Abstract:
A feedback control law steers a reference phase that tracks the phase of a received code sequence. The reference phase clocks a track-reference signal consisting of a series of correlation kernels, over which data is extracted and then summed in various combinations. The correlation kernels are designed in such a manner that errors caused by multipath are eliminated or substantially reduced. Furthermore, the areas of the correlation kernels are balanced across level-transitions of a code and non-transitions to eliminate phase biases when tracking specific satellites. Extra care must be taken to balance the correlation kernels in this manner due to a little known aspect of GPS C/A codes. Specifically, not all C/A codes have the same ratio of level-transitions to non-transitions as has been assumed in prior art.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority in U.S. Provisional Patent Application No. 60/891,906, filed Feb. 27, 2007, which is incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates generally to communication, timing, or positioning devices that receive signals containing, encoded within, a known sequence positive and negative symbols of unknown phase, and particularly to devices that achieve reduction in errors resulting from multipath. 
         [0004]    The invention discloses a method to produce a track reference signal, that when correlated against a code signal, produces a correlative-phase-discriminator that can act as a measure of the offset of the track reference signal relative to the code signal. 
         [0005]    2. Description of the Related Art 
         [0006]    Precise phase estimation is required by ranging and coherent communications systems. Existing ranging systems include Global Navigation Satellite Systems (GNSS), such as the United States Global Positioning System (GPS) and the Russian&#39;s Global Navigation Satellite System (GLONASS). These systems utilize a direct sequence spread spectrum (DSSS) signaling technique which modulates a carrier with a pseudo-random code sequence and a navigation message bit sequence. The navigation message contains precise satellite orbital information, an ionosphere model and timing information. The GNSS receiver tracks the carrier and code signal phases to obtain ranging information which is ultimately used to calculate the user&#39;s position and internal clock error. Consider the GPS Coarse/Acquisition code bit. This code bit has a 1/(1.023×10 6 ) second period which corresponds to a 300 m position resolution. Therefore, even a small 0.5° phase error corresponds to a large 0.4 m range error. Clearly, in the GNSS application, precise phase estimation is important. 
         [0007]    When tracking a code signal, it is generally necessary to down-convert to base-band or near base-band using conventional digital carrier tracking methods such as a Costas loop. At base-band, carrier terms are removed to the degree that the remaining signal has a predominant code signal component. The phase of this code signal component may be tracked using a correlative code phase discriminator. Such a discriminator is the subject of this disclosure. 
         [0008]    Most DSSS code bits, referred to as PN, PRN codes or chips, have a rectangular pulse shape with amplitudes +1 or −1 for the entire code bit period, T Chip . An example code bit sequence is shown in  FIG. 2A . Sometimes the code chips are depicted as 1&#39;s and 0&#39;s since they are digitally generated. It is important to note that in general DSSS systems are not restricted to rectangular code pulses and some systems design the code pulse shape to concentrate the desired power spectral density (dB-Watts/Hz) within a fixed bandwidth. 
         [0009]    In acquiring the PN sequence for subsequent signal de-spreading, a track-reference signal is produced by the tracking hardware. This track reference signal will correlate in some manner with the PN sequence. The function of the code tracking loop is to keep the phase of the track-reference signal aligned to the phase of the incoming code signal by driving the phase error to zero. The control loop will advance or retard the track-reference signal in time until it aligns with the incoming signal (see  FIG. 2B ). 
         [0010]    The code tracking loop consists of a phase discriminator, a loop filter and a Numerically Controlled Oscillator (NCO). The phase discriminator estimates the phase error between the incoming measured signal and the track-reference signal. The filtered phase error is output from the loop filter and provides a delta-phase. This delta-phase is accumulated in the NCO which adjusts the track-reference phase to drive the phase error to zero. 
         [0011]    The control loop described above is referred to as a Delay Locked Loop (DLL). The original, continuous time DLL was originally described by Spilker (1961). He also introduces the derivative as the optimal correlation thereby proving that a DLL discriminator should only process on signal transitions and should remain zero elsewhere. The derivative is the maximum likelihood (ML) code bit transition estimator. The DLL is naturally extended to DSSS signals since the spreading (code bit) sequence is known in advance. This leads to the δ-delay Early-Late (EML) discriminator described by Gill (1966). Polydoros (1985) and Hurd (1970) analyzed loop performance with respect to δ for both low and high SNR and it was determined that the δ values other than ½ could be optimal. 
       SUMMARY OF THE INVENTION 
       [0012]    A feedback control law steers a reference phase that tracks the phase of a received code sequence. The reference phase clocks a track-reference signal consisting of a two separate series of correlation kernels, one that operates on code transitions (a transition meaning a change in sign from one code chip to the next) and one that operates on non-transitions (a non-transition meaning that the sign of two adjacent chips remains the same). The correlation kernels define regions of support over which data from the incoming signal is captured, possibly inverted (and possibly scaled), and then accumulated. The accumulations are correlation outputs that, when properly combined, taking into account the number of transitions and non-transitions, form a correlative phase discriminator. The phase discriminator provides a measure of phase tracking error that is made available to a feedback control loop that aligns the reference phase to the incoming code phase. The correlation kernels are designed in such a manner that errors caused by multipath are eliminated or substantially reduced. Furthermore, the areas of the correlation kernels are balanced across level-transitions of a code and non-transitions to eliminate phase biases when tracking specific satellites. Extra care must be taken to balance the correlation kernels in this manner due to a little known aspect of GPS C/A codes. Specifically, not all C/A codes have the same ratio of level-transitions to non-transitions as has been assumed in prior art. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The drawings constitute a part of this specification and include exemplary embodiments of the present invention and illustrate various objects and features thereof. 
           [0014]      FIG. 1  shows a track feedback control loop for tracking the phase of a code signal. 
           [0015]      FIG. 2A  shows a portion of a code sequence. 
           [0016]      FIG. 2B  shows the process of aligning a model track reference signal sequence with a code sequence. Both sequences are identical other than a time misalignment. 
           [0017]      FIG. 2C  shows the autocorrelation function that results when two similar PN sequences are correlated with one another. The horizontal axis is in chips of misalignment and the vertical axis is proportional to the integrated product of the two misaligned signals (the correlation). 
           [0018]      FIG. 3A  presents and early, prompt, and late code sequence along with an early minus late (EML) code sequences. The early code sequence is ½ of a chip early with respect to prompt, and the late is ½ of a chip late with respect to prompt. The EML, which may be used as a track reference signal, is the difference of early signal with the late signal. 
           [0019]      FIG. 3B  presents the correlation functions of the early and late code sequences with the prompt code sequence. 
           [0020]      FIG. 3C  is the correlation of the EML sequence with the prompt sequence. This correlation may be use as a code phase discriminator in a code tracking loop. 
           [0021]      FIG. 4A  shows a portion of a code signal. 
           [0022]      FIG. 4B  depicts a portion of a track reference signal. 
           [0023]      FIG. 4C  depicts the signal of  FIG. 4A  and the track reference signal of  FIG. 4B  aligned to some relative phase for which the correlation will be performed. 
