Building control system with automated Kalman filter parameter initiation and system identification

1. A building management system comprising:

a processing circuit configured to perform a system identification process to identify one or more parameters of a system model that predicts a behavior of a building system, the one or more parameters comprising one or more model parameters and one or more Kalman gain parameters, the system identification process comprising:

identifying the one or more model parameters;

generating an initial guess of the one or more Kalman gain parameters based on a disturbance estimate resulting from a simulation that uses the one or more model parameters; and

identifying the one or more Kalman gain parameters by initializing a prediction error minimization problem with the initial guess; and

a controller configured to control building equipment to affect the behavior of the building system based on predictions of the system model.

2. The building management system of claim 1 , wherein the processing circuit is configured to identify the one or more Kalman gain parameters by running the prediction error minimization problem to local optimality.

3. The building management system of claim 1 , wherein:

the processing circuit is configured to perform the simulation using the one or more model parameters and a preliminary observer gain; and

the processing circuit is configured to obtain the preliminary observer gain using an assumption that a sensor noise matrix is equal to an identity matrix and that a process disturbance matrix is equal to an identity matrix.

4. The building management system of claim 3 , wherein the processing circuit is configured to obtain the preliminary observer gain by obtaining a root of a Ricatti equation, the Ricatti equation comprising the sensor noise matrix and the process disturbance matrix.

5. The building management system of claim 1 , wherein the processing circuit is configured to generate the initial guess by approximating a process disturbance matrix and a sensor noise matrix based on results of the simulation and the training data.

6. The building management system of claim 5 , wherein the processing circuit is configured to:

obtain a root of an equation, the equation comprising the process disturbance matrix and the sensor noise matrix based on results of the simulation and the training data; and

calculate the initial guess of the one or more Kalman gain parameters using the root.

7. The building management system of claim 5 , wherein the processing circuit is configured to:

compute the sensor noise matrix using an error between measured outputs from the training data and output estimates from the simulation;

compute the process disturbance matrix using an error between estimated states from the simulation and a computed ideal state.

8. A method comprising:

operating building equipment to affect a variable trait of a building and to generate training data relating to behavior of a building system;

performing a system identification process to identify one or more parameters of a system model that predicts the behavior of the building system, the one or more parameters comprising one or more model parameters and one or more Kalman gain parameters, the system identification process comprising:

identifying the one or more model parameters using the training data;

generating an initial guess of the one or more Kalman gain parameters based on a disturbance estimate resulting from a simulation that uses the one or more model parameters; and

identifying the one or more Kalman gain parameters by initializing a prediction error minimization problem with the initial guess; and

controlling the building equipment based on predictions of the system model.

9. The method of claim 8 , wherein identifying the one or more Kalman gain parameters comprises running the prediction error minimization problem to local optimality.

10. The method of claim 8 , comprising:

obtaining a preliminary observer gain using an assumption that a sensor noise matrix is equal to an identity matrix and that a process disturbance matrix is equal to an identity matrix; and

performing the simulation using the one or more model parameters and the preliminary observer gain.

11. The method of claim 10 , comprising obtaining the preliminary observer gain by obtaining a root of a Ricatti equation, the Ricatti equation comprising the sensor noise matrix and the process disturbance matrix.

12. The method of claim 8 , wherein generating the initial guess comprises approximating a process disturbance matrix and a sensor noise matrix based on results of the simulation and the training data.

13. The method of claim 12 , wherein generating the initial guess further comprises:

obtaining a root of an equation, the equation comprising the process disturbance matrix and the sensor noise matrix based on results of the simulation and the training data; and

calculating the initial guess of the one or more Kalman gain parameters using the root.

14. The method of claim 12 , comprising:

computing the sensor noise matrix using an error between measured outputs from the training data and output estimates from the simulation;

computing the process disturbance matrix using an error between estimated states from the simulation and a computed ideal state.

15. One or more non-transitory computer-readable media containing program instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising:

receiving training data relating to a building system;

performing a system identification process to identify one or more parameters of a system model that predicts behavior of the building system, the one or more parameters comprising one or more model parameters and one or more Kalman gain parameters, the system identification process comprising:

identifying the one or more model parameters using the training data;

generating an initial guess of the one or more Kalman gain parameters based on a disturbance estimate resulting from a simulation that uses the one or more model parameters; and

identifying the one or more Kalman gain parameters by initializing a prediction error minimization problem with the initial guess; and

controlling building equipment based on predictions of the system model.

16. The non-transitory computer-readable media of claim 15 , the operations comprising:

obtaining a preliminary observer gain using an assumption that a sensor noise matrix is equal to an identity matrix and that a process disturbance matrix is equal to an identity matrix; and

performing the simulation using the one or more model parameters and the preliminary observer gain.

17. The non-transitory computer-readable media of claim 16 , the operations comprising obtaining the preliminary observer gain by obtaining a root of a Ricatti equation, the Ricatti equation comprising the sensor noise matrix and the process disturbance matrix.

18. The non-transitory computer-readable media of claim 15 , wherein generating the initial guess comprises approximating a process disturbance matrix and a sensor noise matrix based on results of the simulation and the training data.

19. The non-transitory computer-readable media of claim 18 , wherein generating the initial guess further comprises:

obtaining a root of an equation, the equation comprising the process disturbance matrix and the sensor noise matrix based on results of the simulation and the training data; and

calculating the initial guess of the one or more Kalman gain parameters using the root.

20. The non-transitory computer-readable media of claim 19 , the operations comprising:

computing the sensor noise matrix using an error between measured outputs from the training data and output estimates from the simulation;

computing the process disturbance matrix using an error between estimated states from the simulation and a computed ideal state.