Abstract:
A receiver of signals modulated by pseudorandom noise that uses a hierarchy of delay lock loops (DLLs) to maintain code lock. Each DLL in the hierarchy produces a control signal representative of a timing mismatch between the incoming signal and an internally generated pseudorandom noise code, preferably by correlating the incoming signal with early and late instances of the code and subtracting the late correlation from the early correlation. The early correlation is advanced relative to the late correlation by successively shorter spacings in successively lower DLLs in the hierarchy. In each DLL, the control signal is transformed to a code phase signal for adjusting the timing of the code generator. In the lower DLLs, this code phase signal is compared to the delay signal of the immediately higher DLL and adjusted accordingly. This receiver combines the immunity to random noise, associated with short spacings between the early and late correlations, with the immunity to sudden receiver motion associated with long spacings. Multipath error is accounted for by extrapolating the code phase signals to zero spacing between the early and late correlations.

Description:
This is a continuation-in-part of U.S. patent application Ser. No. 09/154,033, filed Sep. 16, 1998, now U.S. Pat. No. 6,289,040. 
    
    
     FIELD AND BACKGROUND OF THE INVENTION 
     The present invention relates to receivers of signals modulated by pseudorandom noise, such as the receivers used in navigation systems, and, more particularly, to a receiver based on a hierarchy of delay lock loops to maintain code lock. 
     Radio navigation systems are used for providing geographic location and time information. Examples of these systems include the United States&#39; Global Positioning System (GPS) and the Russian Global Navigation System (GLONASS). These systems rely on satellites in orbit around the Earth. They allow the derivation of precise navigation information including three-dimensional position, velocity and time. Normally, reception of signals from at least four satellites is required for precise location determination on four dimensions (latitude, longitude, altitude and time). Once the receiver has measured the respective signal propagation delays, the range to each satellite is calculated by multiplying each delay by the speed of light. Then the location and time are found by solving a set of four equations that incorporate the measured ranges and the known locations of the satellites. The highly precise capabilities of the system are maintained by means of atomic clocks on board the satellites and by ground tracking stations which continuously monitor and correct satellite clock and orbit parameters. 
     In the GPS system, each satellite transmits two direct-sequence-coded spread spectrum signals: an L 1  signal at a carrier frequency of 1.57542 GHz and an L 2  signal at a carrier frequency of 1.2276 GHz. The L 1  signal consists of two phase-shift keyed (PSK) spread-spectrum signals modulated in phase quadrature: the P-code signal (“P” stands for “precise”) and the C/A-code signal (C/A stands for “Coarse/Acquisition”). The L 2  signal contains only the P-code signal. The P and C/A codes are repetitive pseudorandom bit sequences which are modulated onto the carriers. These bits are called “chips” in spread spectrum parlance. The clocklike nature of these codes is used by the receiver in making time delay measurements. The codes of each satellite are unique, allowing the receiver to distinguish between signals, from the various satellites, that share a common carrier frequency. Also modulated onto each carrier is a 50 bit-per-second data stream which, for each satellite, contains information about system status and satellite orbit parameters which are needed for the navigation calculations. The P-code signals are encrypted, and are intended to be decrypted only by classified users. The C/A signals are available to all users. 
     The operations performed in a GPS receiver are for the most part typical of those performed in any direct-sequency spread spectrum receiver. The spreading effect of the pseudorandom code modulation must be removed from each signal by multiplying by a time-aligned, locally generated copy of its code, in a process known as despreading. Because the appropriate time alignment, or code phase, is not known at receiver startup, it must be sought during the initial acquisition stage. Once found, proper code time-alignment, also called “code lock”, must be maintained during the tracking phase of receiver operation, as the satellites move relative to the user. 
     Once despread, each signal consists of a 50 bit-per-second PSK signal at some low frequency. This frequency is uncertain because of the Doppler shift caused by relative motion between the satellite and the user, and also because of receiver local clock error. During initial signal acquisition, the signal must be sought in a frequency range which allows for this uncertainty. Once the Doppler frequency offset is determined approximately, carrier demodulation can compensate for it by digital processing means. 
