Methods and apparatuses for reducing multipath errors in the demodulation of pseudo-random coded signals

• US 6,493,378 B1
• Filed: 01/06/1999
• Issued: 12/10/2002
• Est. Priority Date: 01/06/1998
• Status: Expired due to Term

• Current Assignee: Topcon GPS, LLC
• Original Assignee: Topcon GPS, LLC
• Inventors: Zhodzishsky, Mark Isaakovich, Ashjaee, Javad, Veitsel, Victor Abramovich
• Primary Examiner(s): Chin, Stephen
• Assistant Examiner(s): Kim, Kevin
• Application Number:
  US09/226,774
• Time in Patent Office: 1,434 Days
• Field of Search: 375/149, 375/150, 375/362, 375/368, 375/371, 375/373, 375/343
• US Class Current: 375/149
• CPC Class Codes: G01S 19/22 Multipath-related issues
• CPC Class Codes: H04B 1/7085 using a code tracking loop, e.g. a delay-locked loop
• CPC Class Codes: H04B 1/709 Correlator structure
• CPC Class Codes: H04B 2201/70715 with application-specific features

Abstract

The present application is applicable to receivers for Global Positions (GP) systems which use delay-lock loops (DLLs) and, optionally, phase-lock loops (PLLs). The application discloses multipath error reduction techniques which enable the multipath errors in DLL systems to be made much less than the error present in known narrow “early-late” correlators, or their corresponding implementations which use strobe representations of the PR-code. Also disclosed are multipath error reduction techniques that enable multipath errors in the PLL systems to be reduced. The techniques, when applied to both the DLL and PLL systems work synergistically to further reduce multipath errors.

Claims

1. A method of tracking an input code signal comprising a repeating sequence of chips, each chip having a time duration Δ

and a value determined by a preselected series of numbers, each chip in the sequence corresponding to a respective number in the series, said method comprising the steps of;

(a) generating a reference code signal (S(t)) comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration of less than Δ and

having a non-zero average value over its duration, the average values of said strobes being related to the preselected series of numbers, said reference code signal being generated such that the start of its strobe sequence may be adjusted in time with an adjustable time shift ε

from the start of the sequence of the input code signal, the value of said time shift ε

having a first polarity when the sequence start of the reference code signal leads the sequence start of the input code signal and a second polarity opposite to said first polarity when the sequence start of the reference code signal lags the sequence start of the input code signal, said time shift ε

moving in a leading direction when the sequence start of the reference code is advanced in time and moving in a lagging direction when the sequence start of the reference code is retarded in time;

(b) generating a correlation signal (dI) related to the correlation of the input code signal and said reference code signal, the value of said correlation signal being a function of said time shift ε and

being equal to zero when said time shift ε

is at a point ε

₀, the value of said correlation signal having a first polarity when said time shift ε

moves in the leading direction away from said point ε

₀ and a second polarity opposite to said first polarity when said time shift ε

moves in the lagging direction away from said point e₀, said correlation signal further having a first peak value (dI_E) when said time shift ε

moves in the leading direction away from said point ε

₀ and having a second peak value (dI_L) when said time shift ε

moves in the lagging direction away from said point ε

₀, the second peak value (dI_L) being greater than the first peak value (dI_E); and

(c) adjusting said time shift ε

in response to the value of said correlation signal to move said time shift ε

towards said point ε

₀, said correlation signal indicating that said time shift ε

should be advanced when the value of the correlation signal has its second polarity and indicating that said time shift ε

should be retarded when the value of the correlation signal has its first polarity, said point ε

₀ thereby being a point of steady balance and the generation of said reference code signal thereby tracking the input code signal by being adjusted toward maintaining a constant time shift between the sequence starts of the two code signals.

2. The method of claim 1 wherein the preselected series of numbers comprises a pseudo-random code sequence, and wherein each number in the series is either −

1 or +1.

3. The method of claim 1 wherein the magnitude of the second peak value (dI_L) is at least five times the magnitude of the first peak value (dI_E)(|dI_L|≧

|5dI_E|).

4. The method of claim 1 wherein the magnitude of the second peak value (dI_L) is between five times and ten times the magnitude of the first peak value (dI_E).