           [0024]      FIG. 4D  shows the result of multiplying the code signal by the track reference signal. 
           [0025]      FIG. 4E  shows two signals that are multiplied together, but does so more in accordance with today&#39;s digital methods. 
           [0026]      FIG. 4F  shows the result of the multiply of the two signals shown in  FIG. 4E . 
           [0027]      FIG. 5  shows a track reference signal consisting of a series of correlation kernels, themselves made up of individual pulses. The track reference is shown phase-aligned to the code signal. 
           [0028]      FIG. 6A  shows track reference signal containing a Non-Transition correlation kernel and a Low-High (L-H) transition correlation kernel as per one embodiment of the present invention. 
           [0029]      FIG. 6B  shows track reference signal containing a Non-Transition correlation kernel and a High-Low (H-L) transition correlation kernel as per one embodiment of the present invention. 
           [0030]      FIG. 7A  shows the non-zero regions that occur after a non-transition correlation kernel and a L-H correlation kernel multiply a code signal. The areas of these regions are referred to as masses, and for this figure a mass balance exist since masses sum to zero. In  FIG. 7A , the phase of the track reference signal is aligned to the code signal. 
           [0031]      FIG. 7B  shows the result of shifting the track reference signal so that its phase lags the code signal. 
           [0032]      FIG. 7C  shows the result of shifting the track reference signal so that its phase leads the code signal. 
           [0033]      FIG. 8A  shows the arrangement of masses at a transitions and a non-transitions and also shows the phase error ‘x’ relative to these masses. 
           [0034]      FIG. 8B  shows the resulting correlative-phase-discriminator curve as a function of true phase error. 
           [0035]      FIG. 9  is a table that provides information about the C/A PN codes of GPS. It shows total numbers of polarity transitions and non-transitions within the 1023 chip C/A code 
           [0036]      FIGS. 10A and 10B  show direct and multipath error signals superimposed on one another, for the purpose of showing the multipath reducing benefit of the invention.  FIG. 9A  depicts multipath of same polarity as direct signal and  FIG. 9B  depicts opposite-polarity multipath. 
           [0037]      FIG. 11A  through  FIG. 11C  show three different implementations of non-transition correlation kernels. On the right, the corresponding phase discriminators are shown. 
           [0038]      FIG. 12  shows a correlation kernel memory map implementation. 
           [0039]      FIG. 13A  shows an embodiment of transition correlation kernel mapped to total code phase. 
           [0040]      FIG. 13B  shows an embodiment of transition correlation kernel mapped to fractional code phase. 
           [0041]      FIG. 14A  shows an embodiment of a non-transition correlation kernel mapped to total code phase. 
           [0042]      FIG. 14B  shows an embodiment of non-transition correlation kernel mapped to fractional code phase. 
           [0043]      FIG. 15  is a flow chart showing the implementation Mass-Balance and EML Kernel Generator for one embodiment of the present invention. 
           [0044]      FIG. 16  shows a Prompt correlation, an Early-Minus-Late (EML) correlation and a “shifted EML” correlation. 
           [0045]      FIG. 17  shows three shifted EML correlation curves plotted as a function of code phase error. 
           [0046]      FIG. 18A  provides various plots of shifted EML correlations. The shifted EML correlation is shown without multipath added and with the effects of several different multipath delays. 
           [0047]      FIG. 18B , shows an mass-balance correlative-phase-discriminator as well as the negative portion of the shifted EML. 
           [0048]      FIG. 19A  shows left and right shifted EML correlations obtained using a positive and negative prompt correlation to obtain positive and negative shifts. 
           [0049]      FIG. 19B  shows the mass-balance phase-discriminator. 
           [0050]      FIG. 19C  shows the results of adding this discriminator to the shifted correlations of  FIG. 19A . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     1. Introduction 
       [0051]    As required, detailed embodiments and/or aspects of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments/aspects are merely exemplary of the invention, which may be embodied in various forms. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention in virtually any appropriately detailed structure. 
         [0052]      FIG. 1  illustrates the three primary components of a code tracking loop: the phase discriminator  120 , the loop filter  121  and the Numerically Controlled Oscillator (NCO)  122 . The phase discriminator  120  generates an output error signal  123  proportional to the phase difference between the incoming (measured) signal to be tracked  124  and the current phase estimate  125 . The error signal  123  is filtered by the loop filter  121  to reduce noise. The output of the loop filter  126  forms a delta-phase which drives the NCO  122 . The NCO  122  is an accumulator whose new value is obtained by adding the delta-phase to the previous accumulator value. The delta-phase is added to the fractional phase every sample clock period or at some other prescribed rate. The accumulator is finite length so when the register overflows it marks the start of the next code bit in the sequence. Therefore, the NCO accumulator represents the fractional code bit phase with a range between 0 (inclusive) to 1.0 (exclusive). 
         [0053]    The control loop will advance or retard the model in time until it aligns with the incoming signal (see  FIG. 2B ). The phase error, τ, is estimated by the phase discriminator  120  of  FIG. 1  and then filtered by the loop filter  121 . When the phase error is positive then the model is said to be early or advanced in time so the NCO phase accumulations need to be slowed. Consequently a positive phase error must reduce the delta-phase value being accumulated. Conversely, when the phase error is negative then the model is said to be late or retarded in time so the NCO phase accumulations need to be increased. Therefore a negative phase error must increase the delta-phase value being accumulated. 
         [0054]    The basic operation of the EML-based DLL is now described. The incoming signal is de-spread by cross-correlating the model of the code sequence with the measured signal. Specifically, the product is formed between the model and measured signal. This product is integrated over a specified accumulation time-interval and the result temporarily stored for subsequent software processing by the track loop. When the measured code signal and model code signal align, the maximum correlation value occurs. The correlation value as a function of timing error, τ, is shown in  FIG. 2C . The ticks on the horizontal axis represent one clock period, T chip , of the code. The correlation value is essentially zero outside of one clock period. As the codes align to within one clock period  111  or less, the correlation function ramps up linearly as alignment distance diminishes. The peak  110  in the correlation function is when the two code signals are perfectly aligned. 
         [0055]    The EML phase discriminator obtains phase alignment by cross-correlating the incoming signal with a composite track reference signal equal to a δ-chip early model minus a δ-chip late model. Specifically, two exact replicas of the incoming code sequence are produced, whereby one is then shifted δ-chip early and the other shifted δ-chip late in time. The resulting late code sequence is subtracted from the early sequence.  FIG. 3A  below shows the δ=½ chip early sequence  130 , a prompt  131 , (or on-time sequence), a δ=½ chip late sequence  132 , and the composite EML sequence  133 . The prompt, in this case, represents the signal that we wish to track.  FIG. 3B  shows the correlation of the both the early and late sequences with the prompt sequence and  FIG. 3C  shows the correlation of early-minus-late sequence with the prompt. The correlation function is defined such that prompt  131  is the reference and is held stationary. The axis  144  is such that a delay in time alignment, τ, is considered positive and to the right. When the signal arrives earlier than prompt, its resulting correlation function  146  is shifted to the right since the signal must be delayed before it aligns with prompt. When the signal arrives later than prompt, its correlation function  145  is shifted to the left since it must advance to align with prompt. Note that the early-minus-late correlation function  147  crosses zero when τ=0,  143 . That is, when early and late codes are balanced δ-chip on either side of a prompt code. The early-minus-late correlation pattern effectively provides the tracking software an error feedback that drives the track reference phase generator to track the prompt. This error is known as the discriminator of the delay-lock-loop. 