     Most of the functions described so far are performed by digital means. After high speed A/D conversion, despreading is performed using special hardware controlled by a microcontroller. The microcontroller also performs additional digital signal processing tasks, such as data detection, timing recovery and navigation. 
     One mechanism commonly used for maintaining code time-alignment is the so-called “delay-lock loop” (DLL). A DLL tracking system which correlates early, current and late versions of the locally generated pseudorandom noise code signal with the received composite signal typically is used to maintain code lock in each channel. This code lock must be maintained despite multipath propagation and despite sudden motion of the receiver. 
     The DLL, first introduced by Spilker (J. J. Spilker Jr., “GPS Structure and Performance Characteristics”, Navigation Vol. 25 No. 2 pp. 121-146 (1978)), is based on correlating the incoming signal with two time-shifted versions of the pseudorandom noise code generated at the receiver, an early version and a late version. FIG. 1 shows the ideal normalized correlation function between the incoming signal and the pseudorandom noise code. In FIG. 1, the abscissa is the time lag between the incoming signal and the receiver&#39;s code generator, in units of T C , the code chip time. When the receiver&#39;s code generator is exactly synchronized with the incoming signal, the correlation function is almost unity. When the receiver&#39;s code generator leads or lags the incoming signal by more than T c , the correlation function is almost zero. (In the GPS C/A-code signal, for example, chip “epochs” are 1023 chips long, so the correlation function is −1/1023 at leads and lags greater than T c  and 1 at perfect synchrony.) In between, the correlation function is linear. In most prior art receiver architectures, the early (E) and late (L) correlation timings differ initially by 2Δ=T c , as shown in FIG.  1 . In particular, FIG. 1 shows the timing of the early correlation and the late correlation relative to the incoming signal when the current correlation, which is actually used to despread the incoming signal, and which is performed at a time exactly halfway between the early correlation and the late correlation, is exactly synchronized with the incoming signal, i.e., at time zero. At perfect synchrony, the difference between the early correlation and the late correlation is zero. When the current correlation leads or lags perfect synchrony, the difference between the early correlation and the late correlation is as shown by the curve labeled “k=1” in FIG.  2 . This curve is produced by sliding the vertical lines labeled “E” and “L” in FIG. 1 leftward and rightward while maintaining the 2Δ=T c  spacing between the two lines, and is a plot of the difference between the length of the “E” line and the length of the “L” line as a function of the time half way between the two lines. For obvious reasons, this curve is called an “S-curve”. It provides a measure of the timing mismatch between the incoming signal and the receiver&#39;s code generator. 
     FIG. 3 is a block diagram of a coherent delay lock loop tracking system  10  of the prior art. The arrows show the direction of data flow. Pseudorandom noise code is generated by a code generator  12 . An incoming signal C(t) is multiplied by this code in a current multiplier  14 , an early multiplier  16  and a late multiplier  18 . The code input to early multiplier  16  is advanced by Δ (block  24 ) relative to the code input to current multiplier  14 . The code input to late multiplier  18  is delayed by Δ (block  26 ) relative to the code input to current multiplier  14 . The outputs of early multiplier  16 , current multiplier  14  and late multiplier  18  are low pass filtered (blocks  20 ,  21  and  22 , respectively). The outputs of low pass filters  20  and  22  are correlation signals that are subtracted (block  28 ) to produce the corresponding S-curve value. Thus, early multiplier  16  and low pass filter  20  together constitute an early correlator; similarly, late multiplier  18  and low pass filter  22  together constitute a late correlator. The S-curve value is a control signal which is transformed by a loop filter  30  to a control voltage that is proportional to the time shift that must be applied to the code generated by code generator  12  to achieve synchrony with the input signal C(t). This control voltage is applied to a VCO  32 . The output of VCO  32  is a code phase signal that drives code generator  12 . The portion of delay loop tracking system  10  that constitutes the DLL proper is bounded by dashed line  34 . 
