Methods and systems for forming time-differenced navigation satellite system observables

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 NSS signals from NSS satellites,

wherein, hereinafter, a procedure comprising computing time-differenced carrier phase observables by subtracting carrier phase observables of an epoch m from carrier phase observables of a subsequent epoch n is referred to as “delta-carrier-phase-observables-computation procedure m,n ”; and

wherein, hereinafter, u is a measurement update interval;

the method comprising:

receiving the NSS signals at the NSS receiver;

performing delta-carrier-phase-observables-computation procedure a,b based on the NSS signals;

determining that a criterion indicative of

stability of NSS satellite measurement geometry from epoch a to epoch b+u,

is not satisfied, and increasing the value of a;

performing delta-carrier-phase-observables-computation procedure a,b+u , and

determining a positioning solution of the NSS receiver at least based on the time-differenced carrier phase observables computed in the delta-carrier-phase-observables-computation procedure a,b+u .

2 . Method of claim 1 , wherein measurement update interval u has a value that is larger than, or equal to, 0.1 second and smaller than, or equal to, 10 seconds, preferably a value that is larger than, or equal to, 0.1 second and smaller than, or equal to, 2 seconds, more preferably a value that is larger than, or equal to, 0.15 second and smaller than, or equal to, 0.5 second.

3 . Method of claim 1 , further comprising, after performing delta-carrier-phase-observables computation procedure a,b and before performing delta-carrier-phase-observables computation procedure a,b+u ,

determining whether b+u minus a is larger than, or equal to, a threshold time interval, and, if so, increasing the value of a regardless of whether the criterion is satisfied;

wherein the threshold time interval has a value that is larger than twice the measurement update interval u.

4 . Method of claim 3 , wherein the threshold time interval has a value that is smaller than, or equal to, 200 times the measurement update interval u, preferably a value that is larger than, or equal to, 3 times the measurement update interval u and smaller than, or equal to, 100 times the measurement update interval u, more preferably a value that is larger than, or equal to, 4 times the measurement update interval u and smaller than, or equal to, 50 times the measurement update interval u.

5 . Method according to claim 1 , wherein determining whether the criterion is satisfied comprises:

determining whether a measure of quality of the NSS satellite measurement geometry at epoch a, said measure of quality being hereinafter referred to as “measured”, is not significantly worse than a measure of quality of the NSS satellite measurement geometry at epoch b+u, said measure of quality being hereinafter referred to as “measure b+u ”, and

wherein determining whether measure a is not significantly worse than measure b+u comprises:

determining whether measure a is larger than, or equal to, k times measure b+u , where k is a number larger than 0 and smaller than 1, a number larger than 0.4 and smaller than 0.9, or a number larger than 0.6 and smaller than 0.8.

6 . Method of claim 5 , wherein measured is the number of time-differenced carrier phase observables computed when delta-carrier-phase-observables-computation procedure a,b was performed and measure b+u is the number of available carrier phase observables at epoch b+u.

7 . Method of claim 5 , wherein measure a is an inverse geometric dilution of precision based on the time-differenced carrier phase observables computed when delta-carrier-phase-observables-computation procedure a,b was performed and measure b+u is an inverse geometric dilution of precision based on the available carrier phase observables at epoch b+u.

8 . Method according to claim 1 , further comprising, after performing delta-carrier-phase-observables-computation procedure a,b+u , at least one occurrence of the following operations, with the value of b being incremented by u before each occurrence:

determining whether the criterion is satisfied, and, if not, increasing the value of a; and

performing delta-carrier-phase-observables-computation procedure a,b+u .

9 . Method of claim 8 , wherein, hereinafter, the operations comprising:

performing delta-carrier-phase-observables-computation procedure a,b ;

determining whether the criterion is satisfied, and, if not, increasing the value of a; and

performing delta-carrier-phase-observables-computation procedure a,b+u ;

are regarded as forming a processing task, wherein the method comprises performing at least two processing tasks in parallel, and wherein each processing task comprises at least one of:

its own initial value a;

its own initial value b;

its own criterion to decide whether to increase the value of a;

its own time-differenced carrier phase observables computed by subtracting carrier phase observables associated with satellites from a specific NSS; and

its own time-differenced carrier phase observables computed by subtracting carrier phase observables associated with a specific combination of NSS frequencies.