5. The method of claim 1 wherein each strobe of said reference code signal comprises a first pulse and a second pulse, said second pulse following said first pulse in time;

wherein each said pulse has a value, a time duration, and a time-integrated magnitude (area) which is the integral of the pulse'"'"'s absolute value during the pulse'"'"'s time duration;

wherein the second pulse in each strobe has a value which is opposite in polarity to that of the first pulse in the strobe; and

wherein the time-integrated magnitudes of the first and second pulses in each said strobe are different.

6. The method of claim 5 further comprising the step of selecting the time-integrated magnitudes of the first and second pulses of said strobes such that the magnitude of the second peak value (dI_L) of said correlation signal is at least five times the magnitude of the first peak value of said correlation signal (dI_E)(|dI_L|≧

|5dI_E|).

7. The method of claim 5 further comprising the step of selecting the time-integrated magnitude of one pulse in at least one said strobe to have a magnitude which is at least two times the time-integrated magnitude of the other pulse in said strobe.

8. The method of claim 7 further comprising the step of selecting the time-integrated magnitude of one pulse in at least one said strobe to have a magnitude which is between four times and eight times the time-integrated magnitude of the other pulse in said strobe.

9. The method of claim 1 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being equal to or less than one chip duration Δ

;

wherein said first peak value (dI_E) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the leading direction from point ε

₀;

wherein said second peak value (dI_L) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the lagging direction from point ε

₀;

wherein said correlation signal changes from said first peak value (dI_E) to said second peak value (dI_L) in a time shift distance of one duration F to three durations F (3*F).

10. The method of claim 1 wherein said step (a) of generating said reference code signal comprises the step of generating said reference code signal as a discrete-time signal which is provided at periodic intervals spaced from one another in time by a time duration T, and

wherein said step (b) of generating said correlation signal comprises the step of digitizing the input code signal at periodic intervals spaced from one another in time by said time duration T.

11. The method of claim 10 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

;

wherein said first peak value (dI_E) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the leading direction from point ε

₀;

wherein said second peak value (dI_L) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the lagging direction from point ε

₀;

wherein said correlation signal changes from said first peak value (dI_E) to said second peak value (dI_L) in a time shift distance of one front duration F to three front durations F (3*F).

12. The method of claim 1 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M,

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulate by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

; and

wherein the time-shift distance from ε

=0 to said point ε

₀ is not more than twice the value of said duration F.

13. The method of claim 10 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M,

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

; and

wherein the time-shift distance from ε

=0 to said point ε

₀ is not more than twice the value of said duration F.

14. The method of claim 1 wherein, when the sequence start of the first reference code signal is aligned to the sequence start of the input code signal, the reference code signal (S(t)=S_P1(t)) has a strobe corresponding to each chip of the input code signal for which that chip has changed in value from the previous chip'"'"'s value.

15. The method of claim 1 wherein, when the sequence start of the first reference code signal is aligned to the sequence start of the input code signal, the reference code signal (S(t)=S_D(t)) has a strobe corresponding to each chip of the input code signal, each said strobe comprising a pulse in which the time-integrated magnitude of the pulse depends upon whether the corresponding chip in the input code signal has changed in value from the previous chip'"'"'s value.

16. The method of claim 1 comprising the step of initially setting the time shift ε

at a point which lags the point ε

₀ of steady balance before commencing the performance of step (c) of adjusting the time shift ε

.

17. A method of tracking an input code signal comprising a repeating sequence of chips, each chip having a time duration Δ

and a value determined by a preselected series of numbers, each chip in the sequence corresponding to a respective number in the series, said method comprising the steps of;

(a) generating a reference code signal (S(t)) comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration of less than Δ and

having a non-zero average value over its duration, the average values of said strobes being related to the preselected series of numbers, said reference code signal being generated such that the start of its strobe sequence may be adjusted in time with an adjustable time shift ε

from the start of the sequence of the input code signal, the value of said time shift ε

having a first polarity when the sequence start of the reference code signal leads the sequence start of the input code signal and a second polarity opposite to said first polarity when the sequence start of the reference code signal lags the sequence start of the input code signal, said time shift ε

moving in a leading direction when the sequence start of the reference code is advanced in time and moving in a lagging direction when the sequence start of the reference code is retarded in time;