     Loop filter  30  and VCO  32  each are characterized by one or more state variables, with the code phase itself being one of the state variables of VCO  32 . At any time, the output of loop filter  30  depends on both the input from subtraction block  28  and the instantaneous values of the state variables. The state variables themselves may be dynamic functions of time, and may be set and read externally. For example, there is a realization of loop filter  30  wherein one of the state variables is equal to the Doppler frequency shift. The facility of reading from and writing to loop filter  30  and VCO  32  is represented in FIG. 3 by a triple-headed double arrow  36 . 
     Noncoherent DLLs also are known. A noncoherent DLL is identical to DLL  34 , except that the absolute values of the outputs of low pass filters  20  and  22  are subtracted in block  28 . 
     Using a spacing 2Δ equal to T c  to generate the S-curve is known to offer a good tradeoff between immunity to random noise on the one hand, and immunity to receiver motion, on the other. It can be shown that the variance of the code phase due to random noise is proportional to Δ. The tradeoff is that a narrow spacing makes the system more susceptible to loss of lock because of sudden receiver motion. FIG. 2 shows S-curves for Δ equal to 2 −k  (k=1, 2, 3, 4 and 5). The k=1, k=2 and k=3 curves are labeled as such. Note that all five S-curves are linear, with a slope of 2/T c , in their respective intervals [−Δ,Δ]. The increased susceptibility to loss of lock associated with k&gt;1 is caused by the flat portions of the corresponding S-curves. In many prior art receiver architectures, after the signal is acquired, 2Δ is decreased below T c  to reduce the tracking error caused by random noise, but this makes the system more vulnerable to loss of lock. 
     There is thus a widely recognized need for, and it would be highly advantageous to have, a system and method for maintaining code lock, in a receiver of signals modulated by pseudorandom noise, that combines the immunity to loss of lock due to receiver motion of a DLL having a wide correlation spacing with the immunity to random noise and multipath propagation of a DLL having a narrow correlation spacing. 
     SUMMARY OF THE INVENTION 
     According to the present invention there is provided a method for tracking an incoming signal including a plurality of chips of a certain chip duration, including the steps of: (a) generating a plurality of instances of a code, the instances being ordered hierarchically, one of the instances being a first instance, such that for each of the instances other than the first instance, there is a preceding instance; (b) for each of the instances, correlating the incoming signal with the code to produce an early correlation and a late correlation, the early correlation being advanced in time relative to the late correlation by a certain multiple of the chip duration, such that, for each of the instances other than the first instance, the multiple is less than the multiple associated with the preceding instance, thereby producing a control signal representative of a timing mismatch between the incoming signal and the code; (c) for each of the instances, transforming the control signal into a code phase signal that is a function of a respective the multiple of the chip duration, the code phase signal of each of the instances other than the first instance being based both on the control signal and on the code phase signal of the preceding instance; and (d) transforming the code phase signals into a combined code phase signal by extrapolating the code phase signals to zero the multiple of the chip duration. 
     According to the present invention there is provided a method for tracking an incoming signal including a plurality of chips of a certain chip duration, including the steps of: (a) generating a plurality of instances of a code; (b) for each of the instances; correlating the incoming signal with the code to produce an early correlation and a late correlation, the early correlation being advanced in time relative to the late correlation by a certain multiple of the chip duration, thereby producing a control signal representative of a timing mismatch between the incoming signal and the code; (c) for each of the instances, transforming the control signal into a code phase signal that is a function of a respective the multiple of the chip duration; and (d) transforming the code phase signals into a combined code phase signal by extrapolating the code phase signals to zero the multiple of the chip duration. 
     According to the present invention there is provided a method for tracking an incoming signal including a plurality of chips of a certain chip duration, including the steps of: (a) generating a plurality of instances of a code, the instances being ordered hierarchically, one of the instances being a first instance, such that for each of the instances other than the first instance, there is a preceding instance; (b) for each of the instances, producing a control signal representative of a timing mismatch between the incoming signal and the code; (c) for each of the instances, transforming the control signal into a code phase signal; and (d) if the code phase signals differ from each other, transforming the code phase signals into a combined code phase signal according to a piecewise linear model of a correlation of the incoming signal with the code. 