         [0056]    When the incoming signal arrives early with respect to the model, more energy is present in the early correlation result and a positive error is produced. The positive error advances the reference phase and the PN (EML) model moves earlier in time. A negative error arises when the incoming signal arrives late and more energy shows up in the late sequence. This delays the reference phase. The error continuously drives the delay-lock-loop, which thereby adjusts the reference phase generator to maintain zero phase error. 
         [0057]    The discriminator generates an EML signal by subtracting the late from the early codes as they are generated. It then has one EML signal that it multiplies with the incoming signal, accumulating this product and storing the EML correlation result. In either case, the discriminator produces zero error when phase aligns with the prompt signal. 
         [0058]    Many factors affect the code phase discriminator: noise, signal amplitude, carrier offset, transition probability and multipath. All factors will reduce the phase detector gain. The dependence on amplitude can be eliminated by employing an automatic gain controller (AGC). The code tracking loop can function with a small carrier offset which is some fraction of the symbol rate. However, the carrier offset has the effect of reducing the signal&#39;s average amplitude which thereby reduces the phase detector gain. The code bit transition probability is set by the code bit sequence. A phase discriminator bias occurs due to multipath. Moreover, when the incoming signal is band limited at the receiver, some signal power is removed at the higher frequencies. This frequency truncation manifests itself as ringing in the time domain code pulse. This time-domain distortion directly increases the phase estimation variance. Consequently, it is desirable to match the receiver bandwidth to the transmit bandwidth to the extent practical for the system. Also, a non-rational sample rate to code rate ratio is desired to reduce phase estimation bias. 
         [0059]      FIG. 3A  shows the composite EML waveform  133  has four possible EML states:  134  corresponds to when the code transitions from high to low (H-L transition);  135  corresponds to when the code transitions from low to high (L-H transition);  136  corresponds to when the code remains low (non-transition) and finally  137  corresponds to when the code remains high (non-transition). Note that the EML value corresponding to non-transitions is zero; therefore states  136  and  137  are zero. These four states and correlation pulses can be generalized by introducing the notion of a correlation kernel. 
         [0060]    The correlation kernel, or kernel, can have an arbitrary shape. The amplitude of the shape is referred to as weights and the boundary where the kernel is non-zero is called the region of support (ROS). Sub regions within the kernel are called correlation pulses (or just pulses). The ROS describes the non-zero area where the correlation will take place. The weighted average is required for optimal discrimination, in a minimum variance sense: It can include channel equalization and pulse shape filtering (when non rectangular code bits are used). Note that the EML correlation has two non-zero kernels,  134  and  135  in  FIG. 3A  respectively, which have the same weight magnitudes but apposite sign. Note that the weights are even symmetric about the model transition point. 
         [0061]    In general four different correlation kernels exist corresponding to the four transitions states: (1) L-H transition; (2) H-L transition; (3) no transition but corresponding code chip low; and finally (4) no transition but corresponding code chip high. These kernels do not have to be the same; nor are they constrained to have equal energy (sum of kernel weight squared) since separate accumulators can be maintained for each state and the results scaled based upon the ratio of kernel weights. Recall that the EML kernels,  134  and  135  in  FIG. 3A , are even symmetric about the model transition point. This symmetry is not required and other correlative kernels that are non-symmetric can be used. If not symmetric about the zero phase error point, a balancing weight, or mass, is required within the non-transition regions otherwise a phase discriminator bias will result. The phase discriminator will have a non-zero output corresponding to zero phase error. Again, the phase error bias is eliminated in non symmetric transition kernels by introducing a balancing mass such as a non-transition kernel. Consequently, non-symmetric transition kernels accompanied by non-transition kernels must account for transition and non-transition probabilities otherwise a phase discriminator bias will result. Note that in this case non equal transition and non-transition probabilities will result in a phase discriminator bias whereas in the EML case only the discriminator gain is reduced and no bias occurs. 
         [0062]    Each correlation kernel can be formed using the NCO phase to define the region of support. The design of non-symmetric kernels shall be further disclosed as part of this invention. 
         [0063]    The process of correlation involves the multiplication of one signal with another and summing or integrating the result.  FIG. 4A  through  FIG. 4F  illustrate the multiplication of two such signals.  FIG. 4A  shows a portion of a signal  160 . In this invention, signal  160  comprises, at the minimum, a code signal or at least a signal highly correlated with a code signal. For the purpose of illustration, the signal  160  is shown without abrupt edges as would be the case if heavy filtering were applied. The process of converting to base-band by multiplying by sinusoidal terms could add other effects to the signal  160 , but such effects are not shown. Furthermore, there is typically a large amount of noise on the signal  160  that is also not shown. One benefit of the summation or integration that takes place as part of the correlation is that it averages out effects of noise as well as high frequency periodic components. 
         [0064]      FIG. 4B  depicts a portion of a track reference signal  161  that is to be correlated against the signal  160 . In  FIG. 4C , the signal  160  and the track reference signal  161  are shown aligned to some relative phase for which the correlation will be performed. When the track reference signal is designed in accordance with this disclosure, small errors between the phase of the track reference signal  161  and the phase of the code signal  160  are measurable through the correlation output. For small phase errors, the correlation output will be shown to be proportional to phase error. Consequently, this correlation may act as the phase discriminator in a feedback control loop, such loop steering the phase of track reference signal  161  to maintain phase alignment with the code signal  160 . 
         [0065]      FIG. 4D  shows the result of the multiply. During multiplication, the track reference  161  signal acts as an enable, selecting portions of the signal  160  to remain non-zero only at the region of support of the correlation kernels, and areas outside the region of support of these kernels to be zeroed. The non-zero portions may also be scaled in amplitude and sign according to the value of the correlation kernels. As shown in  FIG. 4D , four non-zero regions remain after the multiply. The regions  164  and  166  are seen to reverse sign from the original signal  160  due to track reference signal having a negative correlation kernel over this region. Regions  165  and  167  remain unchanged in sign relative to the original signal  160 . All regions may undergo a scaling in signal amplitude, although this is not shown. 
         [0066]      FIG. 4E  shows, again, two signals that are multiplied together, but does so more in accordance with today&#39;s digital methods. Using today&#39;s digital signal processing techniques, the code signal is typically sampled by an A/D and  FIG. 4E  shows such samples as discrete vertical lines following the envelope of the original continuous signal. Sampling is typically periodic at some sample frequency f s . Again, during a multiply, the track reference signal  161  acts as an enable, passing only samples such as  162  that are within its non-zero region of support. Samples taken outside the region of support, such as the sample at  163 , are discarded. 