(b) generating a correlation signal (dI) related to the correlation of the input code signal and said reference code signal, the value of said correlation signal being a function of said time shift ε and

being equal to zero when said time shift ε

is at a point ε

₀, said correlation signal having a first portion when said time shift ε

moves away from said point ε

₀ in the leading direction and a second portion when said time shift ε

moves away from said point ε

₀ in the lagging direction, the value of said correlation signal having a first polarity in said first portion and a second polarity in the second portion which is opposite to said first polarity, the value of said correlation signal further having a first peak value (dI_E) in said first portion and a first range (L_E) which includes values of the correlation signal which have said first polarity and whose magnitudes are at least 5% of the magnitude of the first peak value (dI_E), and further having a second peak value (dI_L) in said second portion and a second range (L_L) which includes values of the correlation signal which have said second polarity and whose magnitudes are at least 5% of the magnitude of the second peak value (dI_L), said second range (L_L) being greater than said first range (L_E); and

(c) adjusting said time shift ε

in response to the value of said correlation signal to move said time shift ε

towards said point ε

₀, said correlation signal indicating that said time shift ε

should be advanced when the value of the correlation signal has its second polarity and indicating that said time shift ε

should be retarded when the value of the correlation signal has its first polarity, said point ε

₀ thereby being a point of steady balance and the generation of said reference code signal thereby tracking the input code signal by being adjusted toward maintaining a constant time shift between the sequence starts of the two code signals.

18. The method of claim 17 wherein said second range (L_L) is at least four times greater than said first range (L_E).

19. The method of claim 17 wherein said first range (L_E) is less than 20% of a chip time duration Δ

.

20. The method of claim 17 wherein said second range (L_E) is greater than 50% of a chip time duration Δ

.

21. The method of claim 17 wherein said step (a) of generating said reference code signal comprises the step of generating said reference code signal as a discrete-time signal which is provided at periodic intervals spaced from one another in time by a time duration T, and

wherein said step (b) of generating said correlation signal comprises the step of digitizing the input code signal at periodic intervals spaced from one another in time by said time duration T.

22. The method of claim 21 wherein said first range (L_E) is not more than four front durations F (4*F) in time shift distance.

23. The method of claim 21 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

;

wherein said first peak value (dI_E) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the leading direction from point ε

₀;

wherein said second peak value (dI_L) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the lagging direction from point ε

₀;

wherein said correlation signal changes from said first peak value (dI_E) to said second peak value (dI_L) in a time shift distance of not more than five front duration F (5*F).

24. The method of claim 17 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

;

wherein said first peak value (dI_E) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the leading direction from point ε

₀;

wherein said second peak value (dI_L) occurs when the slope of the correlation signal (dI) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the lagging direction from point ε

₀;

wherein said correlation signal changes from said first peak value (dI_E) to said second peak value (dI_L) in a time shift distance of not more than five front duration F (5*F).

25. A method of tracking an input code signal comprising a repeating sequence of chips, each chip having a time duration Δ

and a value determined by a preselected series of numbers, each chip in the sequence corresponding to a respective number in the series, said method comprising the steps of;

(a) generating a reference code signal (S(t)) comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration of less than Δ and

having an average value over its duration, the average values of said strobes being related to the preselected series of numbers, a plurality of said strobes having an asymmetric shape, each said asymmetric strobe comprising a first pulse and a second pulse which follows said first pulse in time, each said pulse having a value, a time duration, and a time-integrated magnitude (area) which is the integral of the pulse'"'"'s absolute value during the pulse'"'"'s time duration, said first and second pulses of each asymmetric strobe having opposite polarities and different time-integrated magnitudes, said reference code signal being generated such that the start of its strobe sequence may be adjusted in time with an adjustable time shift ε

from the start of the sequence of the input code signal, the value of said time shift ε

having a first polarity when the sequence start of the reference code signal leads the sequence start of the input code signal and a second polarity opposite to said first polarity when the sequence start of the reference code signal lags the sequence start of the input code signal, said time shift ε

moving in a leading direction when the sequence start of the reference code is advanced in time and moving in a lagging direction when the sequence start of the reference code is retarded in time;

