Navigation system applications of sigma-point Kalman filters for nonlinear estimation and sensor fusion

• US 20050251328A1
• Filed: 04/04/2005
• Published: 11/10/2005
• Est. Priority Date: 04/05/2004
• Status: Active Grant

• Current Assignee: Eric A. Wan, Rudolph Van Der Merwe, Simon J. Julier
• Original Assignee: Eric A. Wan, Rudolph Van Der Merwe, Simon J. Julier
• Inventors: Merwe, Rudolph van der, Wan, Eric A., Julier, Simon J.
• Granted Patent: US 7,289,906 B2
• Time in Patent Office: Days
• US Class Current: 701/200
• CPC Class Codes: G01C 21/165 combined with non-inertial navigation instruments
• CPC Class Codes: G01S 19/49 whereby the further system is an inertial position system, e.g. loosely-coupled

Abstract

A method of estimating the navigational state of a system entails acquiring observation data produced by noisy measurement sensors and providing a probabilistic inference system to combine the observation data with prediction values of the system state space model to estimate the navigational state of the system. The probabilistic inference system is implemented to include a realization of a Gaussian approximate random variable propagation technique performing deterministic sampling without analytic derivative calculations. This technique achieves for the navigational state of the system an estimation accuracy that is greater than that achievable with an extended Kalman filter-based probabilistic inference system.

Claims

1. A method of estimating the navigational state of a system, the navigational state characterized by random variables of a state space model, the state space model specifying a time evolution of the system and its relationship to sensor observations, comprising:

acquiring observation data produced by measurement sensors that provide noisy information about the navigational state of the system; and

providing a probabilistic inference system to combine the observation data with prediction values of the system state space model to estimate the navigational state of the system, the probabilistic inference system implemented to include a realization of a Gaussian approximate random variable propagation technique performing deterministic sampling without analytic derivative calculations to achieve for the navigational state of the system an estimation accuracy that is greater than that achievable with an extended Kalman filter-based probabilistic inference system.

2. The method of claim 1, in which the measurement sensors include an inertial measurement unit (IMU) operating to estimate a set of navigational state components, the navigational state component set including angular velocity and attitude information relating to an object.

3. The method of claim 2, in which the navigational state component set includes bias and scale factor information associated with the IMU.

4. The method of claim 1, in which the measurement sensors include a global positioning system (GPS) operating to receive raw satellite signal transmissions to estimate a set of navigational state components, the navigational state component set including position and velocity information relating to an object.

5. The method of claim 4, in which the navigational state component set includes phase and timing error information associated with the GPS.

6. The method of claim 1, in which the measurement sensors producing observation data constitute sensors of multiple orbital GPS satellites from which raw satellite signal transmissions propagate.

7. The method of claim 1, in which the observation data include output signals of an inertial measurement unit (IMU) and position and velocity output signals of a global positioning system (GPS), the observation data contributing to the probabilistic inference system to enable complete estimation of the navigational state of the system and IMU specific ancillary parameters.

8. The method of claim 1, in which the observation data include output signals of an inertial measurement unit (IMU) and raw satellite signal transmissions from a global positioning system (GPS), the observation data contributing to the probabilistic inference system to enable complete estimation of the navigational state of the system, IMU specific ancillary parameters, and GPS specific ancillary parameters.

9. The method of claim 1, in which the random variable propagation technique of the probabilistic inference system used to estimate the navigational state of the system includes:

using mean values and square root decomposition of a covariance matrix of a prior random variable to deterministically calculate a set of sigma-points and an associated set of weight values; and

propagating the calculated set of weighted sigma-points through the state space model to produce a posterior set of weighted sigma-points used to calculate posterior statistics.

10. The method of claim 9, in which the state space model is nonlinear.

11. The method of claim 9, in which the calculation of posterior statistics entails the use of closed form functions of the propagated sigma-points and weight values.

12. The method of claim 9, further comprising using the calculated posterior statistics to give an approximately optimal update of the navigational state and its covariance by combining the prediction values of the system state space model and the sensor observations.

13. The method of claim 9, in which the probabilistic inference system used to estimate the navigational state of the system is implemented with one of unscented Kalman filter (UKF) algorithms, central difference Kalman filter (CDKF) algorithms, square root version of UKF, square root version of CDKF, sigma-point particle filter (SPPF) algorithms, or Gaussian mixture sigma-point particle filter (GMSPPF) algorithms.

14. The method of claim 1, in which the observation data provide noisy information about the navigational state of the system at a time that lags a current time because of sensor latency, communication delay, or other processing delay, and further comprising:

maintaining a cross correlation between a navigational state of the system at a current time and the navigational state to which the latency lagged observation data correspond; and

using the cross correlation to optimally combine latency lagged observation data with the prediction values of the system state space model.

15. A computational system for estimating the navigational state of a system, the navigational state characterized by random variables of a state space model, the state space model specifying a time evolution of the system and its relationship to sensor observations, comprising:

measurement sensors producing observation data in the form of noisy information about the navigational state of the system; and

a probabilistic inference system configured to combine the observation data with prediction values of the system state space model to estimate the navigational state of the system, the probabilistic inference system implemented to include a realization of a Gaussian approximate random variable propagation technique performing deterministic sampling without analytic derivative calculations to achieve for the navigational state of the system an estimation accuracy that is greater than that achievable with an extended Kalman filter-based probabilistic inference system.

16. The system of claim 15, in which the measurement sensors include an inertial measurement unit (IMU) operating to estimate a set of navigational state components, the navigational state component set including angular velocity and attitude information relating to an object.

17. The system of claim 15, in which the measurement sensors include a global positioning system (GPS) operating to receive raw satellite signal transmissions to estimate a set of navigational state components, the navigational state component set including position and velocity information relating to an object.

18. The system of claim 15, in which the observation data include output signals of an inertial measurement unit (IMU) and position and velocity output signals of a global positioning system (GPS), the observation data contributing to the probabilistic inference system to enable complete estimation of the navigational state of the system and IMU specific ancillary parameters.

19. The system of claim 15, in which the observation data include output signals of an inertial measurement unit (IMU) and raw satellite signal transmissions from a global positioning system (GPS), the observation data contributing to the probabilistic inference system to enable complete estimation of the navigational state of the system, IMU specific ancillary parameters, and GPS specific ancillary parameters.

20. The system of claim 15, in which the observation data provide noisy information about the navigational state of the system at a time that lags a current time because of sensor latency, communication delay, or other processing delay, and further comprising:

a computational subsystem operable to maintain a cross correlation between a navigational state of the system at a current time and the navigational state to which the latency lagged observation data correspond; and

a computational subsystem operable to use the cross correlation to optimally combine latency lagged observation data with the prediction values of the system state space model.