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,
identifying a subset of at least three pseudorandom sequences from the set of pseudorandom sequences, wherein more pseudorandom sequences are in the set of pseudorandom sequences than in the subset of pseudorandom sequences;
transmitting a first positioning signal, wherein at least a portion of the first positioning signal is modulated in accordance with a first pseudorandom sequence from the subset of pseudorandom sequences; and
transmitting a second positioning signal, wherein at least a portion of the second positioning signal is modulated in accordance with a second pseudorandom sequence from the subset of pseudorandom sequences,
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences, and
wherein the set and the subset are identified such that:
(i) a magnitude of a first autocorrelation function of each member of the set of pseudorandom sequences, within a first region adjacent to a peak value of the first autocorrelation function, is equal to or less than a first prescribed value, and (ii) each magnitude of a first cross-correlation function between each pair of pseudorandom sequences in the subset is below a first specified threshold; or
(i) a maximum magnitude of a second cross-correlation function between any two pseudorandom sequences of the set of pseudorandom sequences is below a second specified threshold, and (ii) all magnitudes of a second autocorrelation function corresponding to the pseudorandom sequences of the subset, within a second region adjacent to a peak value of the second autocorrelation function, are equal to or less than a second prescribed value.
2. The method of claim 1 , wherein the set and the subset are identified such that (i) the magnitude of the first autocorrelation function of each member of the set of pseudorandom sequences, within the first region adjacent to the peak value of the first autocorrelation function, is equal to or less than the first prescribed value, and (ii) each magnitude of the first cross-correlation function between each pair of pseudorandom sequences in the subset is below the first specified threshold.
3. The method of claim 2 , wherein the first 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, or wherein the first prescribed value is +/−1 times the peak value of the first autocorrelation function divided by a non-repeating length of pseudorandom sequences in the subset.
4. The method of claim 2 , wherein a plurality of magnitudes of the first autocorrelation function outside the first region exceed the first prescribed value.
5. The method of claim 2 , wherein the first region adjacent to the peak value of the first autocorrelation function includes at least five pseudorandom sequence symbols.
6. The method of claim 2 , wherein the magnitudes of the first cross-correlation function are within a range of correlation offsets.
7. The method of claim 1 , wherein the set and the subset are identified such that (i) the maximum magnitude of the second cross-correlation function between any two pseudorandom sequences of the set of pseudorandom sequences is below the second specified threshold, and (ii) all magnitudes of the second autocorrelation function corresponding to the pseudorandom sequences of the subset, within the second region adjacent to the peak value of the second autocorrelation function, are equal to or less than the second prescribed value.
8. The method of claim 7 , wherein the second prescribed value is less than or equal to the maximum magnitude of the second cross-correlation function between any two pseudorandom sequences of the set of pseudorandom sequences, or wherein the second prescribed value is +/−1 times the peak value of the second autocorrelation function divided by a non-repeating length of pseudorandom sequences in the subset.
9. The method of claim 7 , wherein two or more magnitudes of the second autocorrelation function, outside of the second region, exceed the second prescribed value.
10. The method of claim 7 , wherein the second region adjacent to the peak of the second autocorrelation function includes at least five pseudorandom sequence symbols.
11. The method of claim 7 , wherein magnitudes of the second cross-correlation function between each pair of pseudorandom sequences in the subset are within a range of correlation offsets.
12. The method of claim 1 , wherein the set includes at least 176 pseudorandom sequences, wherein the subset includes at least three pseudorandom sequences and no more than ten pseudorandom sequences.
13. The method of claim 1 , wherein the first pseudorandom sequence includes a first set of phase angles used to phase modulate the first positioning signal, and wherein the second pseudorandom sequence includes a second set of phase angles used to phase modulate the second positioning signal.
14. The method of claim 1 , wherein the pseudorandom sequences in the set have an alphabet size greater than two, wherein the alphabet size is a power of two.
15. The method of claim 1 , wherein transmitting a first positioning signal comprises transmitting the first positioning signal from a first transmitter, and wherein transmitting a second positioning signal comprises transmitting the second positioning signal from a second transmitter.
16. The method of claim 1 , wherein transmitting a first positioning signal comprises transmitting the first positioning signal from a first transmitter, and wherein transmitting a second positioning signal comprises transmitting the second positioning signal from the first transmitter.
17. The method of claim 1 , wherein the first pseudorandom sequence has a first length, wherein the second pseudorandom sequence has a second length, and wherein the first length and the second length are different.
18. The method of claim 1 , wherein the first and second cross-correlation functions are circular cross-correlation functions, and wherein the first and second autocorrelation functions are circular autocorrelation functions.
19. 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 the method of claim 1 .
20. A system comprising at least one processor that is operable to implement the method of claim 1 .