of determining velocity is to measure the amount of time taken to travel a given distance (e.g., between successive location determinations). However, this typically results in a relatively inaccurate estimate of the Rover&#39;s velocity. Hence, other methods have been developed. In a first method, the velocity of the Rover is estimated by measuring the Doppler shift in the frequency of the signal received from each satellite to obtain the radial velocity of the Rover relative to each satellite. The radial velocity is then converted to a coordinate velocity of the Rover. To reduce random errors in these velocity measurements, various well-known methods of time smoothing the estimated frequencies are used. One method of determining the radial velocity of a Rover is based on measuring the full-phase incursion in the aforementioned PLL during a preset/measured time interval. The radial velocity of the Rover relative to each satellite is determined by dividing the phase incursion by the time interval and then multiplying the result by the carrier wavelength. Performing this calculation for each of the satellites produces a set of radial velocities of the Rover relative to each of the satellites. Further processing using, for example, the least-squares method produces the Rover&#39;s coordinate velocity from this set of radial velocities. 
   One of the major sources of error in calculating velocity vectors of a Rover using satellite navigation receivers is that satellite signals are difficult to detect in certain circumstances. This is because typical Rovers in DGPS systems operate in various noisy signal environments. Tracking systems operating at such noisy signals often have difficulty producing relatively fine Doppler shift measurements. 
   Various techniques have been employed to reduce the effect of such interference on measuring Doppler shift of the carrier phase. These techniques have generally relied on the fact that the frequency change over the measured time interval is essentially linear. Thus, by measuring multiple values of the full phase over the measured time interval, it is possible to determine the estimate of the initial phase and its first and second derivatives. These derivatives can be used to fit the received frequency shift measurements to the expected linear relationship. 
   In another attempt (described in Szames et al, DGPS High Accuracy Aircraft Velocity Determination Using Doppler Measurements, Proceedings of the International Symposium on Kinematic Systems (KIS), Banff, AB, Canada, June 306, 1997), raw Doppler shift derived measurements of velocity are processed using curve-fitting techniques to obtain velocity estimates as good as those using the first order central difference approximation of the carrier phase, without the extra step of determining the first and second order derivatives. 
   SUMMARY OF THE INVENTION 
   The present inventors have invented a digital system and method for estimating the changing frequency of a signal received by a satellite receiver from, illustratively, positioning system satellites, in order to more accurately measure the change in frequency of that signal due to movement of the receiver relative to those satellites. The system comprises a PLL having a numerically controlled oscillator (NCO) and a filter of frequency estimates (FFE). An analog signal is received at the satellite receiver and the PLL tracks the changing signal frequency and outputs non-smoothed frequency estimates into the FFE. The FFE then smoothes noise in the signal to produce a more accurate smoothed frequency estimate of the input signal. Comparing multiple estimates over time allows Doppler shift of the signal frequency received by the satellite receiver to be calculated more precisely, thus resulting in more accurate satellite receiver velocity vector determinations and, hence, position measurements. 

   
     DESCRIPTION OF THE DRAWING 
       FIG. 1  shows an illustrative PLL coupled to an FFE in accordance with the principles of the present invention; 
       FIG. 2   a  shows one variation of an integrating block useful in the PLL of  FIG. 1 ;  FIG. 2   b  shows another variation of an integrating block useful in the PLL of  FIG. 1 ; 
       FIG. 3   a  shows one variation of an FFE that may be used in conjunction with a PLL as illustrated in  FIG. 1 ; and  FIG. 3   b  shows another variation of an FFE that may be used in conjunction with a PLL as illustrated in  FIG. 1 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1  shows a function diagram of an illustrative radio receiver, such as a receiver in a GPS system, in accordance with the principles of the present invention. Referring to that figure, illustrative analog to digital converter (ADC)  116  is connected to PLL  100  which is, in turn connected to Filter of Frequency Estimates (FFE)  113 . PLL  100  is similar to typical PLLs in that PLL  100  has a digital phase discriminator (PD)  103 , a numerically controlled oscillator (NCO)  110  and a loop filter consisting of integrating block (IB)  107  and instantaneous element  106  having constant transfer coefficient k 0 . 
   In operation, an analog signal, such as a signal from a positioning system satellite, is received at a satellite receiver having PLL  100  and is input to ADC  116  where it is converted into a digital signal. Illustratively, the input analog signal is characterized by the equation:
 
