Coding in a wide area positioning system (WAPS)
Embodiments describe determining position by selecting a set of digital pseudorandom sequences. The magnitudes of the cross-correlation between any two sequences of the chosen set are below a specified threshold. A subset of digital pseudorandom sequences are selected from the set such that the magnitudes of the autocorrelation function of each member of the subset, within a specified region adjacent to the peak of the autocorrelation function, are equal to or less than a prescribed value. Each transmitter transmits a positioning signal, and at least a portion of the positioning signal is modulated with at least one member of the subset. At least two transmitters of the plurality of transmitters modulate respective positioning signals with different members of the subset of digital pseudorandom sequences.
1. A positioning system, comprising at least one processor that:
determines an estimated position of a receiver using positioning signals acquired from a plurality of transmitters,
wherein at least a first portion of a first acquired positioning signal is modulated in accordance with a first pseudorandom sequence,
wherein at least a second portion of a second acquired positioning signal is modulated in accordance with a second pseudorandom sequence,
wherein at least a third portion of a third acquired positioning signal is modulated in accordance with a third pseudorandom sequence,
wherein the first, second and third pseudorandom sequences are members of a subset of at least three pseudorandom sequences from a set of pseudorandom sequences,
wherein a maximum magnitude of a cross-correlation function between any two sequences of the set of pseudorandom sequences is below a specified threshold,
wherein all magnitudes of an autocorrelation function corresponding to the members of the subset, within a specified region adjacent to a peak of the autocorrelation function, are equal to or less than a prescribed value, and
wherein two or more magnitudes of the autocorrelation function, outside of the specified region, are greater than the prescribed value.
2. The system of claim 1 , wherein the prescribed value is less than or equal to the maximum magnitude of the cross-correlation function between any two pseudorandom sequences of the set of pseudorandom sequences.
3. The system of claim 1 , wherein the prescribed value is the peak value of the autocorrelation function divided by a non-repeating length of the pseudorandom sequences.
4. The system of claim 1 , wherein the specified region adjacent to the peak of the autocorrelation function includes at least five (5) pseudorandom sequence symbols.
5. The system of claim 1 , wherein the specified region adjacent to the peak of the autocorrelation function includes at least ten (10) pseudorandom sequence symbols.
6. The system of claim 1 , wherein at least one digital pseudorandom sequence of the set of digital pseudorandom sequences has a truncated sequence length, wherein the truncated sequence length is shorter than a standard sequence length.
7. The system of claim 1 , wherein at least one digital pseudorandom sequence of the set of digital pseudorandom sequences has an extended sequence length, wherein the extended sequence length is longer than a standard sequence length.
8. The system of claim 1 , wherein a second portion of the first acquired positioning signal is modulated in accordance with a member of the subset of digital pseudorandom sequences.
9. The system of claim 8 , wherein the member of the subset of digital pseudorandom sequences used to modulate the first portion has a first sequence length, and the member of the subset of digital pseudorandom sequences used to modulate the second portion has a second sequence length, and the first sequence length is different from the second sequence length.
10. The system of claim 8 , wherein the member of the subset of digital pseudorandom sequences used to modulate the first portion is different from the member of the subset of digital pseudorandom sequences used to modulate the second portion.
11. The system of claim 1 , wherein the set of digital pseudorandom sequences have an alphabet size greater than two (2).
12. The system of claim 11 , wherein the set of digital pseudorandom sequences is a set of quaternary sequences.
13. The system of claim 11 , wherein the alphabet size is a power of two (2).
14. The system of claim 1 , wherein one of the positioning signals includes data describing timing differences between transmissions from different transmitters of the plurality of transmitters.
15. The system of claim 1 , wherein each of the positioning signals is initially synchronized to a time reference, and timing corrections corresponding to the synchronization are acquired and used by the at least one processor.
16. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals using high resolution, earliest time of arrival estimates that include an estimated reference correlation function.
17. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals using high resolution, earliest time of arrival estimates that include a partitioning of signal and noise subspaces.
18. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals by cross-correlating received samples with a sequence transmitted from a transmitter, and extracting a peak vector that includes a first number of samples left of a peak of the cross-correlation function and a second number of samples right of the peak.
19. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals by generating a reference peak vector from a correlation function measured in a channel environment that has low noise and at least one of easily separable multipath and no-multipath components, and improving a signal-to-noise ratio in the peak vector by coherently averaging across at least a plurality of pseudorandom code periods.
20. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals by calculating a Fourier Transform of the peak vector, and generating a frequency domain estimate of a channel corresponding to the transmitted sequence using the Fourier Transform of a measured peak vector and the Fourier Transform of the reference peak vector.
21. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals by generating a reduced channel estimate vector from the frequency domain estimate of the channel, defining an estimated covariance matrix of the reduced channel estimate vector, and performing singular value decomposition on the estimated covariance matrix.
22. The system of claim 1 , wherein the at least one processor identifies multipath components of at least one of the positioning signals by generating a vector of sorted singular values, and using the vector of sorted singular values to separate signal and noise subspaces, generating a noise subspace matrix, and estimating time of arrival of a first path using the noise subspace matrix.
