Outlier-tolerant navigation satellite system positioning method and system

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 parameters useful to determine a position, the NSS receiver observing a NSS signal from each of a plurality of NSS satellites over multiple epochs, the method comprising:

receiving input data comprising at least one of: NSS signals observed by the NSS receiver, and information derived from said NSS signals; and

operating a first filter, hereinafter referred to as “robustifier”, and a second filter, hereinafter referred to as “main estimator”, wherein:

each of the robustifier and main estimator uses state variables, and computes the values of their respective state variables at least based on the received input data;

the robustifier identifies, within the received input data, any measurement that does not match a stochastic model assigned thereto;

for each measurement identified by the robustifier as not matching its stochastic model, at least one of the following applies:

the robustifier rejects the measurement, and the main estimator does not use the rejected measurement;

the robustifier adjusts the stochastic model assigned to the measurement, and the main estimator uses the adjusted stochastic model; and

the robustifier corrects the measurement, and the main estimator uses the corrected measurement; and

the robustifier uses fewer state variables than the main estimator.

2. Method of claim 1 , wherein the main estimator comprises at least one of a Kalman filter, and a least squares estimator.

3. Method of claim 1 , wherein the robustifier comprises at least one of:

an M-estimator,

a BIBER estimator,

a least median squares (LMS) estimator,

a least trimmed squares (LTS) estimator,

an S-estimator, and

an L1 estimator.

4. Method according to claim 1 , wherein the robustifier uses at least the following state variables:

three state variables representing at least one of:

the position of the NSS receiver,

an offset in the position of the NSS receiver relative to another position, and

a change in the position of the NSS receiver; and

a state variable representing at least one of:

a NSS common bias term for at least one NSS,

an offset in said NSS common bias term relative to another NSS common bias term, and

a change in a NSS common bias.

5. Method of claim 4 , wherein the robustifier uses only:

said three state variables representing at least one of:

the position of the NSS receiver,

an offset in the position of the NSS receiver relative to another position, and

a change in the position of the NSS receiver; and

said state variable representing at least one of:

the NSS common bias term for at least one NSS,

an offset in said NSS common bias term relative to another NSS common bias term, and

a change in a NSS common bias.

6. Method according to claim 1 , wherein

each of the multiple epochs over which the NSS receiver observes a NSS signal from each of a plurality of NSS satellites is hereinafter referred to as “receiver epoch”, and,

at each receiver epoch, the robustifier

identifies, within the received input data, any measurement that does not match the stochastic model assigned thereto, and

for each measurement identified as not matching its stochastic model, performs at least one of the following operations:

rejecting the measurement,

adjusting the stochastic model assigned to the measurement, and

correcting the measurement.

7. Method according to claim 1 , wherein the received input data is corrected for systematic errors before the robustifier uses said received input data.

8. Method according to claim 1 , wherein measurements comprised in the received input data are assigned their stochastic model before the robustifier uses said received input data.

9. Method according to claim 1 , wherein the robustifier further

receives, from the main estimator, values of state variables used by the main estimator;

identifies an error within the received values; and

provides feedback thereon to the main estimator.

10. 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, for estimating parameters useful to determine a position, the NSS receiver being configured to observe a NSS signal from each of a plurality of NSS satellites over multiple epochs,

the system being configured for receiving input data comprising at least one of: NSS signals observed by the NSS receiver, and information derived from said NSS signals; and

the system is configured to operate a first filter, hereinafter referred to as “robustifier”, and a second filter, hereinafter referred to as “main estimator”, wherein the robustifier and the main estimator are configured so that, in operation:

each of the robustifier and main estimator uses state variables, and computes the values of their respective state variables at least based on the received input data;

the robustifier identifies, within the received input data, any measurement that does not match a stochastic model assigned thereto;

for each measurement identified by the robustifier as not matching its stochastic model, at least one of the following applies:

the robustifier rejects the measurement, and the main estimator does not use the rejected measurement;

the robustifier adjusts the stochastic model assigned to the measurement, and the main estimator uses the adjusted stochastic model; and

the robustifier corrects the measurement, and the main estimator uses the corrected measurement; and

the robustifier uses fewer state variables than the main estimator.

11. System of claim 10 , wherein the main estimator comprises at least one of a Kalman filter, and a least squares estimator.

12. System of claim 10 , wherein the robustifier comprises at least one of:

an M-estimator,

a BIBER estimator,

a least median squares (LMS) estimator,

a least trimmed squares (LTS) estimator,

an S-estimator, and

an L1 estimator.

13. System according to claim 10 , wherein the robustifier is configured so that, in operation, it uses at least the following state variables:

three state variables representing at least one of:

the position of the NSS receiver,

an offset in the position of the NSS receiver relative to another position, and

a change in the position of the NSS receiver; and

a state variable representing at least one of:

a NSS common bias term for at least one NSS,

an offset in said NSS common bias term relative to another NSS common bias term, and

a change in a NSS common bias.

14. System of claim 13 , wherein the robustifier is configured so that, in operation, it uses only:

said three state variables representing at least one of:

the position of the NSS receiver,

an offset in the position of the NSS receiver relative to another position, and

a change in the position of the NSS receiver; and

said state variable representing at least one of:

the NSS common bias term for at least one NSS,

an offset in said NSS common bias term relative to another NSS common bias term, and

a change in a NSS common bias.

15. System according to claim 10 , wherein

each of the multiple epochs over which the NSS receiver is configured to observe a NSS signal from each of a plurality of NSS satellites is hereinafter referred to as “receiver epoch”, and,

the robustifier is configured so that, at each receiver epoch, it

identifies, within the received input data, any measurement that does not match the stochastic model assigned thereto, and

for each measurement identified as not matching its stochastic model, performs at least one of the following operations:

rejecting the measurement,

adjusting the stochastic model assigned to the measurement, and

correcting the measurement.

16. System according to claim 10 , wherein the system is further configured so that, in operation, robustifier

receives, from the main estimator, values of state variables used by the main estimator;

identifies an error within the received values; and

provides feedback thereon to the main estimator.

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 according to claim 1 .