 U   C   =A  cos(∫2π f   c ( t ) dt )  (Equation 1)
 
where U c  is the signal, A is the amplitude of the signal, f c (t) is the frequency of the signal, which, illustratively, changes over time due to Doppler shift of the signal due to the relative motion of the signal source and the receiver. One skilled in the art will recognize that typical signals received by a receiver may contain a noise component due to, illustratively, additive thermal Gaussian noise. This noise component, also referred to herein as U N  typically either constructively or destructively interferes with the signal as it is input into the ADC. Thus, the combined U C +U N  signal is transformed by the ADC into a digital signal with illustrative discretization frequency f s . Digital quadrature samples I NCO  and Q NCO  output from the NCO are multiplied by signal samples at the ADC output by multipliers  101  and  102  and are then input into digital low pass filters. Here, illustratively, the low-pass filters are represented by accumulators  104  and  105 . Accumulators  104  and  105  have, illustratively, a reset rate f r  (the rate at which the PLL operates) defined as:
 
 f   r   =f   s   /n   r   (Equation 2)
 
where f s  is the discretization (sampling) frequency discussed above and n r  is an integer. This integer n r  is illustratively chosen to reduce the PLL reset rate f r  (also referred to herein as the PLL control rate), while at the same time maintaining f r  at a level higher than the PLL bandwidth. Reducing the reset frequency f r  is desirable because such a low frequency functions to reduce the frequency of operating circuits and/or digital signal processor loading. However, frequency f r  is the frequency at which the PLL will iteratively operate to maintain phase lock on a signal. If a PLL operates any lower than its bandwidth capability, it will not maintain lock on the phase of the signal as accurately as it otherwise would. Therefore, it is desirable to maintain the reset frequency f r  significantly above the bandwidth of the PLL. Therefore, integer n r  may illustratively be selected at the lowest value possible to maintain f, at a desired level over the bandwidth of the PLL.
 
   Accumulators  104  and  105  output quadrature samples I c  and Q c  and provide those signals to the digital phase discriminator  103 . The phase discriminator  103  then generates a phase difference signal Δ PD , which is a function of the phase difference between the phase of said signal and the phase of a reference signal generated by an oscillator (NCO), illustratively where Δ PD =arctg(Q c /I c ). This signal Δ PD  is then input both into the instantaneous element  106  which has a constant transfer coefficient k 0 , as well as into the integrating block (IB)  107 . 
   Different implementations of IB  107  are possible. For example,  FIG. 2A  shows a first illustrative embodiment of IB  107  having a single instantaneous element  201  having transfer coefficient k 1  and a single accumulator  202 . One skilled in the art will recognize that such an implementation will ensure a second order of astaticism.  FIG. 2B  shows a second illustrative embodiment of IB  107  having, for example, instantaneous elements  203  and  204 , accumulators  205  and  206 ; and adder  207 . The incoming signal in IB  107  of  FIG. 2B  is input into instantaneous elements  203  and  204  having transfer coefficients k 2  and k 1 , respectively. The resulting signal from instantaneous element  203  is then input into accumulator  205  and is then input into adder  207 , where it is added with the signal output from instantaneous element  204 . This added signal is then processed by accumulator  206  before being output from the integrating block. One skilled in the art will recognize that the output from the integrating block of  FIG. 2B  will guarantee that the PLL has a third order of astaticism due to the two accumulators  205  and  206 . 
   Referring once again to  FIG. 1 , switch  108  has, illustratively, two possible positions, referenced in  FIG. 1  as position  108 A and position  108 B. In  FIG. 1 , switch  108  is illustratively shown in a first position  108 A which leads to the NCO being controlled only by frequency. In this mode, IB  107  functions to convert the phase difference Δ PD  generated by PD  103  into a frequency estimate f IB  of the incoming signal U C . This estimate is then added by adder  109  to the transfer coefficient-adjusted Δ PD  in order to generate an adjusted frequency. This adjusted frequency, f NCO , is then used to adjust the frequency of the NCO over the current control interval of the PLL in accordance with the equation:
 