     The present invention achieves the stated objective by using a hierarchy of DLLs, having successively narrower correlation spacings. In all the DLLs except the one with the widest correlation spacing, the code phase obtained by VCO  32  is compared with the code phase presently being used by the DLL with the next widest correlation spacing, and adjusted accordingly. Preferably, there are four DLLs in the hierarchy, with correlation spacings 2Δ of T c , T c /2, T c /4 and T c /8 respectively. 
     Fenton, in U.S. Pat. No. 5,414,729, also uses correlations of the incoming signal with several instances of the pseudorandom noise code, each instance shifted with respect to the incoming signal by a different fraction of T c , to account for multipath distortion by fitting the various correlations to a model of the multipath distortion; but the various correlations are computed independently, and the code phase associated with one correlation is not used to constrain the code phase associated with another correlation, as in the present invention. 
     The model of multipath distortion used by Fenton is rather complicated, being parametrized by relative time delays and relative phases of a plurality of multipath signals. The scope of the present invention includes a much simpler method of accounting for multipath distortion, inspired by a simple piecewise linear model of the correlation function which is not parametrized explicitly in terms of the parameters of the multipath signals. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is herein described, by way of example only, with reference to the accompanying drawings, wherein: 
     FIG. 1 is a plot of the correlation function between an incoming signal and pseudorandom noise code; 
     FIG. 2 is a plot of S-curves corresponding to the correlation function of FIG. 1; 
     FIG. 3 is a block diagram of a prior art delay lock loop; 
     FIG. 4 is a high level block diagram of a hierarchical DLL tracking system of the present invention; 
     FIG. 5 illustrates the motivation of the preferred algorithm of the present invention; 
     FIG. 6 illustrates the cause of multipath error; 
     FIG. 7 illustrates the piecewise linear model of a correlation function between an incoming signal and pseudorandom noise code in the presence of multipath error 
     FIG. 8 is a high level block diagram of another hierarchical DLL tracking system of the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention is of a receiver, of signals modulated by pseudorandom noise, which is more immune to various sources of error than similar prior art receivers. Specifically, the present invention can be used as a navigational receiver, for example in the GPS navigation system. 
     The principles and operation of a navigational receiver according to the present invention may be better understood with reference to the drawings and the accompanying description. 
     Referring again to the drawings, FIG. 4 is a high level block diagram of a hierarchical DLL tracking system  40  of the present invention, including four DLLs  44 ,  46 ,  48  and  50 . Each DLL is labeled by its half correlation spacing Δ k : in DLL  44 , Δ 0 , which typically is T c /2; in DLL  46 , Δ 1 &lt;Δ 0 ; in DLL  48 , Δ 2 &lt;Δ 1 ; and in DLL  50 , Δ 3 &lt;Δ 2 . The inputs to all four DLLs is the incoming signal C(t). Each of DLLs  44 ,  46 ,  48  and  50  is essentially identical to DLL  34  of FIG. 3, including facilities, represented by the double-headed arrows labeled “s 0 ”, “s 1 ”, “s 2  ” and “s 3 ”, for exchanging state variables S k  with a logic block  60 . Logic block  60  also receives, from DLLs  44 ,  46 ,  48  and  50 , signals d k  representative of the code phases that must be applied to the code generated by code generators  12  to achieve synchrony with input signal C(t). In the simplest implementation of tracking system  40 , the signals d k  are the code phases themselves from VCO  32 . The arrow labeled “d 0 ” is single-headed, to indicate that code phase signal do is only output from DLL  44 . The arrows labeled “d 1 ”, “d 2 ” and “d 3 ” are double-headed, to indicate that for each k&gt;0, logic block  60  compares code phase signal d k  with code phase signal d k−1  and adjusts d k  accordingly. 
     FIG. 4 shows the output of code generator  12  of DLL  44  being input to current multiplier  14  for despreading the incoming signal C(t). The output of code generator  12  of any one of DLLs  44 ,  46 ,  48  and  50  may be used for despreading. Using the output of code generator  12  of a DLL with a wide Δ k  for despreading gives relative resistance to loss of code lock. Using the output of code generator  12  of a DLL with a narrow Δ k  for despreading gives relative resistance to random noise. 