(b) correlating the input code signal and said reference code signal to generate a correlation signal (dI), the value of said correlation signal being a function of said time shift ε and

being equal to zero when said time shift ε

is at a point ε

₀, the value of said correlation signal having a first polarity when the sequence start of the reference code signal moves in the leading direction away from the time shift value ε

₀ and a second polarity opposite to said first polarity when said sequence start moves in the lagging direction away from the time shift value ε

₀; and

(c) adjusting said time shift ε

in response to the value of said correlation signal to move said time shift ε

towards said point ε

₀, said correlation signal indicating that said time shift ε

should be advanced when the value of the correlation signal has its second polarity and indicating that said time shift ε

should be retarded when the value of the correlation signal has its first polarity, said point ε

₀ thereby being a point of steady balance and the generation of said reference code signal thereby tracking the input code signal by being adjusted toward maintaining a constant time shift between the sequence starts of the two code signals.

26. The method of claim 25 wherein the preselected series of numbers comprises a pseudo-random sequence of numeric values, the numeric values being selected from the group of −

1 and +1.

27. The method of claim 25 further comprising the step of selecting the time-integrated magnitude of one pulse in at least one of said asymmetric strobes to have a magnitude which is at least two times the time-integrated magnitude of the other pulse in said asymmetric strobe.

28. The method of claim 25 further comprising the step of selecting the time-integrated magnitude of one pulse in at least one of said asymmetric strobes to have a magnitude which is between two times and four times the time-integrated magnitude of the other pulse in said asymmetric strobe.

29. The method of claim 25 further comprising the step of selecting the time duration of one pulse in at least one of said asymmetric strobes to be at least twice as long as the time duration of the other pulse in said asymmetric strobe.

30. The method of claim 25 further comprising the step of selecting the time duration of the first pulse in at least one of said asymmetric strobes to be at least twice as long as the time duration of the second pulse in said asymmetric strobe.

31. The method of claim 25 further comprising the step of selecting the value of one pulse in at least one of said asymmetric strobes has a magnitude which is at least twice as large as the magnitude of the other pulse in said asymmetric strobe.

32. The method of claim 25 further comprising the step of selecting the value of the first pulse in at least one of said asymmetric strobes has a magnitude which is at least twice as large as the magnitude of the second pulse in said asymmetric strobe.

33. The method of claim 25 wherein said step (a) of generating said reference code signal comprises the step of generating said reference code signal as a discrete-time signal which is provided at periodic intervals spaced from one another in time by a time duration T, and

wherein said step (b) of correlating the input code signal and said reference code signal comprises the step of digitizing the input code signal at periodic intervals spaced from one another in time by said time duration T.

34. The method of claim 33 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

;

wherein the duration of each of said first and second pulses in said asymmetric strobes is not more than three front durations F.

35. The method of claim 33 wherein a plurality of said asymmetric strobes have a first pulse which has a time duration of not more than three front durations and a second pulse which has a time duration of not more than two front durations F.

36. A method of tracking an input carrier signal which is modulated by an input code signal, said input code signal comprising a repeating sequence of chips, each chip having a time duration Δ

and a value determined by a preselected series of numbers, each chip in the sequence corresponding to a respective number in the series, said method comprising the steps of;

(a) generating a reference carrier signal such that its phase may be adjusted, the difference in the phases between the input carrier signal and said reference carrier signal being indicated by a difference φ

_P;

(b) frequency down-converting the modulated input carrier signal using said reference carrier signal to generate an in-phase baseband code signal representative of the input code signal and a quadrature baseband code signal representative of the input code signal;

(c) generating a first reference code signal (S(t)) comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration of less than the chip duration Δ and

comprising at least a first pulse, the values of said first pulses being related to the preselected series of numbers, said first reference code signal being generated such that the start of its strobe sequence may be adjusted in time with an adjustable time shift ε

from the start of the sequence of the input code signal;

(d) generating a second reference code signal (S₂(t−

ε

_S)) comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration of less than the chip duration Δ and

comprising at least a pulse, the values of said pulses being related to the preselected series of numbers, said second reference code signal being generated such that its sequence start is displaced from the sequence start of the first reference code signal by a time offset ε