 F   NCO   i+1   =ΔF   NCO   *f   NCO   i+1   (Equation 3)
 
where i is the number of the control interval, ΔF NCO  is the increment of NCO frequency, or the change of NCO frequency at changing f NCO  by unit The time span of the current control interval is determined by the equation
 
 T   r   =n   r   /f   s   (Equation 4)
 
where, as before, n r  is an integer and f s  is the discretization frequency used to sample the incoming analog signal and convert it into a digital signal. In this manner, frequency synchronization is maintained between the PLL and the incoming signal U C .
 
   Switch  108  can also illustratively be set to position  108 B. In this position, the estimated phase φ NCO , obtained from the Δ PD  generated by PD  103 , is used separately as an input to the NCO along with the frequency F IB  without adding. NCO uses this φ NCO  signal to control the phase Φ NCO  of the NCO  110  according to the equation:
 
Φ NCO   i=1 =Φ NCO   i +ΔΦ NCO *φ NCO   i   (Equation 5)
 
where I is the number of the control interval, ΔΦ NCO  is the NCO phase increment or, in other words, the change of the NCO phase at changing φ NCO   i  by unit. Thus, when switch  108  is in position  108 B, NCO  110  receives both a phase signal and a frequency signal separately and uses them to generate Φ NCO  and F NCO  of the control signal represented by the I NCO  and Q NCO  components output from NCO  110 .
 
   While the above-described PLL  100  is sufficient to maintain frequency and phase synchronization with an incoming signal, the accuracy of this synchronization may not be sufficient for certain applications. For example, as discussed above, extremely fine frequency and phase synchronization is required to accurately detect the motion vector, and hence the precise position, of a Rover receiver in a differential GPS system. Simply using the PLL as described above may be insufficient to achieve this degree of accuracy. As a result, it is desirable to further process, or smooth, the frequency estimates in order to obtain a more accurate synchronization with the incoming analog signal and, accordingly, generate a better estimate of the received frequency. This in turn will enable a more precise location measurement based on the Doppler shift of the received frequency over a discrete time difference. 
   This enhanced accuracy is achieved in accordance with the principles of the present invention by using a filter of frequency estimates (FFE)  113  to produce a smoothed frequency estimate f e  of the frequency f C  of signal U C . Once again, referring to  FIG. 1 , FFE  113  has an input switch  112  that has  2  positions, position  112 A and position  112 B. If switch  108  is in position  108 A (corresponding to frequency control of the PLL, then the position of switch  112  will determine whether the frequency f IB  is selected (position  112 A) or the frequency f NCO  (position  112 B) is selected as an input into the FFE  113 . Alternatively, if switch  108  is in position  108 B (corresponding to frequency/phase control of the PLL), then there also exists two possible inputs into the FFE  113 . Once again, if switch  112  is in position  112 A, then the input into FFE  113  will be the frequency f IB  output by IB  107 . If, on the other hand, switch  112  is set in position  112 B, then the adder sums the f NCO  signal with the added signal output from adder  114 , which is the sum of two separate signals. The first signal input into adder  114  is the frequency f NCO =f IB  traveling to adder  114  along path  117 . The second signal input into adder  114  is the phase φ NCO  multiplied by constant coefficient h in instantaneous element  111 . The added signal output from adder  114  is a frequency f PFC  defined by the equation:
 
 f   PFC   =f   NCO   +h*φ   NCO   (Equation 6)
 
where constant coefficient h is defined by the equation:
 
                 h   =       ΔΦ   NCO       2   ⁢   π   *     T   r     *     ΔF   NCO                 (     Equation   ⁢           ⁢   7     )               
where the variables are defined as was discussed previously in association with the discussion of Equations 3, 4 and 5. The result of any of the aforementioned combinations of settings for switches  108  and  112  are that an unsmoothed estimated frequency f g , which is an estimate of the input signal U C  frequency f C , is input into the FFE  113 .
 