         [0067]      FIG. 4F  shows the result of the multiply of the two signals shown in  FIG. 4E . Digital samples remain only at the regions of support of the track reference signal. Some are inverted, such as the sample  168  while others, such as the sample  169  remain unchanged in sign. The scaling of the multiply is preferably (though not necessarily) left at unity in order to reduce computational overhead. As such, the track reference signal simply acts as an enable, allowing the desired samples to pass to an accumulator, perhaps with inverted sign. 
         [0068]    The final step in correlation is the accumulation (or summation) of the samples that were enabled by the multiply. This accumulation occurs over some prescribed correlation time-window, at which point the accumulation is latched and a new accumulation begins. The length of time may correspond to the length of a repeating code such as the GPS C/A code, but this is not necessary. 
         [0069]    When performing correlations on a digitally sampled signal, summations are use rather than the integrations that would be used when performing correlations on the original continuous-time signal. The summation produces results similar to those obtained by integrating the original continuous-time signal provided certain conditions are met. One condition is that the sample rate, f s , should be sufficiently fast to satisfy Nyquist requirements. Another condition is that the samples should be distributed, on average, uniformly within the correlation kernels of the track reference signal. Generally, this implies a sufficiently large number of samples in order to meet statistical requirements for uniformity. A track reference signal, such as described in this patent, has repeating, identically shaped correlation kernels aligned to a fundamental frequency, f chip . High repetition of such correlation kernels helps to assure the statistical assumption of a uniform distribution. Proper selection of the sample frequency is also beneficial in this regard. If the ratio of sample frequency f s , to the chip frequency, f chip  is irrational, it reduces the likelihood that the location of the first sample within any correlation kernel will repeat at a subsequent correlation kernel. 
         [0070]    The remainder of the figures within this patent will deal only with a continuous-time representation of the various signals used in the correlation such as those shown in  FIG. 4C . This is for simplicity of presentation. It is understood, by those skilled in the art, that the continuous-time representation is easily translated into a digital implementation. 
         [0071]      FIG. 5  shows a track reference signal,  209 , that consists of a series of correlation kernels, themselves made up of individual pulses. The track signal,  209  is shown aligned to the code signal  210  with zero phase error. By this we mean that the phase of the track reference signal is defined to exactly align with the phase of the code signal  210  in the position shown. 
         [0072]    In  FIG. 5 , the width of each code chip is shown to be of duration T chip . The code signal  210  is seen to change sign three times at chip boundaries  215 ,  220  and  221 . A Low-High Transition (L-H Transition) in sign occurs at  215  and  221  and a High-Low Transition (H-L Transition) in sign occurs at  220 . Following the chip boundary  215 , the code remains high for three consecutive chips. It then goes low for one chip and back high for two more chips. Many combinations H-L, L-H and non-transitions of chips will arise in practice. 
         [0073]    The design of the track reference signal,  209 , involves knowledge of the code signal  210 . In one embodiment of the present invention, the correlation kernels of the track reference signal consists of high and low pulses at appropriate times relative to the code signal, generally near the code signal&#39;s chip boundaries. At non-transitions of the code signal, the correlation kernels, such as  211 ,  216 , and  217  occur for a short duration near the end of the chip. The pulses comprising the correlation kernel take the same sign as the code chip, positive when the code is positive and negative when the code is negative. 
         [0074]    The correlation kernels take a different characteristic at L-H and H-L transitions of the code. On L-H transitions such as  215 , the correlation kernel pulse  212  occurs prior to the L-H transition. The pulse  212  remains in effect until after the transition, at which point a pulse  214  of opposite sign occurs. The first pulse,  212 , takes the sign of the code chip immediately following the transition  215 , thus  212  is positive. 
         [0075]    On H-L transitions of the code such as  220 , the pulses of the correlation kernel reverse sign. That is pulse  218  is negative to match the sign of the upcoming code chip. Following pulse  218 , the pulse  219  occurs with a sign flipped back to positive. 
         [0076]    In another embodiment of the present invention, all signs of the track reference signal  209  could be reversed relative to the code. The end result is that the error discriminator will reverse, and the tracking loop that drives the phase of the track reference phase will then need to flip the sign back to give the correct feedback. 
         [0077]    The track reference signal depicted in  FIG. 5  could be modified regarding placement, number, and size of the correlation kernels and still maintain the desired properties brought forth in this patent. The scope and impact of such modifications will become clear by subsequent teachings of this patent. 
         [0078]      FIG. 6A  and  FIG. 6B  give further explanation as to the shape of the correlation kernels. The code signal,  300  is shown in both  FIG. 6A  and  FIG. 6B , undergoing a L-H transition  307  in  FIG. 6A  and a H-L transition  317  in  FIG. 6B . 
         [0079]    Referring to  FIG. 6A , the track reference signal  301  is shown to contain Non-Transition correlation kernel  302 , and a L-H transition correlation kernel consisting of pulses  303 , and  304 . The code takes a L-H transition coincident with pulse  303 , dividing it into two regions, one having an area A 1  and the having an area A 3 . Pulse  302 , having an area A 4 , is shown aligned to the end of a non-transition code chip (one for which the sign does not change in the next chip). Pulse  304  of area A 2  follows pulse  303  and is of opposite sign. 
         [0080]    When the track signal  301  is aligned in phase to the code signal  300 , the area A 1  is equal to A 2  and the area A 3  is equal to A 4 . We henceforth refer to this equalization as a mass balance, borrowing from the terminology one might use if the areas depicted were actually plates of material having equal thickness and composition. 
         [0081]    Referring to  FIG. 6B , we depict the code having opposite transition and non-transition signs relative those shown in  FIG. 6A . Consequently the pulses  312 ,  313 , and  314  of the correlation kernel are reversed relative to pulses  302 ,  303 , and  304 . Again, the area A 1  is balanced to A 2  and the area A 3  is balanced to A 4  when the phase of the track reference signal matches that of the code signal. 
         [0082]    The track reference signal  301  acts as a multiplier and enable for the code signal  300 . The product is zero wherever the track reference signal  301  is zero, and non-zero wherever the correlation kernels exist. The non-zero portion has an amplitude that is the product of both the amplitude of the code and the amplitude of the track reference, including sign. For example, if the code signal amplitude is −0.5 and track reference signal amplitude is −1, the product is of amplitude +0.5. 
         [0083]      FIG. 7A  shows the product of the track reference signal and the code signal when both are phase aligned. The product pulses  341 ,  342 ,  343  and  344  have areas M 1 , M 2 , M 3  and M 4  respectively and we will refer to such product pulses as masses. The areas of these masses are proportional to the corresponding areas A 1 , A 2 , A 3  and A 4  of the track reference signal, but are scaled in amplitude by the height of the code signal. The masses also contain some sign reversals relative to the original pulses due to multiplication by the code signal. Sign reversals occur whenever the code is negative. A change in sign of the code occurs at the chip level transition  340 . 
         [0084]      FIG. 7A  holds for both L-H transitions, and H-L transitions. That is, regardless of the direction of the code transition (H-L or L-H), M 2  and M 3  are negative while M 1  and M 4  are positive. This is by design. 
         [0085]    A further property of the invention relates to the areas of M 1 , M 2 , M 3  and M 4 . When the track reference signal and the code signal are aligned in phase, the areas cancel to zero when summed together. Specifically 
         [0000]    
       