, the magnitude of said time offset ε

_S being between zero and one chip duration Δ

;

(e) generating a first correlation signal (dI) related to the correlation of the in-phase baseband code signal and said first reference code signal, the value of said first correlation signal being a function of said time shift ε

;

(f) adjusting said time shift ε

to move it toward a predetermined point ε

₀ of steady balance by advancing or retarding the generation of the first and second reference code signals in time based on the value of said first correlation signal;

(g) generating a second correlation signal (dQ) related to the correlation of the quadrature baseband code signal and said second reference code signal, the value of said second correlation signal being a function of said time shift ε and

said phase difference φ

_P, said second correlation signal having a value which varies in relation to the quantity sin(φ

_P), said second correlation signal further having a non-zero value dQ₀ when said time shift ε

is at said predetermined point ε

₀ and said phase difference φ

_P is at a value of (K+½

)π

for any integer K, the magnitude of said second correlation signal decreasing from the magnitude of dQ₀ by a first incremental amount when said time shift ε

is advanced from said predetermined point ε

₀ by an amount of 0.1Δ and

changing by a second incremental amount when said time shift ε

is retarded from said point ε

₀ by an amount of 0.1Δ

, said first incremental amount being larger than said second incremental amount; and

(h) adjusting the phase of said reference carrier signal based on the value of said second correlation signal to cause said phase difference φ

_P to move toward a value of zero.

37. The method of claim 36 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

;

wherein said second correlation signal (dQ) has, when said phase difference φ

_P is at a value of (K+½

)π

, a peak value dQ_MAX at time shift ε

value different from said point ε

₀, wherein the magnitude of dQ₀ is at least 70% of the magnitude of dQ_MAX, and wherein the magnitude of said second correlation signal decreases from the magnitude of dQ₀ to less than 10% of the magnitude of dQ_MAX when said time shift ε

is advanced from said point ε

₀ by an amount of duration F.

38. The method of claim 37 wherein the magnitude of dQ₀ is not more than 90% of the magnitude of dQ_MAX.

39. The method of claim 36 wherein said step (d) of generating said second reference code signal comprises the step of generating said second reference code signal as a discrete-time signal which is provided at periodic intervals spaced from one another in time by a time duration T,

wherein said step (g) of generating said correlation signal comprises the step of digitizing the input code signal at periodic intervals spaced from one another in time by said time duration T.

40. The method of claim 39 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have corresponding values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

;

wherein said second correlation signal (dQ) has a peak value dQ_MAX which occurs when the slope of the second correlation signal (dQ) with respect to the time shift value ε

first reaches zero as the time shift value ε

moves in the lagging direction from point ε

₀;

wherein the magnitude of dQ₀ is at least 70% of the magnitude of dQ_MAX; and

wherein the magnitude of said second correlation signal decreases from the magnitude of dQ₀ to less than 10% of the magnitude of dQ_MAX when said time shift ε

is advanced from said point ε

₀ by an amount of not more than five front durations F (5F).

41. The method of claim 36 wherein each of the pulses of said second reference code signal comprises a rectangular shape and has a duration “

d”

of less than the chip duration Δ

, and

wherein said second reference code signal is generated such that the start of each of its pulses is displaced in time from a respective strobe of said first reference code signal by said time offset ε

_S; and

wherein said time offset ε

_S is constant.

42. The method of claim 41 where the step (g) of generating said second correlation signal comprises the step of selecting the values of ε

_S and d to provide the values of dQ₀, the first incremental amount, and the second incremental amount.

43. The method of claim 41 wherein each number in the preselected series of numbers is either −

1 or +1 and wherein the values of corresponding chips of said input code signal have values of either −

M or +M;

wherein the input code signal is generated by the step of receiving a broadcasted satellite signal at an antenna, said broadcast satellite signal comprising a carrier signal which is modulated by code signal which comprises a repeating sequence chips whose values are based upon said preselected series of numbers, and further by the step of demodulating the received satellite signal to produce said input code signal;

wherein the input code signal has a transition period F in which it changes value between adjacent chips having different values, said duration F being less than one chip duration Δ

; and

wherein the value of d is between F/2 and 2F.

