System and method of improved kalman filtering for estimating the state of a dynamic system
View Patent ↗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.
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.