     FIGS. 3A and 3B  show two different illustrative embodiments of FFE  113  in accordance with the principles of the present invention. The FFEs of both figures each have a difference element  301  (which operates as a discriminator), an accumulator  304 , an instantaneous element  302  with transfer coefficient k f , an adder  305  and an integrating block  303 . Both FFEs each have two outputs,  306  and  307 , respectively. The difference between the FFEs of  FIGS. 3A and 3B  is the position of accumulator  304  in the circuit relative to other circuit components. In the first illustrative embodiment of FFE  113 , shown in  FIG. 3A , the output of difference element  301  is input into the instantaneous element  302  as well as IB  303 . The output of instantaneous element  302  is the first input signal to adder  305 . The output of IB  303  is the second input into adder  305 . The output of IB  303  is also directed to FFE output  307 . The output of adder  305  is input, in turn, into accumulator  304 . The output of accumulator  304  is then fed back to adder  301  as well as to FFE output  306 . Thus, for example, with the FFE of  FIG. 3A  having IB  107  of  FIG. 2A , the signal flow following the input of unsmoothed estimated frequency f g  can be described as a set of numbers at the input and/or output of the various components of the FFE  113 . Unsmoothed frequency f g , for example, is input into FFE  113 , and can be represented as input number N input   i  input into FFE  113 . Thus, the signal flow between the components of the FFE of  FIG. 3A  can be defined as:
   N   a     1     i+1   =N   input   i   −N   Σ     f     i   (Equation 8A)   N   Σ     1     i+1   =N   Σ     i     i   +k   1   *N   a     1     i+1   (Equation 8B)   N   IB   i+1   =N   Σ     1     i+1   (Equation 8C)   N   Σ     f     i+1   =N   Σ     f     i   +k   f   *N   a     1     i   +N   IB   i+1   (Equation 8D) 
where i is the number of the control interval, N a     1     1  is the number at the output of element a 1    301 ; N Σ   f   i  is the number at the output of element Σ f    304 ; N IB   i  is the number at the output of element IB  303 ; N Σ     1     i  is the number at the output of element Σ 1    202 . If the IB of  FIG. 2B  is used in place of the IB of  FIG. 2A , then equation 8B becomes:
   N   Σ     1     i+1   =N   Σ     1     i   +N   Σ     2     i+1   +k   1   *N   a     1     i+1   (Equation 9A) where:   N   Σ     2     i+1   =N   Σ     2     i   +k   2   *N   a     1     i+1   (Equation 9B) 
where N Σ     2     i  is the number at the output of element Σ 2    205 . One skilled in the art will recognize that Equation 8C above describes the smoothed frequency estimate signal, also referred to herein as smoothed frequency, f e , that is output at FFE output  307  in  FIG. 3A . Similarly, Equation 8D describes the smoothed frequency, f e , that is output at FFE output  306  in  FIG. 3A .
 