     FIGS. 5A and 5B illustrate the motivation of the preferred algorithm for adjusting code phase signals d k , k&gt;0, on the basis of d k−1 . The principal behind the algorithm is that the correlation function between the incoming signal and the pseudorandom noise code has to be a single-valued function. Because of systematic effects such as multipath propagation, real correlation functions are not symmetric, like the ideal correlation function of FIG. 1, but are asymmetric, as shown in FIG.  5 A. When DLL  44  has converged to code lock, the early and late correlators of DLL  44  produce identical correlations, so the corresponding points on the correlation function are those labeled “E” and “L” at the two ends of horizontal line  130 , spaced 2Δ 0 =T c  apart. Similarly, when DLL  46  has converged to code lock, the early and late correlators of DLL  46  produce identical correlations, so the corresponding points on the correlation function are those labeled “E” and “L” at the two ends of horizontal line  132 , spaced 2Δ 1 &lt;T c  apart. The code phase signal d 0  output by DLL  44  corresponds to the projection  134  onto the abscissa (time axis) of the midpoint of line  130 . The code phase signal d 1  output by DLL  46  corresponds to the projection  136  onto the abscissa of the midpoint of line  132 . Because line  132  is shorter than line  130  and the correlation function is single valued, code phases  134  and  136  must differ by less than Δ 0 −Δ 1 . For code phases  134  and  136  to differ by more than Δ 0 −Δ 1 , the correlation function must be multivalued, as shown in FIG. 5B, which is mathematically impossible. 
     Therefore, the code phase signals are adjusted as follows. In a transparent change of notation, let d k  represent the k-th code phase itself, for the k-th DLL of the hierarchy, rather than a signal representative of the k-th code phase. Let s k  represent the k-th set of state variables. The algorithm is as follows: 
     IF (d k −d k−1 &gt;Δ k−1 −Δ k ) THEN 
     d k :=d k−1 +(Δ k−1 −Δ k ) 
     s k :=s k−1    
     ELSE IF (d k −d k−1 &lt;Δ k Δ k−1 ) THEN 
     d k :=d k−1 −(Δ k−1 −Δ k ) 
     s k :=s k−1    
     ELSE 
     (leave d k  and S k  unchanged) 
     END IF 
     The notation “:=” means replacement. If d k  is so different from d k−1  that such a difference is mathematically impossible, it is assumed that the k-th DLL has lost code lock, and d k  is replaced by the extreme value permitted mathematically on the basis of d k−1 . If d k  is unreliable, S k  is presumed to also be unreliable, and is replaced by S k−1 . 
     In the presence of multipath signals whose delays, relative to the direct signal, are less than 2T c , the correlation function between the total incoming signal and the pseudorandom noise code is not symmetrical as shown in FIG. 1, but is asymmetrical. This phenomenon is illustrated in FIG. 6, which shows the ideal normalized correlation function (dashed) of the direct signal with the pseudorandom noise code, the ideal correlation function (dotted) of a multipath signal, half as strong as the direct signal and delayed by T c /2, with the pseudorandom noise code, and the total correlation function (solid), which is the sum of the dashed and dotted curves. Although the separate correlation functions of the direct signal and the multipath signal with the pseudorandom noise code are symmetrical, their sum is not symmetrical. The fact that the slopes of segments AB and BC of the total correlation function do not have the same magnitudes implies that when a DLL with a half-correlation spacing Δ k  less than T c /3 (half the spacing between points A and C) converges to code lock, the code phase signal d k  output by this DLL is greater than zero. Note that the slopes of segments AB and CD of the total correlation function have opposite signs but identical magnitudes, so that the code phase signals output by DLLs with half-correlation spacing between T c /3 and 2T c /3 (half the spacing between point A and point E along segment CD where the total correlation function has a value of 0.5) all are identical. This suggests the simple piecewise linear model of the total correlation function that is shown in FIG.  7 . This model has three segments: a left segment FG, a middle segment GH and a right segment HI. Segments FG and HI have slopes that are equal in magnitude and opposite in sign. The slope of segment GH has the same sign as, and a lower magnitude than, the slope of segment HI. A horizontal line projected leftward from point H intersects segment FG at point J. The base of triangle GHJ, line segment JH, has a length 2L. As a result, although point G is at the arrival time T 0  of the direct signal, a DLL whose half-correlation spacing Δ is less than or equal to L produces an estimate T (the code phase signal of the DLL after convergence to code lock) of the arrival time of the direct signal such that the deviation of T from T 0  is a linear function of Δ: 
     
