Protection level generation methods and systems for applications using navigation satellite system (NSS) observations
Some embodiments of the invention relate to methods carried out by an NSS receiver and/or a processing entity capable of receiving data therefrom, for estimating parameters derived from NSS signals useful to determine a position, and for generating protection level(s) for an application relying on NSS observations to produce an estimate of said parameters. A float solution is computed using NSS signals observed by the NSS receiver. A best integer ambiguity combination that minimizes an error norm is identified based on the float solution. Additional integer ambiguity combinations are identified, which have the smallest error norms that, together with the error norm of the best integer ambiguity combination, jointly satisfy the integrity risk. A measure of spread of the best and additional integer ambiguity combinations is computed. The protection level(s) is then generated from the measure of spread. Systems and computer programs are also disclosed. Some embodiments may for example be used for safety-critical applications such as highly-automated driving and autonomous driving.
1. Method, carried out by at least one of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, and a processing entity capable of receiving data from the NSS receiver, for estimating, or processing a prior estimation of, parameters derived from NSS signals useful to determine a position, and for generating at least one protection level for an application relying on NSS observations to produce an estimate of said parameters or a combination thereof, wherein a protection level is a statistical error bound ensuring that the estimate only exceeds the protection level with a probability, hereinafter referred to as an “integrity risk”, the method comprising:
computing a float solution using NSS signals observed by the NSS receiver;
searching for, based on the float solution, and identifying an integer ambiguity combination that minimizes an error norm, the identified integer ambiguity combination being hereinafter referred to as “best integer ambiguity combination”;
identifying, among a set of other integer ambiguity combinations determined based on the float solution, those integer ambiguity combinations, hereinafter referred to as “additional integer ambiguity combinations”, having the smallest error norms that, together with the error norm of the best integer ambiguity combination, jointly satisfy the integrity risk;
computing a measure of spread of at least one of:
(i) the best integer ambiguity combination and the additional integer ambiguity combinations, and
(ii) values of a parameter or of parameters derivable from the best integer ambiguity combination and the additional ambiguity combinations; and
generating the at least one protection level based on the computed measure of spread.
2. Method of claim 1 , wherein an alert limit is associated with each protection level, the alert limit being a maximum allowable uncertainty in the estimate that is considered acceptable for the application, the method further comprising:
determining whether any of the at least one protection level exceeds its respective alert limit; and
if so, refraining from using the estimate, or part of the estimate, for the application.
3. Method of claim 1 , wherein the integrity risk is a number set according to an integrity requirement of the application.
4. Method according to claim 1 , wherein the integrity risk is a number equal to or smaller than 10 −3 per NSS receiver epoch, preferably a number comprised between 10 −5 and 10 −9 per NSS receiver epoch, and more preferably a number comprised between 10 −7 and 10 −9 per NSS receiver epoch.
5. Method according to claim 1 , further comprising, between, first, computing the float solution and, second, searching for and identifying the best integer ambiguity combination:
transforming the float solution into a more orthogonal space through a decorrelation technique.
6. Method according to claim 1 , further comprising, between, first, computing the float solution and, second, searching for and identifying the best integer ambiguity combination:
determining that ambiguities of the float solution have sufficiently converged.
7. Method according to claim 1 , wherein the error norm of an integer ambiguity combination represents a distance from the integer ambiguity combination to the float solution.
8. Method according to claim 1 , further comprising, between, first, searching for and identifying the best integer ambiguity combination and, second, identifying the additional integer ambiguity combinations:
computing a variance of unit weight based on the error norm of the best integer ambiguity combination; and
at least one of:
if the variance of unit weight is larger than 1, scaling a covariance matrix of the float solution by multiplying it by the variance of unit weight, and adjusting the error norm;
if the variance of unit weight is larger than 1 plus a margin, scaling the float solution's covariance matrix by multiplying it by the variance of unit weight, and adjusting the error norm, wherein the margin is a number comprised between 0.001 and 0.1, preferably 0.05;
if the variance of unit weight is larger than 1 plus a margin determined from a critical value of a statistical test, preferably a chi-squared test, scaling the float solution's covariance matrix by multiplying it by the variance of unit weight, and adjusting the error norm;
if the variance of unit weight is smaller than 1, scaling the float solution's covariance matrix by multiplying it by the variance of unit weight, and adjusting the error norm;
if the variance of unit weight is smaller than 1 minus a margin, scaling the float solution's covariance matrix by multiplying it by the variance of unit weight, and adjusting the error norm, wherein the margin is a number comprised between 0.001 and 0.1, preferably 0.05; and
if the variance of unit weight is smaller than 1 minus a margin determined from the critical value of the statistical test, preferably a chi-squared test, scaling the float solution's covariance matrix by multiplying it by the variance of unit weight, and adjusting the error norm.
