System and method of improved kalman filtering for estimating the state of a dynamic system

• US 8,027,741 B2
• Filed: 04/30/2009
• Issued: 09/27/2011
• Est. Priority Date: 05/29/2008
• Status: Active Grant

• Current Assignee: Department of Health and Human Services (State of Victoria)
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: Kahn, Aaron D.
• Primary Examiner(s): CHANG, SUNRAY
• Application Number:
  US12/432,809
• Publication Number:
  US 20090299494A1
• Time in Patent Office: 880 Days
• Field of Search: 700/28, 700/54, 702/155, 702/175
• US Class Current: 700/28
• CPC Class Codes: G05B 13/04 involving the use of models or simulators

Abstract

Embodiments include systems and methods of estimating at least one state of a modeled dynamic system. In particular, in one embodiment, an observer such as an extended Kalman filter is used to estimate the state of a modeled dynamic system. A covariance matrix associated with state variables of the observer is periodically checked for compliance with a specified condition, e.g., positive definiteness. If the matrix deviates from the specified condition, the matrix is set to a specified value.

Claims

1. A method of estimating the state of a modeled dynamic system, the method comprising:

generating an observer in an electronic device for estimating of at least one state variable associated with the system,

wherein said observer defines a covariance matrix statistically relating the at least one state variable;

receiving sensor data at a electronic device from a sensor, the sensor data being associated with the at least one state variable;

updating, in a memory of the electronic device, the at least one state variable based on the received sensor data and the generated observer;

updating, in a memory of the electronic device, the covariance matrix based on the updated at least one state variable;

determining whether an element of the main diagonal of the updated covariance matrix has a value that is less than zero; and

storing a specified value to the covariance matrix in the memory of the electronic device based on the determining.

2. The method of claim 1, further comprising outputting a vector of real-valued numerical elements which are based on the updated at least one state variable.

3. The method of claim 2, further comprising outputting a control signal based on the vector.

4. The method of claim 1, wherein the observer comprises at least one of a Kalman filter or an extended Kalman filter.

5. The method of claim 1, wherein the modeled dynamical system comprises a point mass moving in inertial space.

6. The method of claim 5, wherein the modeled dynamical system comprises a vehicle, said vehicle comprising least one of an aircraft or a spacecraft.

7. The method of claim 6, wherein the sensor data comprises flight sensor data, and wherein the at least one state variable is indicative of a state variable of the aircraft.

8. A system for estimating at least one state of a modeled dynamic system, the system comprising:

a processor configured to;

provide an observer configured to estimate at least one state variable associated with the modeled dynamic system,

wherein said observer defines a covariance matrix statistically relating the at least one state variable;

a memory configured to store data associated with the observer, said stored data comprising the at least one state variable and the covariance matrix;

wherein the processor is further configured to;

receive sensor data in electronic form from a sensor, the sensor data being associated with the at least one state variable;

update, in the memory, the at least one state variable of the observer based on the received sensor data;

update the covariance matrix in the memory based on the updated at least one state variable;

determine whether an element of the main diagonal of the updated covariance matrix has a value that is less than zero; and

store a specified value to the covariance matrix in the memory based on the determination.

9. The system of claim 8, wherein the processor is configured to output a vector of real-valued numerical elements which are based on the updated at least one state variable.

10. The system of claim 9, further comprising a control system configured to control the modeled dynamic system based on the output vector.

11. The system of claim 8, wherein the observer comprises at least one of a Kalman filter or an extended Kalman filter.

12. The system of claim 8, wherein the modeled dynamic system comprises a point mass moving in inertial space.

13. The system of claim 12, wherein the modeled dynamic system comprises a vehicle, said vehicle comprising least one of an aircraft or a spacecraft.

14. The system of claim 13, wherein the sensor data comprises flight sensor data, and wherein the at least one state variable is indicative of a state variable of an aircraft.

15. A computer-program product for estimating the state of a modeled dynamic system, comprising:

a computer-readable medium having stored thereon codes executable by at least one processor to perform the method comprising;

generating an observer in an electronic device for estimating of at least one state variable associated with the system,

wherein said observer defines a covariance matrix statistically relating the at least one state variable;

receiving sensor data at a electronic device from a sensor, the sensor data being associated with the at least one state variable;

updating, in a memory of the electronic device, the at least one state variable based on the received sensor data and the generated observer;

updating, in a memory of the electronic device, the covariance matrix based on the updated at least one state variable;

determining whether an element of the main diagonal of the updated covariance matrix has a value that is less than zero; and

storing a specified value to the covariance matrix in the memory of the electronic device based on the determining.

16. The product of claim 15, wherein the executable codes further comprise codes executable by the processor to further perform outputting a vector of real-valued numerical elements which are based on the updated at least one state variable.

17. The product of claim 16, wherein the executable codes further comprise codes executable by the processor to further perform outputting a control signal based on the output vector.

18. The product of claim 15, wherein the observer comprises at least one of a Kalman filter or an extended Kalman filter.

19. The product of claim 15, wherein the modeled dynamical system comprises a point mass moving in inertial space.

20. The product of claim 19, wherein the modeled dynamical system comprises a vehicle, said vehicle comprising least one of an aircraft or a spacecraft.

21. The product of claim 20, wherein the sensor data comprises flight sensor data, and wherein the at least one state variable is indicative of a state variable of the aircraft.

22. A system for estimating at least one state of a modeled dynamic system, the system comprising:

means for processing configured to;

provide an observer configured to estimate the at least one state variable associated with the modeled dynamic system,

wherein said observer defines a covariance matrix statistically relating the at least one state variable;

means for storing data associated with the observer, said stored data comprising the at least one state variable and the covariance matrix;

wherein the processing means is further configured to;

receive sensor data in electronic form from a sensor, the sensor data being associated with the at least one state variable;

update, in the memory, the at least one state variable of the observer based on the received sensor data;

update the covariance matrix in the storing means based on the updated at least one state variable;

determine whether an element of the main diagonal of the updated covariance matrix has a value that is less than zero; and

store a specified value to the covariance matrix in the storing means based on the determination.