      
       M 
       2 
       =−M 
       1  
      
     
         [0000]      and 
         [0000]    
       
      
       M 
       3 
       =−M 
       4  
      
     
         [0000]    and so, 
         [0000]        M   1   +M   2   +M   3   +M   4 =0 
         [0000]    Thus, the track reference signal is mass-balanced about to the code signal so as to yield a zero summation. 
         [0086]      FIG. 7B  shows the result of delaying the track reference signal relative to the code by a positive phase offset. That is, the track reference signal lags the code signal. The masses  351 ,  352 ,  353  and  354  of the track signal are seen to shift right relative to the code&#39;s level transition  340 . The mass  351  gains positive area so that M 1  increases by a positive amount. The mass  353  loses negative area, so that M 3  also effectively increases by a positive amount. Thus, there is a net positive increase in mass (or correlation) relative to  FIG. 7A . Precisely, 
         [0000]        M   1   +M   2   +M   3   +M   4 =2×δ 
         [0000]    Where δ is the increase in the area of M 1  and also the increase in area of M 3 . 
         [0087]      FIG. 7C  shows the case when the track reference signal leads the code signal. The pulses  361 ,  362 ,  363  and  364  are seen to shift left relative to the code sign transition  340 . The mass  361  loses positive area so that M 1  decreases in value. The mass  363  gains negative area, so that M 3  also decreases. Thus, there is a net decrease in mass relative to  FIG. 7A . Precisely, 
         [0000]        M   1   +M   2   +M   3   +M   4 =−2×δ 
         [0000]    Where is δ the decrease in area of both M 1  and M 3 . 
         [0088]    The mass summations represent the process of computing a correlation between the track-reference signal and the code signal. The correlation acts as a measure phase error between the track reference signal and the code signal. Specifically, the sum of all masses, M, across all chips gives a result that is proportional to phase error for small phase errors. We therefore refer to this correlation as a correlative-phase-discriminator. 
         [0089]    Referring to  FIG. 8A , the chip transition,  385 , acts as the zero-phase reference. Phase error is thus measured by a displacement ‘x’,  380 , relative to zero. Positive ‘x’ is taken so the code signal leads the track reference signal. At zero phase error (x=0), the masses  381 ,  382 ,  383 , and  384  balance. For some positive constants γ and σ, the relationship is 
         [0000]        M   1 =γ/2 
         [0000]        M   2 =−γ/2 
         [0000]        M   3 =σ/2 
         [0000]        M   4 =−σ/2 
         [0000]      So that  M   1   +M   2   +M   3   +M   4 =0 
         [0090]      FIG. 8B  shows a plot of the correlative-phase-discriminator as a function of true phase error ‘x’ for a phase error of x=+1 to x=−1 chip. The phase error x, is shown in the positive sense  374 , and the negative sense  373 . Notice that, as stated, the point of zero phase error gives a zero mass balance and hence zero phase discriminator  376 . The phase discriminator curve  371  for small phase errors is of constant slope (linear) and is positive for positive phase error (code phase leading reference phase). It reaches a maximum of σ on the right-hand end of the linear region, at a phase error of w 3 —the width of the M 3  pulse at zero phase error. As true phase error continues in the positive direction, the correlative-phase-discriminator levels off to a constant value as shown by  370 . Similarly, moving left, it reaches a peak negative value of −γ at a phase error of −w 1  and then slopes back to zero as phase error becomes more negative, reaching zero at −2w 1 . The correlative-phase-discriminator becomes zero over the region  372  with a slight bump  375  outside of a phase error of −1 chip. Due to its derivation from the mass-balance concept, we refer to this as a mass-balance correlative-phase-discriminator. 
         [0091]    Employing the correlative-phase-discriminator as a measure of phase error, conventional linear control techniques can be utilized to maintain near zero phase error. During tracking, the phase error will typically reside within the linear portion  371 , and linear control assumptions hold true. Even larger positive phase errors, up to one chip in duration, are zeroed out by a feedback control loop since the phase discriminator remains non-zero and positive when phase error is positive. However, due to the asymmetric nature of the mass-balance phase discriminator curve, reverse is not true. If phase error exceeds a value of −2w 1 , the phase discriminator goes to zero,  372 , where it remains for negative phase errors up to −1 chip. In the region  372 , the feedback control will not be able to zero out the phase error. A solution for this problem, however, is disclosed subsequently. 
         [0092]    In the disclosure presented thus far, an important point has been overlooked. The phase discriminator is calculated by correlating over a period of time that includes many code chips, some with transitions in sign and some without. There is no guarantee that the number of transitions will be equal to the number of non transitions. If the mass balance is to produce the desired results, then this mismatch of level transitions to non-transitions must be taken into account. 
         [0093]    Referring again to  FIG. 8A , recall the mass M 3  at the sign transition must balance the mass M 4  at the non-transition whenever the track reference signal and code signal are aligned. But taking into account all chips within the code sequence the mass balance becomes 
         [0000]        N   T   ×M   1   +N   T   ×M   2 =0 
         [0000]      and 
         [0000]        N   T   ×M   3   +N   N   ×M   4 =0 (only if  N   T   ×M   3   =−N   N   ×M   4 ) 
         [0000]    where N T  is the number of sign transitions (both L-H and H-L), and N N  is the number of non-transitions. 
         [0094]    But simply having M 2 =−M 1  and M 3 =−M 4  non longer produces a zero mass balance unless N N =N T . 
         [0095]    We thus introduce a scale factor α for which the final correlation of all non-transitions is multiplied. We compute α as 
         [0000]      α=( N   T   ×|M   3 |)/( N   N   ×|M   4 |) 
         [0000]    When |M 3 |=|M 4 |, which is the case described so far and also convenient for implementation then 
         [0000]      α= N   T   /N   N    
         [0000]    The mass balance then becomes 
         [0000]        N   T   ×M   1   +N   T   ×M   2 =0 
         [0000]      and 
         [0000]        N   T   ×M   3   +α×N   N   ×M   4 =0 
         [0000]    which indeed holds true for any nonzero N N  and N T . 
         [0096]    Generally, many arrangements of scaling the transition correlation to the non-transition correlation are possible. For example, choose any numbers β 1  and β 2  such that 
         [0000]      β 2 /β 1 =α 
         [0000]    And then multiply the transition correlation by β1 and the non-transition correlation by β2 to satisfy the mass balance. This will give a mass balance 
         [0000]      β 1 ×( N   T   ×M   1   +N   T   ×M   2 )=0 
         [0000]      and 
         [0000]      β 1   ×N   T   ×M   3 +β 2   ×N   N   ×M   4 =0 
         [0097]    In summary, to produce a correlative-phase-discriminator per this invention that is unbiased and gives a zero value for zero phase error, two correlations must be performed and summed together with appropriate scaling. One correlation involving all code sign transitions (L-H and H-L) and the other involving all non-transitions. There is at least one work-around, but it is less desirable. The work-around would be to move the mass M 4  to the lie within a transition chip and perform correlations only on transition chips. 
         [0098]    The need for two correlations may not seem necessary to those who are familiar with the GPS C/A gold code, and who incorrectly assume that the number of transitions to non-transitions is balanced for each C/A code. 
         [0099]    The table of  FIG. 9  illustrates the point. This table provides the totals of the chip-edge events that occur within the C/A code of GPS. 
         [0100]    As mentioned, the need for two correlations stems form the fact that the invention disclosed here correlates data from both transition and non-transition chips, and these chips do not necessarily equal in number of occurrence. The advantage of the present invention is that it gives rise to a mass-balance phase discriminator as shown  FIG. 8B . One benefit of such a discriminator is that for positive phase errors (code signal leading the track reference signal) up to one full chip in magnitude, a control loop using the discriminator as a measure of phase error will have feedback of the correct sign to drive the phase error to zero. This is not true for negative phase errors (code signal lagging) due to the zero-region  372  which provides no discriminator feedback for phase errors that are more negative −2w 1 . Phase error will, however, able when &gt;−2w 1 . 
         [0101]    The mass-balance phase discriminator curve, having a zero region in the left-half, is beneficial for reducing multipath. This is shown in  FIG. 10  where the phase discriminator curve  400  for the code signal is shown along with phase discriminator curves  401  and  402  that result from signals that are similar to the code, but delayed in time such as is the case of multipath. Multipath is always delayed with respect to the direct signal and thus the offset  403  of the multipath delayed discriminators is always to the right of zero. The delayed discriminator  401  in  FIG. 10A  is a result of a delayed code multipath signal having the same polarity as the direct signal, but it is equally likely that the multipath will be of opposite polarity to the direct signal as shown by  402  of  FIG. 10B . Since multipath enters the system linearly, superposition holds. That is, the total correlative-phase-discriminator is the sum of phase discriminator  400  from the direct signal and the discriminator  401  or  401  from the multipath signal. When the multipath signal is delayed by more than the duration of 2w 1  it no longer has an effect on the zero crossing point  404  of the direct signal&#39;s discriminator curve when summed with the delayed discriminator. The adverse effects of the multipath on the summed discriminator zero crossing are thus eliminated for multipath delayed by more than 2w 1 . 
         [0102]    The benefit of reducing multipath can be achieved by building an mass-balance phase discriminator choosing areas as outlined in  FIG. 7 . That is 
         [0000]    
       
