Coding in a positioning system
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 method for identifying pseudorandom sequences for use in transmitting signals from one or more transmitters to one or more receivers, the method comprising:
identifying a set of pseudorandom sequences,
wherein a magnitude of an autocorrelation function of each member of the set of pseudorandom sequences, within a range adjacent to the peak value of the autocorrelation function, is equal to or less than a prescribed value; and
identifying a subset of pseudorandom sequences from the set of pseudorandom sequences,
wherein each magnitude of a cross-correlation function between each pair of pseudorandom sequences in the subset is below a specified threshold.
2. The method of claim 1 , wherein the prescribed value is less than or equal to a maximum magnitude of the cross-correlation function of any pair of pseudorandom sequences in the subset of pseudorandom sequences.
3. The method of claim 1 , wherein the prescribed value is +/−1 times the peak value of the autocorrelation function divided by a non-repeating pseudorandom sequence length.
4. The method of claim 1 , wherein a plurality of magnitudes of the autocorrelation function outside the range exceed the prescribed value.
5. The method of claim 1 , wherein the set includes at least 176 pseudorandom sequences, wherein the subset includes at least three pseudorandom sequences, and wherein the subset includes no more than ten pseudorandom sequences.
6. The method of claim 1 , wherein the pseudorandom sequences in the set have an alphabet size greater than two.
7. The method of claim 6 , wherein the alphabet size is a power of two.
8. The method of claim 1 , wherein the range adjacent to the peak value of the autocorrelation function includes at least five pseudorandom sequence symbols.
9. The method of claim 1 , the method further comprising:
transmitting a first signal from a first transmitter, wherein at least a portion of the first signal is modulated with a first pseudorandom sequence of the subset; and
transmitting a second signal from a second transmitter, wherein at least a portion of the second signal is modulated with a second pseudorandom sequence of the subset,
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences.
10. The method of claim 1 , the method further comprising:
transmitting a first signal from a transmitter, wherein the first signal is modulated with a first pseudorandom sequence of the subset; and
transmitting a second signal from the transmitter, wherein the second signal is modulated with a second pseudorandom sequence of the subset,
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences.
11. The method of claim 1 , wherein the magnitudes of the cross-correlation function are within a range of correlation offsets.
12. The method of claim 1 , wherein the magnitudes of the cross-correlation function correspond to all possible correlation offsets.
13. The method of claim 1 , wherein the cross-correlation and autocorrelation functions are circular cross-correlation and autocorrelation functions.
14. The method of claim 9 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the portion of the first signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the portion of the second signal.
15. The method of claim 10 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the first signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the second signal.
16. A non-transitory processor readable memory storing program instructions that, when executed by one or more processors, cause the one or more processors to implement a method for identifying pseudorandom sequences for use in transmitting signals from one or more transmitters to one or more receivers, the method comprising:
identifying a set of pseudorandom sequences,
wherein a magnitude of an autocorrelation function of each member of the set of pseudorandom sequences, within a range adjacent to the peak value of the autocorrelation function, is equal to or less than a prescribed value; and
identifying a subset of pseudorandom sequences from the set of pseudorandom sequences,
wherein each magnitude of a cross-correlation function between each pair of pseudorandom sequences in the subset is below a specified threshold.
17. The non-transitory processor readable memory of claim 16 , wherein the prescribed value is less than or equal to a maximum magnitude of the cross-correlation function of any pair of pseudorandom sequences in the subset of pseudorandom sequences.
18. The non-transitory processor readable memory of claim 16 , wherein the prescribed value is +/−1 times the peak value of the autocorrelation function divided by a non-repeating pseudorandom sequence length.
19. The non-transitory processor readable memory of claim 16 , wherein a plurality of magnitudes of the autocorrelation function outside the range exceed the prescribed value.
20. The non-transitory processor readable memory of claim 16 , wherein the set includes at least 176 pseudorandom sequences, wherein the subset includes at least three pseudorandom sequences, and wherein the subset includes no more than ten pseudorandom sequences.
21. The non-transitory processor readable memory of claim 16 , wherein the pseudorandom sequences in the set have an alphabet size greater than two.
22. The non-transitory processor readable memory of claim 21 , wherein the alphabet size is a power of two.
23. The non-transitory processor readable memory of claim 16 , wherein the range adjacent to the peak value of the autocorrelation function includes at least five pseudorandom sequence symbols.
24. The non-transitory processor readable memory of claim 16 , wherein the method further comprises:
transmitting a first signal from a first transmitter, wherein at least a portion of the first signal is modulated with a first pseudorandom sequence of the subset; and
transmitting a second signal from a second transmitter, wherein at least a portion of the second signal is modulated with a second pseudorandom sequence of the subset,
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences.
25. The non-transitory processor readable memory of claim 16 , wherein the method further comprises:
transmitting a first signal from a transmitter, wherein the first signal is modulated with a first pseudorandom sequence of the subset; and
transmitting a second signal from the transmitter, wherein the second signal is modulated with a second pseudorandom sequence of the subset,
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences.
26. The non-transitory processor readable memory of claim 16 , wherein the magnitudes of the cross-correlation function are within a range of correlation offsets.
27. The non-transitory processor readable memory of claim 16 , where the magnitudes of the cross-correlation function correspond to all possible correlation offsets.
28. The non-transitory processor readable memory of claim 16 , wherein the cross-correlation and autocorrelation functions are circular cross-correlation and autocorrelation functions.
29. The non-transitory processor readable memory of claim 24 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the portion of the first signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the portion of the second signal.
30. The non-transitory processor readable memory of claim 25 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the first signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the second signal.