Kalman filter with adaptive measurement variance estimator

A method for estimating the variance of a measured quantity used to predict the current state of a discrete, vector-state, scalar-measurement system, the method comprising:

• estimating the variance of a measured quantity for use in filtering an input quantity and the measured quantity;
• determining a smoothed estimate of an instantaneous prediction error's variance;
• and
• filtering the input quantity and the measured quantity through a Kalman filter using the estimated input variance of the measured quantity signal.

A method for estimating the current state of a discrete, vector-state, scalar-measurement system, the method comprising:

• determining a current state vector prediction from a previous state vector estimate and an input vector;
• determining a current state vector prediction covariance matrix associated with the current state vector prediction from a previous state vector covariance matrix associated with the previous state vector estimate;
• estimating the variance of a measured quantity, wherein estimating the variance includes:
• determining a squared instantaneous prediction error of the measured quantity from the measured quantity and one of the current state vector estimate and the previous state vector estimate;
• smoothing the squared instantaneous prediction error;
• and
• estimating the variance of the measured quantity from the smoothed squared instantaneous prediction error;
• determining a current Kalman filter gain vector from the current state vector prediction covariance matrix and the measured quantity variance estimate;
• determining a current state vector estimate from the Kalman filter gain, the current state vector prediction, and the measured quantity;
• determining the current state vector covariance matrix associated with the current state vector estimate from the Kalman filter gain and the current state vector prediction covariance matrix;
• and
• iterating the above.

A apparatus for estimating the variance of a measured quantity used to predict the current state of a discrete, vector-state, scalar-measurement system, the method comprising:

• means for estimating the variance of a measured quantity for use in filtering an input quantity and the measured quantity;
• means for determining a smoothed estimate of an instantaneous prediction error's variance;
• and
• means for filtering the input quantity and the measured quantity through a Kalman filter using the estimated input variance of the measured quantity signal.

A program storage medium encoded with instructions that, when executed by a computing apparatus, perform a method for estimating the variance of a measured quantity used to predict the current state of a discrete, vector-state, scalar-measurement system, the method comprising:

• estimating the variance of a measured quantity for use in filtering an input quantity and the measured quantity;
• determining a smoothed estimate of an instantaneous prediction error's variance;
• and
• filtering the input quantity and the measured quantity through a Kalman filter using the estimated input variance of the measured quantity signal.

A computing apparatus programmed to perform a method for estimating the variance of a measured quantity used to predict the current state of a discrete, vector-state, scalar-measurement system, the method comprising:

• estimating the variance of a measured quantity for use in filtering an input quantity and the measured quantity;
• determining a smoothed estimate of an instantaneous prediction error's variance;
• and
• filtering the input quantity and the measured quantity through a Kalman filter using the estimated input variance of the measured quantity signal.