      
       M 
       2 
       =−M 
       1  
      
     
         [0000]      and 
         [0000]    
       
      
       M 
       3 
       =−M 
       4  
      
     
         [0000]    Although the pulses of the track-reference signal shown thus far have all been rectangular, they need not be. The pulses of the track-reference signal can have rounded tops or tops with various curvatures so long as their areas satisfy the mass balance and sign conventions introduced. When processing digital samples, curvature on the top of the pulses amounts to different weightings on samples. 
         [0103]    It is also possible to modify the correlation kernels track-reference signal without affecting the mass balance provided that the modifications follow certain rules. For example, additional pulses may be added to the correlation kernel provided the pulses result in masses that cancel one another at zero phase error. And it is possible move the locations of the correlation kernel somewhat without affecting the mass balance.  FIG. 11A  through FIG  11 C show some rearrangements of the area corresponding to a non-transition chip. In the left-hand side of  FIG. 11A , a code signal  422  is shown for which there is a non-transition  423  and an L-H transition  424 . The correlation kernels of the track reference signal  421  are depicted according to one embodiment of the present invention. The corresponding discriminator curve  425  is shown to the right. Note the small hump  426  lying just outside on chip of negative phase error. 
         [0104]      FIG. 11B  depicts another embodiment of the present invention where a modification to the correlation kernel at the non-transition has been made by adding two pulses of canceling area. The pulse  431  and  432  are shown with equal area and opposite sign. In fact, the arrangements of the pulses at the transition and at the non-transition are now similar, and as such, the track-reference signal shown in  FIG. 11B  may be simpler to implement than the one shown in  FIG. 11A . The corresponding phase discriminator  435  is also shown in  FIG. 11B  where is evident that the hump that was present in  FIG. 11A  is no longer present. Hence, there is a flatness of the discriminator at  436  and the discriminator remains at a zero value. The elimination of the hump may be advantageous in situations where multipath of approximately one chip delay is present. 
         [0105]    In  FIG. 11C , the correlation kernel pulse  441  of area A 4  has been delayed (shifted right) so that it occurs immediately following a non-transition chip boundary, rather than before the boundary. The mass balance is still satisfied, but a change occurs in the corresponding phase discriminator  445 . The hump  446  now appears larger than in  FIG. 11A  and has moved within one chip&#39;s distance of the point of zero phase error. The hump  446  may be disadvantageous when experiencing multipath arriving approximately one-chip delayed relative to the direct signal. 
         [0106]    In addition to the aforementioned modifications to the correlation kernels and their areas, we note that correlation kernels corresponding to chip transitions can be changed in size relative to correlation kernels corresponding to non transitions, provided such changes are accounted for by the scale factors α or β 1  and β 2 . 
         [0107]    Kernels that satisfy the mass-balance across transition and non-transition chips will be referred to as mass-balance kernels. The correlative code-phase discriminator resulting from summing or accumulating these kernels will be referred to as the mass-balance discriminator. 
         [0108]      FIG. 12  shows one possible implementation of the invention utilizing a 2 N  by M bit memory  550  to build the kernel. The N bit address, A N-1  . . . A o , consists of a 2 bit transition state  551  and the upper N-2 bits of the code NCO  552 . The M bit memory output  553 , D M-1  . . . D o , consists of the kernel weight associated with the fractional code NCO phase and transition state. The 2 bit transition state, A N-1 ,A N-2 , is defined as: 
         [0000]    
       
         
               
             
               
               
             
           
               
                   
               
               
                 A N−1 , A N−2  Definition 
               
             
          
           
               
                 A N−1 , A N−2   
                 Meaning 
               
               
                   
               
               
                 0 
                 Non-Transition of code, but code chip low 
               
               
                 1 
                 Non-Transition of code, but code chip high 
               
               
                 2 
                 H-L code transition 
               
               
                 3 
                 L-H code transition 
               
               
                   
               
             
          
         
       
     