       
         
           T=T 
           0 
           +mΔ 
         
       
     
     and which lies on the line segment GP; and a DLL whose half-correlation spacing Δ is greater than or equal to L produces an estimate T of the arrival time of the direct signal that lies on the vertical line segment PQ. 
     Consider, now, a hierarchical tracking system of the present invention that has K DLLs, with Δ K  and Δ K−1 =2Δ K  both less than L. The estimate of T 0  produced by DLL K is 
     
       
         
           T 
           K 
           =T 
           0 
           +mΔ 
           K 
         
       
     
     The estimate of T 0  produced by DLL K−1 is 
     
       
           T   K−1   =T   0   +mΔ   K−1   =T   0 +2 mΔ   K   
       
     
     Simple algebra produces 
     
       
           T   0 =2 T   K−   T   K−1   
       
     
     Therefore, according to the present invention, the corrected estimate used for T 0  is 2T K −T K−1 , where T K  is the estimate of T 0  obtained from the DLL with the shortest half-correlation spacing, and T K−1  is the estimate of T 0  obtained from the DLL with the next shortest half-correlation spacing. 
     According to the piecewise linear model of FIG. 7, if both Δ K  and Δ K−1  are less than or equal to L, then the estimate T 0 =2T K −T K−1  is accurate. If Δ K  is less than L but Δ K−1  is greater than L, then this estimate is inaccurate by less than L. If both Δ K  and Δ K−1  are greater than L, then this estimate, being on line segment PQ, is inaccurate by the displacement of line segment PQ rightward from T 0 . Thus, according to the piecewise linear model of FIG. 7, the error in the estimate of T 0  provided by the present invention is strictly bounded from above. 
     Of course, the piecewise linear model of FIG. 7 is a gross oversimplification of the total correlation function. The model of FIG. 7 does not even capture the features of the correlation function of FIG. 6 that lie to the left of point A or to the right of point D. The total correlation function of FIG. 6 is itself a simplification of reality. Real total correlation functions are band-limited, and so do not have sharp corners. Furthermore, real total correlation functions are likely to include the effects of several multipath signals. 
     Therefore, in the most preferred embodiment of the present invention, the values of T k  produced by several DLLs, each with its own half-correlation spacing Δ k , are extrapolated to Δ=0 to obtain the corrected estimate of T 0 . Using two values of T k  from two DLLs, T(Δ) is modeled as a linear function of Δ, as described above. Using more than two values of T k  from more than two DLLs, T(Δ) is modeled as a nonlinear function of Δ. The simplest such nonlinear function is a polynomial:          T        (   Δ   )       =       ∑     j   =   0     J            a   j          Δ   j                                
     Using K different DLLs (J=K−1) to produce K different values of T k  corresponding to K different half-correlation spacings Δ k  (k=1, . . . K) gives K equations in K unknowns:          T   k     =       T        (     Δ   k     )       =       ∑     j   =   0     J            a   j          Δ   k   j                                  
     These K equations are solved for the K unknown coefficients {a j }, and a 0  is the desired estimate of T 0 . 
     FIG. 8 is a high level block diagram of a hierarchical DLL tracking system  40 ′ of the present invention. DLL tracking system  40 ′ is similar to DLL tracking system  40 , and like reference numerals in FIGS. 4 and 8 refer to like components of the two tracking systems. DLL tracking system  40 ′ is modified from DLL tracking system  40  to account for multipath distortions of the total correlation function. The difference between tracking system  40  and tracking system  40 ′ is that instead of using the output of a code generator  12  of one of the four DLLs  44 ,  46 ,  48  or  50  to despread the incoming signal C(t), DLL tracking system  40 ′ extrapolates the code phase signals d k  of DLLs  44 ,  46 ,  48  and  50  to zero correlation spacing, as described above, and uses the extrapolated code phase signal {circumflex over (d)} to drive a separate code generator  12 ′, with the output of code generator  12 ′ being used to despread the incoming signal C(t). 
     It is to be understood that the receiver of the present invention includes more components than are described herein. The discussion herein focuses on the components needed for code tracking. All the other components of a receiver of the present invention, for example, the front end that acquires and demodulates the incoming signal to produce input signal C(t), and the navigational back end that uses the output of the DLL hierarchy of the present invention, are substantially identical to their counterparts in prior art receivers. It will be obvious to one ordinarily skilled in the art how to interpolate the DLL hierarchy of the present invention into a conventional navigational receiver. 
     While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made.