23. The system of claim 1 , wherein the at least one processor acquires assistance data that includes at least one of system time at a rising edge of a pulse of a waveform, system time at a falling edge of a pulse of a waveform, geocode data of the plurality of transmitters, geocode data of transmitters adjacent to the plurality of transmitters, index of a sequence used by at least one transmitter in proximity of the plurality of transmitters, clock timing corrections for at least one transmitter, local atmospheric corrections, relationship of WAPS timing to GNSS time, indication of local environment to aid the receiver in pseudorange resolution, and at least one of an offset from base index of a set of pseudorandom sequences, a list of pseudorandom number sequences from a set of transmitters, and a list of transmitters that utilize a particular pseudorandom number sequence.
24. A method for determining an estimated position of a receiver, the method comprising:
determining an estimated position of a receiver using positioning signals acquired from a plurality of transmitters,
wherein at least a first portion of a first acquired positioning signal is modulated in accordance with a first pseudorandom sequence,
wherein at least a second portion of a second acquired positioning signal is modulated in accordance with a second pseudorandom sequence,
wherein at least a third portion of a third acquired positioning signal is modulated in accordance with a third pseudorandom sequence,
wherein the first, second and third pseudorandom sequences are members of a subset of at least three pseudorandom sequences from a set of pseudorandom sequences,
wherein a maximum magnitude of a cross-correlation function between any two sequences of the set of pseudorandom sequences is below a specified threshold,
wherein all magnitudes of an autocorrelation function corresponding to the members of the subset, within a specified region adjacent to a peak of the autocorrelation function, are equal to or less than a prescribed value, and
wherein two or more magnitudes of the autocorrelation function, outside of the specified region, are greater than the prescribed value.
25. The method of claim 24 , wherein the prescribed value is less than or equal to the maximum magnitude of the cross-correlation function between any two pseudorandom sequences of the set of pseudorandom sequences.
26. The method of claim 24 , wherein the prescribed value is the peak value of the autocorrelation function divided by a non-repeating length of the pseudorandom sequences.
27. The method of claim 24 , wherein the specified region adjacent to the peak of the autocorrelation function includes at least five (5) pseudorandom sequence symbols.
28. The method of claim 24 , wherein the specified region adjacent to the peak of the autocorrelation function includes at least ten (10) pseudorandom sequence symbols.
29. The method of claim 24 , wherein at least one digital pseudorandom sequence of the set of digital pseudorandom sequences has a truncated sequence length, wherein the truncated sequence length is shorter than a standard sequence length.
30. The method of claim 24 , wherein at least one digital pseudorandom sequence of the set of digital pseudorandom sequences has an extended sequence length, wherein the extended sequence length is longer than a standard sequence length.
31. The method of claim 24 , wherein a second portion of the first acquired positioning signal is modulated in accordance with a member of the subset of digital pseudorandom sequences.
32. The method of claim 31 , wherein the member of the subset of digital pseudorandom sequences used to modulate the first portion has a first sequence length, and the member of the subset of digital pseudorandom sequences used to modulate the second portion has a second sequence length, and the first sequence length is different from the second sequence length.
33. The method of claim 31 , wherein the member of the subset of digital pseudorandom sequences used to modulate the first portion is different from the member of the subset of digital pseudorandom sequences used to modulate the second portion.
34. The method of claim 24 , wherein the set of digital pseudorandom sequences have an alphabet size greater than two (2).
35. The method of claim 34 , wherein the set of digital pseudorandom sequences is a set of quaternary sequences.
36. The method of claim 34 , wherein the alphabet size is a power of two (2).
37. The method of claim 24 , the method further comprising:
identifying multipath components of at least one of the positioning signals using high resolution, earliest time of arrival estimates that include an estimated reference correlation function.
38. The method of claim 24 , the method further comprising:
identifying multipath components of at least one of the positioning signals using high resolution, earliest time of arrival estimates that include a partitioning of signal and noise subspaces.
39. The method of claim 24 , the method further comprising:
identifying multipath components of at least one of the positioning signals by cross-correlating received samples with a sequence transmitted from a transmitter, and extracting a peak vector that includes a first number of samples left of a peak of the cross-correlation function and a second number of samples right of the peak.
40. The method of claim 24 , the method further comprising:
identifying multipath components of at least one of the positioning signals by generating a reference peak vector from a correlation function measured in a channel environment that has low noise and at least one of easily separable multipath and no-multipath components, and improving a signal-to-noise ratio in the peak vector by coherently averaging across at least a plurality of pseudorandom code periods.
41. The method of claim 24 , the method further comprising:
identifying multipath components of at least one of the positioning signals by calculating a Fourier Transform of the peak vector, and generating a frequency domain estimate of a channel corresponding to the transmitted sequence using the Fourier Transform of a measured peak vector and the Fourier Transform of the reference peak vector.
42. The method of claim 24 , the method further comprising:
identifying multipath components of at least one of the positioning signals by:
generating a reduced channel estimate vector from the frequency domain estimate of the channel, defining an estimated covariance matrix of the reduced channel estimate vector, and performing singular value decomposition on the estimated covariance matrix, or
generating a vector of sorted singular values, using the vector of sorted singular values to separate signal and noise subspaces, generating a noise subspace matrix, and estimating time of arrival of a first path using the noise subspace matrix.
43. A non-transitory machine-readable medium embodying program instructions adapted to be executed to implement the method of claim 24 .