44. The method of claim 36 wherein, when the sequence start of the second reference code signal (S₂(t)) is aligned to the sequence start of the input code signal, the reference code signal has a strobe corresponding to each chip of the input code signal for which that chip has changed in value from the previous chip'"'"'s value.

45. A method of tracking an input code signal, said input code signal comprising a repeating sequence of chips, each chip having a time duration Δ

and a value determined by a preselected series of numbers, each chip in the sequence corresponding to a respective number in the series, said method comprising the steps of;

(a) generating a reference code signal (S_A(t) or S_B(t)) comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration equal to or less than the chip duration Δ and

comprising at least a first pulse, the values of said first pulses being related to the preselected series of numbers, said first reference code signal being generated such that the start of its strobe sequence may be adjusted in time with an adjustable time shift ε

from the start of the sequence of the input code signal, the value of said time shift ε

having a first polarity when the sequence start of the first reference code signal leads the sequence start of the input code signal and a second polarity opposite to said first polarity when the sequence start of the first reference code signal lags the sequence start of the input code signal, said time shift ε

moving in a leading direction when the sequence start of the first reference code signal is advanced in time and moving in a lagging direction when the sequence start of the first reference code signal is retarded in time;

(b) generating a first correlation signal (dI₁) related to the correlation of the input code signal and said first reference code signal, said first correlation signal having a value which is a function of said time shift ε

, said first correlation signal further having a first range of values in said time shift ε

between a first point ε

_A and a second point ε

_B where the signal'"'"'s value is non-zero and a second range of values in said time shift ε

between said first point ε

_A and a third point ε

_C where the signal'"'"'s value is zero, said first correlation signal further having a point ε

₀ within said first range where the signal'"'"'s value is non-zero and has a non-zero rate of change with respect to a change in said time shift ε

away from said point ε

₀ in each of the leading and lagging directions, said second range being adjacent to said first range such that said time shift ε

is advanced to move from said point ε

₀ to a point within the second range;

(c) generating a control signal (Ed or Ed′

) from said first correlation signal, said control signal having a value which is a function of said time shift ε

, said value being zero at said point ε

₀ and having a non-zero rate of change at said point ε

₀ with respect to a change in said time shift ε

away from said point ε

₀ in each of the leading and lagging directions, the value of said control signal having a first polarity when said time shift ε

moves in the leading direction away from said point ε

₀ and a second polarity opposite to said first polarity when said time shift ε

moves in the lagging direction away from said point ε

₀; and

(d) adjusting said time shift ε

to move it toward said point ε

₀ by advancing the generation of the first reference code signal in time when the value of the control signal has its second polarity and retarding the generation of the first reference code signal in time when the value of the control signal has its first polarity, said point ε

₀ thereby being a point of steady balance and the generation of said first reference code signal thereby tracking the input code signal by being adjusted toward maintaining a constant time shift between the sequence starts of the two code signals.

46. The method of claim 45 wherein first correlation signal (dL₁) has a non-zero rate of change with respect to said time shift ε

in the range between said first point ε

_A and said second point ε

_A, and has a zero rate of change at said second point ε

_B where it reaches a peak magnitude value of dI_MAX, and wherein said step (c) of generating said control signal (Ed) comprises the steps of;

(d) generating a normalized version (e.g., K*dI₁) of said first correlation signal which has a normalized peak magnitude value of dI_NORM when said first correlation signal (dI₁) has said peak magnitude value dI_MAX at said second point ε

_B; and

(e) adding a constant displacement Y to said normalized version of said first correlation signal, the value of displacement Y being such that the value of said control signal at said point ε

₀ of steady balance is zero.

47. The method of claim 46 wherein said step (c) of generating said control signal (Ed) further comprises the steps of:

(f) generating a second reference code signal comprising a repeating sequence of pulses, the start of each pulse being spaced in time from the start of the next pulse by an integer number of chip durations Δ

, each said pulse having a duration equal to or less than the chip duration Δ

, the values of said pulses being related to the preselected series of numbers, said second reference code signal being generated such that its sequence start is displaced from the sequence start of the first reference code signal by a time offset ε

_K (or ε

_N);

(g) generating a second correlation signal (I or I_N) related to the correlation of the input code signal and said second reference code signal, said second correlation signal having a value which is a function of said time shift ε and

said time offset ε

_K (or ε

_N); and

wherein said step (d) of generating said normalized version of said first correlation signal (dI₁) comprises the step of dividing said first correlation signal (dI₁) by said second correlation signal (I or I_N) to form said normalized version.