9. Method according to claim 1 , wherein identifying, among the set of other integer ambiguity combinations determined based on the float solution, the additional integer ambiguity combinations comprises:
computing a search region bound based on the error norm of the best integer ambiguity combination and on the integrity risk; and
determining the set of other integer ambiguity combinations based on the float solution and the computed search region bound.
10. Method according to claim 1 , wherein identifying, among the set of other integer ambiguity combinations determined based on the float solution, the additional integer ambiguity combinations comprises:
determining the set of other integer ambiguity combinations by selecting a number, hereinafter referred to as “candidate number”, of integer ambiguity combinations around the float solution, wherein, preferably, the candidate number is a number equal to or larger than 10 3 , and, more preferably, a number comprised between 10 5 and 10 7 .
11. Method according to claim 1 , further comprising, after identifying the additional integer ambiguity combinations:
determining that a number of identified additional integer ambiguity combinations is smaller than a threshold.
12. Method according to claim 1 , wherein identifying the additional integer ambiguity combinations comprises:
identifying those integer ambiguity combinations having the smallest error norms that, together with the error norm of the best integer ambiguity combination, jointly satisfy the integrity risk under an assumption that the float solution has a leptokurtic error distribution, preferably an error distribution with a kurtosis larger than 3.05, and more preferably an error distribution with a kurtosis larger than 3.1.
13. Method according to claim 1 , wherein identifying the additional integer ambiguity combinations comprises:
identifying those integer ambiguity combinations having the smallest error norms that, together with the error norm of the best integer ambiguity combination, jointly satisfy the integrity risk under an assumption that the float solution has an error distribution selected from among a group comprising a Student's t-distribution, a Pearson type IV distribution, a Laplace distribution, a logistic distribution, and an empirically derived distribution.
14. Method according to claim 1 , wherein computing a measure of spread comprises at least one of:
computing a difference between the maximum and minimum values among the positions in a coordinate frame corresponding to the best integer ambiguity combination and additional integer ambiguity combinations; and
computing the difference between the maximum and minimum values among the values of the parameter, or differences between the maximum and minimum values among the values of the parameters, derivable from the best integer ambiguity combination and additional ambiguity combinations.
15. Method according to claim 1 , wherein generating the at least one protection level based on the computed measure of spread comprises generating at least one of:
a horizontal position protection level;
a vertical position protection level;
an along-track position protection level;
a cross-track position protection level;
a position protection level up relative to a track;
a radial position protection level relative to a track;
an ionospheric bias protection level;
a tropospheric bias protection level;
a satellite ephemeris bias protection level;
a satellite clock bias protection level;
a code multipath protection level; and
a GLONASS frequency-dependent bias protection level.
16. Method of claim 15 , wherein generating the at least one protection level based on the computed measure of spread comprises generating, for each of a plurality of satellites, at least:
an ionospheric bias protection level;
a tropospheric bias protection level;
a satellite ephemeris bias protection level;
a satellite clock bias protection level; and
a code multipath protection level.
17. Computer program or set of computer programs comprising computer-readable instructions configured, when executed on a computer or set of computers, to cause the computer or set of computers to carry out the method claim 1 .
18. Computer program product or storage mediums comprising a computer program or set of computer programs according to claim 17 .
19. System comprising at least one of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, and a processing entity capable of receiving data from the NSS receiver, the system being for estimating, or processing a prior estimation of, parameters derived from NSS signals useful to determine a position, and for generating at least one protection level for an application relying on NSS observations to produce an estimate of said parameters or a combination thereof, wherein a protection level is a statistical error bound ensuring that the estimate only exceeds the protection level with a probability, hereinafter referred to as an “integrity risk”, and the system being configured for:
computing a float solution using NSS signals observed by the NSS receiver;
searching for, based on the float solution, and identifying an integer ambiguity combination that minimizes an error norm, the identified integer ambiguity combination being hereinafter referred to as “best integer ambiguity combination”;
identifying, among a set of other integer ambiguity combinations determined based on the float solution, those integer ambiguity combinations, hereinafter referred to as “additional integer ambiguity combinations”, having the smallest error norms that, together with the error norm of the best integer ambiguity combination, jointly satisfy the integrity risk;
computing a measure of spread of at least one of:
(i) the best integer ambiguity combination and the additional integer ambiguity combinations, and
(ii) values of a parameter or of parameters derivable from the best integer ambiguity combination and the additional ambiguity combinations; and
generating the at least one protection level based on the computed measure of spread.
20. Vehicle comprising a system according to claim 19 .