State Estimation

Abstract

The basic full state observer for linear, time-invariant, single input, single output plants is first developed. The separation principle and transparency property are covered and the design procedure given. The full state observer is then extended for the estimation of external disturbances together with the plant state. The discrete version is then developed together with the design procedure. The continuous full state observer for linear time-invariant multivariable plants and its design procedure is then presented.

The remainder of the chapter is devoted to the effects of measurement noise and plant noise on the state estimate and how this may be taken into account in observer design using power spectral density and variance information. The discrete Kalman filter algorithm is then introduced and comparisons made with the discrete observer algorithm for linear time-invariant multivariable plants. A derivation of the discrete Kalman gain algorithm is given. Comparisons are made with the continuous version.

The appendix contains two approaches to nonlinear observer design restricted to plants of full relative degree. The first comprises a set of filtered output derivative estimators constituting a state estimate, practicable provided the measurement noise levels are not too high. The second affords more measurement noise filtering by using the output derivative estimates of the first approach as raw measurements for a special observer in which the nonlinear elements of the plant model are excluded from the correction loop.