48. The method of claim 47 wherein said second correlation signal (I or I_N) has a peak magnitude value I_MAX (or I_N,MAX) over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal, said second correlation signal further having a value I_E0 (or I_N,E0) at said point ε

₀ of steady balance for said given power level, and wherein said time offset ε

_K (or ε

_N) of said second reference code signal is selected such that the magnitude of said value I_E0 (or I_N,E0) is at least 90% of its peak magnitude value I_MAX (or I_N,MAX).

49. The method of claim 48 wherein said first correlation signal (dI₁) has a value dI₀ at said point ε

₀ of steady balance, and wherein the magnitude of said value dI₀ is between 5% and 10% of said peak magnitude value of dI_MAX.

50. The method of claim 49 further comprising the step of selecting said displacement Y and said point ε

₀ such that said value dI₀ is between 5% and 10% of said peak magnitude value of dI_MAX.

51. The method of claim 46 wherein said step (d) of generating said normalized version of said first correlation signal dI₁ comprises the steps of:

(f) generating a second reference code signal comprising a repeating sequence of strobes, said sequence of strobes comprising a scaled replica of said first reference code signal but shifted in time, said second reference code signal being generated such that its sequence start is displaced from the sequence start of the first reference code signal by a time offset ε

_K (or ε

_N);

(g) generating a second correlation signal I (or I_N) related to the correlation of the input code signal and said second reference code signal, said second correlation signal having a value which is a function of said time shift ε and

said time offset ε

_K (or ε

_N); and

(h) dividing said first correlation signal dI₁ by said second correlation signal I (or I_N) to form said normalized version.

52. The method of claim 51 wherein said second correlation signal I (or N) has a peak magnitude value I_MAX (or I_N,MAX) over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal;

wherein said second correlation signal further has, at said given power level, a value I_E0 (or I_N,E0) when said time shift ε

is at said point ε

₀ of steady balance; and

wherein said time offset ε

_K (or ε

_N) of said second reference code signal is selected such that the magnitude of said value I_E0 (or I_N,E0) is at least 90% of its peak magnitude value of I_MAX (or I_N,MAX).

53. The method of claim 52 wherein said time offset ε

_K (or ε

_N) has a range of values for which the magnitude of said value I_E0 (or I_N,E0) is at least 90% of I_MAX (or I_N,MAX), said range having a minimum value and a maximum value, and wherein the value of said time offset ε

_K (or ε

_N) is closer to said minimum value of said range than said maximum value.

54. The method of claim 53 wherein the value of said time offset ε

_K (or ε

_N) is equal to said minimum value.

55. The method of claim 54 wherein said first correlation signal dI₁ has a value dI₀ at said point ε

₀ of steady balance, and wherein the magnitude of said value dI₀ is between 5% and 10% of said peak magnitude value of dI_MAX.

56. The method of claim 55 further comprising the step of selecting said displacement Y and said point ε

₀ such that said value dI₀ is between 5% and 10% of said peak magnitude value of dI_MAX.

57. The method of claim 45 wherein said step of generating said control signal (Ed) comprises the step of:

(d) adding a displacement Y to said first correlation signal (dI₁), the value of displacement Y being related to the peak magnitude of said input code signal.

58. The method of claim 57 wherein said displacement Y is proportionally related to the peak magnitude of the input code signal by a coefficient q, the sign and value of said coefficient q being selected to set the location of said point CO of steady balance.

59. The method of claim 58 wherein said step (d) of adding said displacement Y comprises the steps of:

(e) generating a second reference code signal comprising a repeating sequence of strobes, the start of each strobe being spaced in time from the start of the next strobe by an integer number of chip durations Δ

, each strobe having a duration equal to or less than the chip duration Δ and

comprising at least a pulse, the values of said pulses being related to the preselected series of numbers, said second reference code signal being generated such that its sequence start is displaced from the sequence start of said first reference code signal by a time offset ε

_K;

(f) generating a second correlation signal (I or I_N) related to the correlation of the input code signal and said second reference code signal, said second correlation signal having a value which is a function of said time shift ε and

said time offset ε

_K (or ε

_N);

said second correlation signal (I or I_N) being related to the peak magnitude of the input code signal; and

(g) generating said displacement Y in proportion to said second correlation signal.