         [0109]    The memory of  FIG. 12  is referred to as the Kernel Map. This embodiment produces a highly flexible correlation kernel than can even compensate for channel distortion and perform PRN pulse filtering. 
         [0110]    At the minimum, to account for the imbalance in transitions and non transitions, two correlations must be formed, one for transitions (H-L or L-H), and one for non-transitions. These will be termed, XTionSum and NoXTionSum respectively. 
         [0111]    The XTionSum and NoXTionSum correaltions used to form the mass-balance discriminator are obtained using the following steps:
       1. Load the Kernel Map memory after a system reset.   2. Every sample clock update the Code NCO.   3. Form address bits A N-1  . . . A o  by concatenating the 2 bit state transition value and the upper N-2 bits of the fractional code NCO phase.   4. Read the Kernel Map memory to obtain the kernel weight.   5. Calculate Mass=kernel weight times the digitally sampled codes (note the digitally sampled code need-not not be pure and may contain artifacts as a result of noise or conversion to base-band).   6. With the transition state coding described above, the A N-1  address bit is set when the NCO phase is within a code bit transition region. When the code phase is within a bit transition region, add Mass to the transition accumulator. XTionSum: otherwise add Mass to the non-transition accumulator. NoXTionSum.   7. At the end of the correlation accumulation period, usually at the end of each PRN epoch for GPS, copy the XTionSum and NoXTionSum values into registers XTionReg and NoXTionReg and then reset both XTionSum and NoXTionSum to zero. The XTionReg and NoXTionReg registers are used by the processor for subsequent processing of the Mass Balance discriminator.       
 
         [0119]    The mass-balance transition and non-transition kernels described above as well as the EML kernel are simple kernels which can be efficiently implemented within combinational logic. The preferred embodiment compares the upper K bits of the fractional code NCO phase against programmable phase boundaries to form a wide range of kernels including the mass-balance kernels as well as the EML kernel. Note that the fractional NCO code phase ranges from 0 (inclusive) to 1.0 (exclusive); where 1.0 represents the next code bit.  FIG. 13A  and  FIG. 13B  illustrates how the transition kernel is mapped from the code phase to the fractional code phase.  FIG. 14A  and  FIG. 14B  illustrates the mapping for the non-transition kernel.  FIG. 15  contains the algorithm implemented within the preferred embodiment. 
         [0120]    The mass-balance transition kernel was originally presented in  FIG. 6A   303  and  304 . It is redrawn in  FIG. 13A   560  to show how it is a function of the code phase  561 . The kernel weights are determined by comparing the code phase against the phase boundaries P 0  through P 5  ( 565 ,  562 ,  563 ,  564 ,  566 , and  567  respectively). The kernel is 0 at zero code phase and becomes 1 at code phase boundary  562  (P 1 ). It remains 1 through code phase boundary  566  (P 4 ). The kernel transitions to −1 at  566  (P 4 ) and remains −1 until  567  (P 5 ). The kernel transitions back to 0 at  567  (P 5 ). 
         [0121]      FIG. 13B  maps the mass-balance transition kernel based upon the total code phase ( 560 ) into the fractional NCO code phase  570  between at 0 (inclusive) and 1.0 (exclusive). Within  FIG. 13B ,  571  and  572  represent the remapped kernel. Note that  573  and  574  both represent the same fractional code NCO phase of zero. Also, note that the kernel region of support does not include phase  580  (0.5), so  576 &lt; 580  (P 5 &lt;0.5) and  577  &gt; 580  (P 1 &gt;0.5). 
         [0122]    The mass-balance non-transition kernel was originally presented in  FIG. 6A   302  and is redraw in  FIG. 14A   590  as a function of the total code phase  591 . The kernel starts at boundary  592  (P 2 ) and stops at boundary P 0 .  FIG. 14B  maps the mass-balance non-transition kernel  592  into the fractional NCO code phase  596 . 
         [0123]    Note that by defining the six code phase boundaries, P 0  through P 5 , many different kernels can be implemented within the same algorithm including the mass-balance kernels as well as the EML kernel. Recall that P 0  always corresponds to zero fractional NCO code phase. Refer to  FIG. 15  for the kernel generation algorithm used by the preferred embodiment. 
         [0124]    The initialization step  600  occurs after every accumulation period and consists of reloading the phase boundaries, P 1  through P 5 , the discriminator type (DiscrimType) and clearing the XTionSum and NoXTionSum correlation sums. The DiscrimType can take on many different values including MassBalanceType 1 , MassBalanceType 2  and EMLType. MassBalanceType 1  is associated with the kernels presented in  FIG. 6A  and  FIG. 6B . MassBalanceType 2  is associated with the mass-balance transition kernel for both transitions and non-transitions. EMLType is associated with the variable delay EML kernel. 
         [0125]    At each sample clock the upper K bits of the code NCO are read into the variable NCOPhase as shown in step  601 . 
         [0126]    The starting phase range (PStartRange) and the stopping phase range (PStopRange) are determined conditioned upon DiscrimType and the transition state (bNoXtion) as shown in step  602 . Statements of the form, a=c?x:y, are equivalent to “if c is true then a=x else a=y.” 
         [0127]    Boolean phase range flags are calculated as shown in step  603 . The flags are set conditioned upon where the current fractional NCO code phase (NCOPhase) falls within the boundaries P 1  through P 5 . 
         [0128]    An intermediate kernel weight is calculated as shown in step  604 . The intermediate weight is conditioned on the range flags in  603  and the transition state (bNoXtion). The sign(x) function returns +1 if x&gt;0, −1 if x&lt;0 and 0 if x=0. The final kernel value (weight) is set by  605  and  606 . 
         [0129]    The correlation mass is calculated in  607  where it is added to the appropriate correlation sum. NoXTionSum and XTionSum, based upon the transition state (bNoXtion)  608 . 
         [0130]    The accumulation period (or epoch) is checked  609  to see if it is complete. If the period is complete then the accumulation sums are stored in holding registers  610  for additional discriminator processing: otherwise, the process repeats at  601  following the next sample clock. 
         [0131]    The mass-balance correlative-phase-discriminator, having a zero-region to the left, has been shown to be beneficial when measuring phase alignment between the track-reference signal and the code signal in the presence of delayed multipath signals. However, the mass-balance discriminator has the draw-back of not giving a measure of negative phase errors when those negative phase errors become large enough to fall within the zero-region. Such large errors may occur during the initial hand-off from acquisition of a code signal to the tracking of that code signal. As a means to allow for the detection and correction of large negative phase errors while tracking, dead-zone compensation may be added. 
         [0132]      FIG. 16  shows a Prompt correlation,  620 , an Early-Minus-Late (EML) correlation,  621 , and a “shifted EML” correlation  622  that is computed as 0.25×Prompt+EML. The EML correlation uses conventional one-half-chip early and one-half-chip late spacing and is computed as 
         [0000]        EML= ½(Early−Late) 
         [0000]    where “Early” is the correlation the code signal with a reference code signal shifted ½ chip early and “Late” is the correlation the code signal with a reference code signal shifted ½ chip late. “Prompt” is the on-time correlation of code and reference code. The ½ chip early/late spacing is not a requirement, other spacings would be permissible. 
         [0133]    An important property of the shifted EML correlation is that it crosses the x-axis at  622  which is to the right of the zero phase error point  623 . 
         [0134]    Generally, the shifted EML correlation is of the form: 
         [0000]      Shifted  EML  correlation=η×Prompt+ EML    
         [0000]    where η is a positive or negative number. 
         [0135]      FIG. 17  shows three shifted EML correlation curves  630 ,  631 , and  632  plotted as a function of code phase error. The x-axis crossing points  633 ,  634 , and  635  are controlled by the selection of the constant η. The smaller the value of η, the closer the x-axis crossing moves towards the point  636  of zero phase error. Three values of η are shown, specifically, η=0.5, η=0.3 and η=0.1. 
         [0136]    The value of η is chosen as a compromise between keeping the correlation&#39;s x-axis crossing negative, but as close to the zero code-phase error point  633  as possible, and keeping it far enough to the left of this zero point to be tolerant of multipath-induced shifts. If the crossing shifts to the right of zero, it will introduce a tracking bias when utilizing the shifted EML correlation for dead-zone compensation in a code phase tracking loop. 
         [0137]      FIG. 18A  provides various plots of a shifted EML correlation, all using η=0.25. The shifted EML correlation is shown without multipath added  640  and, for illustrative purposes, with the effects of several different multipath delays. In all cases, the amplitude of the multipath is taken as 0.4 times the amplitude of the direct signal. The shifted EML correlation  640 , having been produced without multipath added, is shown to cross the x-axis to the left of zero code-phase error,  643 , as do all the other correlations for which multipath has been added. All shifted EML correlations are seen to cross the x-axis within the circle  641 , and all thus experience negative x-axis crossings as desired. Notice that the correlation  642  crosses the x-axis the left of the shifted EML correlation  640 , while all other correlations cross to the right. This is a consequence of the fact that the correlation  642  corresponds to multipath having a sign that is opposite to the direct signal while the remaining correlations are for multipath of the same sign. 
         [0138]    The shifted EML correlation may be used as dead-zone compensation for the mass-balance phase-discriminator disclosed here. With such compensation, a feedback control loop can remove code-phase errors that reside in the zero region  372  of  FIG. 8B , whereas, with just the non-compensated mass-balance discriminator, the feedback control loop could not remove such code-phase errors. 
         [0139]    The dead-zone compensation is performed by adding the negative portion of the shifted EML correlation to the mass-balance phase-discriminator. More specifically first compute the shifted EML correlation, and if negative, add it to the mass-balance phase-discriminator. This compensation effectively removes the zero-region on the left of the mass-balance discriminator, but does not affect the zero-crossing of the mass-balance discriminator. By design, the shifted EML correlation is tolerant of certain levels of multipath in the sense that, when added to the mass-balance discriminator, it will not alter the zero-crossing for multipath meeting the design conditions. 
         [0140]    Referring to  FIG. 18B , we see the mass-balance phase-discriminator  653  as well as the negative portion of the shifted EML  650 . Additional shifted EML correlations are shown having distortions caused by multipath added to the direct signal as was presented in  FIG. 14A . In spite of the multipath-induced distortions, all x-axis crossings  651  remain negative. Consequently, adding the negative portion of the shifted EML  650  to the mass-balance discriminator  653  will effectively result in a new discriminator that maintains its zero-crossing  652  at zero phase error, even in the presence of certain multipath. As mentioned, the benefit of this new discriminator is that negative phase errors of relatively large magnitude (less than a chip) can be detected and thus corrected, whereas with the original mass-balance phase-discriminator they could not. 
         [0141]    The mass-balance correlative-phase-discriminator, compensated for dead zone, can be computed with the following simple steps:
       1. Compute the mass-balance correlative-phase-discriminator.   2. Compute the shifted EML correlation=η×Prompt+EML.   3. If the shifted EML correlation is negative, add it to mass-balance correlative-phase-discriminator.       
 
