Nonlinear variable lag smoother
View Patent ↗An extended Kalman filter (EKF) is combined with a fixed epoch smoother (FES) to produce a new variable lag smoother (VLS). The fixed epoch lags EKF measurement time-tags with variable time lag. The combination of EKF and FES is referred to herein as a variable lag smoother (VLS).
1. A variable lag smoother comprising:
an extended Kalman filter (EKF) configured to receive data over a time period and to provide data representative of an estimate of a state of a device, wherein the state comprises state parameters at a current time t within the time period; and
a plurality of fixed epoch smoothers, wherein each fixed epoch smoother (FES) is in communication with the EKF and is configured to:
operate within a time window defined by an epoch start time and an epoch stop time;
receive data from the EKF beginning when the current time t is equal to the epoch start time and ending when the current time t is greater than the epoch stop time; and
provide an updated estimate of the state of the device as of the epoch start time.
2. The variable lag smoother of claim 1 , wherein the time windows of each of the plurality of FESs do not overlap.
3. The variable lag smoother of claim 1 , wherein the time windows of each of the plurality of FESs overlap by a fixed amount of time.
4. The variable lag smoother of claim 1 , wherein the time windows of each of the plurality of FESs is a fixed time interval.
5. The variable lag smoother of claim 1 , wherein the epoch stop time is determined when a time-varying criterion is satisfied.
6. The variable lag smoother of claim 1 , wherein the time-varying criterion comprises an accuracy threshold.
7. The variable lag smoother of claim 5 , wherein the epoch stop time is determined by the earlier of when a time-varying criterion is satisfied and when a maximum time window threshold is satisfied.
8. The variable lag smoother of claim 1 , wherein the FES is a Fraser fixed-epoch smoother.
9. The variable lag smoother of claim 1 , wherein the FES is a Carlton-Rauch fixed-epoch smoother.
10. The variable lag smoother of claim 1 , wherein the device comprises a spacecraft and the state parameters are selected from the group consisting of a spacecraft position, spacecraft velocity, atmospheric density, ballistic coefficient, photon solar pressure, clock biases, spacecraft maneuver parameters, albedo acceleration, troposphere bias, ionosphere biases, station location biases, antenna phase center biases, multi-path biases and measurement biases.
11. A method of estimating a state of a device comprising:
configuring an extended Kalman filter (EKF) to receive data over a time period and to provide data representative of an estimate of a state of the device, wherein the state comprises state parameters at a current time within the time period; and
configuring a plurality of fixed epoch smoothers, wherein each fixed epoch smoother (FES) is in communication with the EKF and is configured to:
operate within a time window defined by an epoch start time and an epoch stop time;
receive data from the EKF beginning when the current time t is equal to the epoch start time and ending when the current time t is greater than the epoch stop time; and
provide an updated estimate of the state of the device as of the epoch start time.
12. The method of claim 11 , wherein the time windows of each of the plurality of FESs do not overlap.
13. The method of claim 11 , wherein the time windows of each of the plurality of FESs overlap by a fixed amount of time.
14. The method of claim 11 , wherein the time windows of each of the plurality of FESs is a fixed time interval.
15. The method of claim 11 wherein the epoch stop time is determined when a time-varying criterion is satisfied.
16. The method of claim 11 , wherein the time-varying criterion comprises an accuracy threshold.
17. The method of claim 15 , wherein the epoch stop time is determined by the earlier of when a time-varying criterion is satisfied and when a maximum time window threshold is satisfied.
18. The method of claim 11 , wherein the FES is a Fraser fixed-epoch smoother.
19. The method of claim 11 , wherein the FES is a Carlton-Rauch fixed-epoch smoother.
20. The method of claim 11 , wherein the device comprises a spacecraft and the state parameters are selected from the group consisting of a spacecraft position, spacecraft velocity, atmospheric density, ballistic coefficient, photon solar pressure, clock biases, spacecraft maneuver parameters, albedo acceleration, troposphere bias, ionosphere biases, station location biases, antenna phase center biases, multi-path biases and measurement biases.