60. The method of claim 59 wherein said second correlation signal (I or I_N) has a peak magnitude value I_MAX (or I_N,MAX) over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal;

wherein said second correlation signal further has, at said given power level, a value I_E0 (or I_N,E0) when said time shift ε

is at said point ε

₀ of steady balance; and

wherein said time offset ε

_K (or ε

_N) of said second reference code signal is selected such that the magnitude of said value I_E0 (or I_N,E0) is at least 90% of its peak magnitude value I_MAX (or I_N,MAX).

61. The method of claim 60 wherein said time offset ε

_K (or ε

_N) has a range of values for which the magnitude of said value I_E0 (or I_N,E0) is at least 90% of I_MAX (or I_N,MAX), said range having a minimum value and a maximum value, and wherein the value of said time offset ε

_K (or ε

_N) is closer to said minimum value of said range than said maximum value.

62. The method of claim 59 wherein said first correlation signal (dI₁) has a peak magnitude dI_MAX over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal;

wherein said step (g) generates said displacement Y as said second correlation signal multiplied by a constant of proportionality; and

wherein the values of said coefficient β and

said point ε

₀ are selected such that the magnitude of said displacement Y is between 5% and 10% of said peak magnitude dI_MAX.

63. The method of claim 58 wherein said first correlation signal (dI₁) has a peak magnitude dI_MAX over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal; and

wherein the values of said coefficient q and said point ε

₀ are selected such that the magnitude of said displacement Y is between 5% and 10% of said peak magnitude dI_MAX.

64. The method of claim 59 wherein each of said pulses of said second reference code signal has a duration equal to said chip duration Δ

.

65. The method of claim 57 wherein said step (d) of adding a displacement Y to said first correlation signal (dI₁) comprises the steps of:

(e) generating a second reference code signal comprising a repeating sequence of strobes, said sequence of strobe substantially being a scaled replica of said first reference code signal, said second reference code signal being generated such that its sequence start is displaced from the sequence start of the first reference code signal by a time offset ε

_N; and

(g) generating a second correlation signal (I_N) related to the correlation of the input code signal and said second reference code signal, said second correlation signal having a value which is a function of said time shift ε and

said time offset ε

_N, said second correlation signal (I_N) being related to the peak magnitude of the input code signal; and

(h) generating said displacement Y in proportion to said second correlation signal.

66. The method of claim 65 wherein said second correlation signal (I_N) has a peak magnitude value I_N,MAX over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal;

wherein said second correlation signal further has, at said given power level, a value I_N,E0 when said time shift ε

is at said point ε

₀ of steady balance; and

wherein said time offset ε

_N of said second reference code signal is selected such that the magnitude of said value I_N,E0 is at least 90% of I_MAX.

67. The method of claim 65 wherein said time offset ε

_N has a range of values for which the magnitude of said value I_N,E0 is at least 90% of I_N,MAX, said range having a minimum value and a maximum value, and wherein the value of said time offset ε

_N is closer to said minimum value of said range than said maximum value.

68. The method of claim 65 wherein said first correlation signal (dI₁) has a peak magnitude dI_MAX over a range of said time shift ε

from −

Δ

to +Δ

for a given power level of the input code signal;

wherein said step (g) generates said displacement Y as said second correlation signal multiplied by a constant β

of proportionality; and

wherein the values of said coefficient β and

said point ε

₀ are selected such that the magnitude of said displacement Y is between 5% and 10% of said peak magnitude dI_MAX.

69. The method of claim 45 wherein, when the sequence start of the reference code signal is aligned to the sequence start of the input code signal, the reference code signal (S_B(t)) has a strobe corresponding to each chip of the input code signal for which that chip has changed in value from the previous chip'"'"'s value.

70. The method of claim 45 comprising the step of initially setting the time shift ε

at a point which lags the point ε

₀ of steady balance before commencing the performance of step (d) of adjusting the time shift ε

.