Sequential Estimation in a Real-Time Positioning or Navigation System Using Historical States

1 . A method of performing a sequential estimation, the method comprising, at each iteration:

propagating a first state estimate into a state prediction,

wherein the first state estimate is valid at a first time and comprises estimated values of a plurality of state parameters, the plurality of state parameters including at least one state parameter referring to a time earlier than the first time; and

forming a second state estimate, by updating the state prediction using state measurements,

wherein the second state estimate is valid at a second time and comprises estimated values of said plurality of state parameters, the plurality of state parameters including at least one state parameter referring to a time earlier than the second time, and

wherein the state measurements comprise:

measurements relating to state parameters at the second time; and

measurements relating to state parameters at the time earlier than the second time.

2 . A method as claimed in claim 1 , comprising propagating the first state estimate into the state prediction by means of a state transition matrix.

3 . A method as claimed in claim 2 , wherein the state transition matrix is such that, in the second state estimate, an estimated value of at least one state parameter referring to a time earlier than the second time is derived from an estimated value of a state parameter referring to the first time in the first state estimate.

4 . A method as claimed in claim 1 , wherein at least one state parameter in the state prediction is obtained by copying a value of a state parameter in the first state estimate.

5 . A method as claimed in claim 1 , wherein

the first state estimate comprises at least one respective state parameter referring to each of a plurality of times earlier than the first time.

6 . A method as claimed in claim 1 , wherein the first state estimate comprises a number of state parameters referring to a time earlier than the first time that is smaller than the number of state parameters referring to the first time.

7 . A method as claimed in claim 1 , wherein the measurements relating to state parameters at the time earlier than the second time comprise a measurement that can be obtained only with a latency.

8 . A method as claimed in claim 1 , wherein the measurements relating to state parameters at the time earlier than the second time comprise a correction and replacement of a measurement previously used for updating the state prediction.

9 . A method as claimed in claim 1 , wherein the measurements relating to state parameters at the time earlier than the second time comprise a refinement of a measurement previously used for updating the state prediction.

10 . A method as claimed in claim 1 , wherein the measurements relating to state parameters at the time earlier than the second time comprise a measurement relating to a time period between the first time and the second time.

11 . A method as claimed in claim 1 , comprising a method of positioning, wherein the state measurements are obtained from a GNSS system.

12 . A method as claimed in claim 1 , comprising a method of inertial navigation, wherein the measurements relating to state parameters at the time earlier than the second time comprise Zero Velocity Updates.

13 . An estimation system, configured to perform a sequential estimation according to the method as claimed in claim 1 .

14 . An estimation system as claimed in claim 13 , comprising a positioning system, configured to receive state measurements from a GNSS receiver.

15 . A computer program product, comprising computer-readable instructions for performing the method as claimed in claim 1 .