     FIG. 3B  shows a second embodiment of an FFE  113 . In that figure, all components are arranged the same as in  FIG. 3A  with the exception that the input of the accumulator  304  is the output of difference element  301  and that the output of the accumulator is fed into both the IB  303  as well as the instantaneous element  302 . Likewise, since the accumulator  304  has been moved to a different position in the circuit, the output of adder  305  is now directly fed into both difference element  301  as well as FFE output  306 . Therefore, for the FFE embodiment of  FIG. 3B  and IB  107  of  FIG. 2A , the following equations describe the signal flow among the components in  FIG. 3B :
   N   a     1     i+1   =N   input   i −( k   f   *N   Σ     f     i   +N   IB   i )  (Equation 10A)   N   Σ   f   i+1   =N   Σ     f     i   +N   a     1     i+1 .  (Equation 10B)   N   Σ   i   i+1   =N   Σ     i     i   +k   1   *N   Σ     f     i+1 .  (Equation 10C)   N   IB   i+1   =N   Σ     i     i+1 .  (Equation 10D) 
where the elements of equations 10A–10D are as described above. As before, one skilled in the art will recognize that Equation 10D above describes the smoothed frequency estimate signal, also referred to herein as smoothed frequency, f e , that is output at FFE output  307  in  FIG. 3B . Similarly, the number N a     2     i  at the output of element a 2 , which is equal to N a     2     i   =k   f *NΣ   f     i   N   IB   i , describes the smoothed frequency, f e , that is output at FFE output  306  in  FIG. 3B . Once again, if the IB of  FIG. 2B  is used in the FFE of  FIG. 3B , equation 10C then becomes:
   N   Σ     i     i+1   =N   Σ     i     i   +N   Σ     2     i+1   +k   1   *N   Σ     f     i+1   (Equation 11A) where:   N   Σ     2     i+1   =N   Σ     2     i   +k   2   *N   Σ     f     i+1 .  (Equation 11B) 
   Thus, in both illustrative FFEs of  FIGS. 3A and 3B , respectively, an unsmoothed frequency estimate f g  of the input frequency f C  is input into the FFE and a smoothed frequency estimate f e  can be obtained from FFE output  306  or FFE output  307 . Whichever output is selected, the smoothed coded frequency estimate f e  can provide an actual frequency value F e  in hertz units according to the equation:
 
 F   e [Hz]= f   e   *ΔF   NCO   (Equation 12)
 
   One skilled in the art will recognize that, in either the embodiment of  FIG. 3A  or the embodiment of  FIG. 3B , if output  306  is selected, the smoothed frequency estimate f e  will be the same. Referring once again to  FIG. 1 , a switch  115  may be added in a way such that, if position  115 A is selected, the output  306  of FFE  113  in  FIG. 3  may be sampled and if position  115 B is selected, the output  307  of FFE  113  in  FIG. 3  may be sampled. 
   One skilled in the art will also recognize that, as discussed above, in addition to the different positions of switch  115 , a number of different settings are possible for the PLL/FFE combinations shown in  FIGS. 1 ,  2  and  3 . Specifically switches  108  and  112  (as well as switch  115 ) each have two separate settings FFE  113  may have two optional configurations, as represented by  FIGS. 3A and 3B , respectively. Additionally, IB  107  and IB  303  may also be either the configuration shown in  FIG. 2A  or the configuration shown in  FIG. 2B . Accordingly, there are illustratively a total of  32  different configurations of the PLL/FFE/IB arrangement embodied in  FIG. 1 . The choice of configuration of PLL/FFE/IB arrangement may be made based on the intended implementation of the arrangement taking into account the simplicity and ease of implementation. Whichever configuration is chosen, the result of coupling FFE  113  with PLL  100  is that a refined, smoothed frequency estimate of the input signal U c  in  FIG. 1  may be obtained. These refined frequency estimates may then be used to determine the Doppler frequency shift of a signal received by that receiver to generate the velocity vector of the receiver. This may illustratively be used to more accurately determine the position of the receiver as compared to receivers using only a PLL to track the frequency and phase of an incoming signal. 
   One skilled in the art will recognize that the various embodiments described herein may take different forms. For example, the embodiments described above may be implemented in both hardware and/or firmware. Additionally, switches  108 ,  112  and  115  are illustrative in nature and are merely included to show the various possible embodiments described herein. One skilled in the art will recognize in light of the foregoing that a particular implementation may be chosen and these switches may be eliminated from the circuitry as implemented. Finally, while the above description describes the illustrative embodiment where Differential GPS (DGPS) is used, one skilled in the art will also understand that the foregoing may be used in modes where the Rover operates in a stand-alone mode and does not use the signals from the Base. 
   The foregoing Detailed Description is to be understood as being in every respect illustrative and exemplary, but not restrictive, and the scope of the invention disclosed herein is not to be determined from the Detailed Description, but rather from the claims as interpreted according to the full breadth permitted by the patent laws. It is to be understood that the embodiments shown and described herein are only illustrative of the principles of the present invention and that various modifications may be implemented by those skilled in the art without departing from the scope and spirit of the invention. Those skilled in the art could implement various other feature combinations without departing from the scope and spirit of the invention.