10 . Method of claim 9 , further comprising processing outputs of the at least two processing tasks by at least one of:

comparing the outputs of the processing tasks and selecting one of the outputs to exclude outliers, wherein, preferably, this is carried out for at least three processing tasks using a majority voting approach to exclude outliers;

forming a weighted mean combination of parameter estimates, where a weighting factor used for the weighted mean is determined from formal precisions of the parameter estimates; and,

selecting parameter estimates from the processing task that produced the best precisions.

11 . Method according to claim 1 , wherein, in the definition of delta-carrier-phase-observables-computation procedure m,n , the term “subsequent” means “following in time”.

12 . Method according to claim 1 , wherein,

in the definition of delta-carrier-phase-observables-computation procedure m,n , the term “subsequent” means “following in order”;

the method is carried out at least partially in a post-processing manner; and

the epochs are ordered in reverse time at least for the purpose of

performing delta-carrier-phase-observables-computation procedure a,b ;

determining whether the criterion is satisfied, and, if not, increasing the value of a; and

performing delta-carrier-phase-observables-computation procedure a,b+u .

13 . A non-transitory computer readable program or programs storing instructions that when executed by a processor causes the processor to carry out the method according claim 1 .

14 . 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 parameters useful to determine a position, the NSS receiver observing NSS signals from NSS satellites,

wherein, hereinafter, a procedure comprising computing time-differenced carrier phase observables by subtracting carrier phase observables of an epoch m from carrier phase observables of a subsequent epoch n is referred to as “delta-carrier-phase-observables-computation procedure m,n ”; and

wherein, hereinafter, u is a measurement update interval;

and the system being configured for performing steps comprising:

performing delta-carrier-phase-observables-computation procedure a,b ;

determining that a criterion indicative of

stability of NSS satellite measurement geometry from epoch a to epoch b+u,

is not satisfied, and increasing the value of a;

performing delta-carrier-phase-observables-computation procedure a,b+u , and

determining a positioning solution of the NSS receiver at least based on the time-differenced carrier phase observables computed in the delta-carrier-phase-observables-computation procedure a,b+u .

15 . Vehicle comprising a system according to claim 14 , the vehicle preferably being at least one of: a motor vehicle, an agricultural tractor, a combine harvester, a crop sprayer, a construction equipment, a truck, a bus, a train, a motorcycle, an autonomous vehicle, a self-driving vehicle, a driverless vehicle, a robotic vehicle, a highly automated vehicle, an aircraft, and an unmanned aerial vehicle.

16 . System according to claim 14 , wherein the criterion is further indicative of continuity of carrier phase measurements from epoch a to epoch b+u.

17 . Method according to claim 16 , wherein determining whether the criterion is satisfied comprises at least one of:

determining whether the number of time-differenced carrier phase observables computed when delta-carrier-phase-observables-computation procedure a,b was performed is larger than, or equal to, a threshold, hereinafter referred to as “minimum-number-of-delta-carrier-phase-observables threshold”;

determining whether the number of available carrier phase observables at epoch b+u is larger than, or equal to, a threshold, hereinafter referred to as “minimum-number-of-carrier-phase-observables threshold”; and

determining whether the number of time-differenced carrier phase observables that is still computable in delta-carrier-phase-observables-computation procedure a,b+u with the current value of a is larger than, or equal to, a threshold, hereinafter referred to as “minimum-number-of-still-computable-delta-carrier-phase-observables threshold”.

18 . Method of claim 17 , wherein the minimum-number-of-delta-carrier-phase-observables threshold is equal to 4.

19 . Method of claim 17 , wherein the minimum-number-of-carrier-phase-observables threshold is a minimum number of available carrier phase observables required to form a positioning solution using an estimation process, hereinafter referred to as “estimator”, wherein the estimator uses state variables and computes the values of its state variables at least based on the time-differenced carrier phase observables computed in delta-carrier-phase-observables-computation procedure m,n .

20 . Method according to claim 17 , wherein the minimum-number-of-still-computable-delta-carrier-phase-observables threshold is equal to, or larger than, 4.