         [0145]    Shifted EML&#39;s can also be utilized to contend with positive phase errors. This is accomplished by using a negative q and taking only the positive portion of the shifted EML correlation. 
         [0146]      FIG. 19A  shows left and right shifted EML correlations obtained using a positive and negative η, respectively. The left correlation curve,  660 , obtained using positive η, has utilized only the negative portion of the shifted EML correlation. The right correlation curve  661  is just the opposite—computed with a negative η and only positive portion utilized. Both right and left correlations are biased away from zero so as to remain in their respective left- and right-half planes in the presence of multipath. 
         [0147]      FIG. 19B  shows the mass-balance phase-discriminator, and  FIG. 19C  shows the results of adding this discriminator to the shifted correlations of  FIG. 19A . The result is a combined discriminator that has the benefit of canceling out multipath in a manner similar to that of the original mass-balance phase-discriminator, but having an improved measure of larger code-phase errors. Specifically, the discriminator becomes large in magnitude as phase-error becomes large in magnitude. Of particular benefit is that the dead zone of the mass-balance discriminator is eliminated or nearly eliminated. Furthermore, such a discriminator can be applied immediately following the acquisition mode of a tracking system, the feedback of such discriminator resulting in rapid pull-in of large errors by a feedback control loop. 
         [0148]    The steps corresponding to  FIG. 19A  through  FIG. 19C  are:
       1. Compute mass-balance correlative-phase-discriminator.   2. Compute a first shifted EML correlation=η×Prompt+EML.   3. If first shifted EML correlation is negative, add it to the mass-balance correlative-phase-discriminator.   4. Compute a second shifted EML correlation=−η×Prompt+EML.   5. If second shifted EML correlation is positive, add it to the mass-balance correlative-phase-discriminator.       
 
         [0154]    The method of circumventing a dead-zone in phase discriminator, or widening a pull-in region using a shifted EML can be applied to virtually any correlative-phase-discriminator in the art today, not just the mass-balance discriminators described in this patent. The method is especially relevant to those correlative-phase-discriminators that are intended to reduce multipath, and thus have reduced pull-in capability. 
         [0155]    Furthermore, there are additional techniques than may be employed to generate a shifted EML. For example, rather than adding a prompt correlation to an EML correlation, any constant can be added to an EML correlation to shift its x-axis crossing point. It is advantageous to have this constant proportional to the prompt correlation so that the location of the x-axis crossing is more-or-less invariant to signal power fluctuations. 
         [0156]    Another method to generate a shifted correlation is to simply shift in time the early and late (or early-minus-late) codes used to generate the correlation. 
         [0157]    Yet another method is to use the EML correlation without adding a signal to shift its value. Instead, assign a threshold and when the EML correlation exceeds the threshold, use the EML directly for dead-zone compensation. Otherwise do not use the EML correlation. 
         [0158]    It is to be understood that while certain embodiments and/or aspects of the inventions have been shown and described, the invention is not limited thereto and encompasses various other embodiments and aspects.