At the first eonferenee of the International Federation of Automatie Control (IFAC), Kalman (1960) introdueed the dual eoneept of eontrollability and observability. At the same time Kalman demonstrated that when the system dynamie equations are linear and the performanee eriterion is quadratie (LQ eontrol), then the mathematieal problem has an explieit solution whieh provides an optimal eontrol law. Also Kalman and Buey (1961) developed the idea of an optimal filter (Kalman filter) whieh, when eombined with an optimal eontroller, produeed linear-quadratie-Gaussian (LQG) eontrol. [Pg.3]

This work was extended by Kalman and Buey (1961) who designed a state estimation proeess based upon an optimal minimum varianee filter, generally referred to as a Kalman filter. [Pg.285]

The Kalman filter single variable estimation problem [Pg.285]

The Kalman filter is a eomplementary form of the Weiner filter. Let be a measurement of a parameter x and let its varianee Pa be given by [Pg.285]

The Kalman filter multivariable state estimation problem [Pg.286]

The general form of the Kalman filter usually eontains a diserete model of the system together with a set of reeursive equations that eontinuously update the Kalman gain matrix K and the system eovarianee matrix P. [Pg.286]

Equations (9.71)-(9.76) are illustrated in Figure 9.7 whieh shows the bloek diagram of the Kalman filter. [Pg.287]

The reeursive equations (9.74)-(9.76) that ealeulate the Kalman gain matrix and eovarianee matrix for a Kalman filter are similar to equations (9.29) and (9.30) that [Pg.287]

A control system that contains a LQ Regulator/Tracking controller together with a Kalman filter state estimator as shown in Figure 9.8 is called a Linear Quadratic Gaussian (LQG) control system. [Pg.288]

The full LQG system, eomprising of the LQ optimal eontroller and Kalman filter was then eonstrueted. Figure 9.17 shows a set of moisture eontent measurements z ikT) together with the estimated moisture eontent x ikT). [Pg.299]

If the forward velocity of the ship is the state variable u, a best estimate of which is given by the Kalman filter, the gain scheduling controller can be expressed as [Pg.300]

The plant deseribed in Example 9.8 by equations (9.185) and (9.186) is to be eontrolled by a Linear Quadratie Gaussian (LQG) eontrol seheme that eonsists of a LQ Regulator eombined with the Kalman filter designed in Example 9.8. The [Pg.322]

Continuous Linear Quadratic Estimator (Kalman Filter] [Pg.411]

The script file kalfild.m solves, in forward-time, the discrete solution of the Kalman filter equations, using equations (9.74), (9.75) and (9.76) in a recursive process. The MATLAB command Iqed gives the same result. [Pg.411]

Discrete solution of Kalman filter equations %Init ialize [Pg.412]

Pearson, A.R., Sutton, R., Burns, R.S. and Robinson, P. (2000) A Kalman Filter Approach to Fault Tolerance Control in Autonomous Underwater Vehicles. In Proc. 14th International Conference on Systems Engineering, Coventry, 12-14 September, 2, pp. 458 63. [Pg.431]

An important property of a Kalman filter is that during the measurement and estimation process, regions of the measurement range can be identified where the model is invalid. This allows us to take steps to avoid these measurements affecting the accuracy of the estimated parameters. Such a filter is called the adaptive Kalman fdter. An increasing number of applications of the Kalman filter [Pg.576]

In this chapter we discuss the principles of the Kalman filter with reference to a few examples from analytical chemistry. The discussion is divided into three parts. First, recursive regression is applied to estimate the parameters of a measurement equation without considering a systems equation. In the second part a systems equation is introduced making it necessary to extend the recursive regression to a Kalman filter, and finally the adaptive Kalman filter is discussed. In the concluding section, the features of the Kalman filter are demonstrated on a few applications. [Pg.577]

Before we introduce the Kalman filter, we reformulate the least-squares algorithm discussed in Chapter 8 in a recursive way. By way of illustration, we consider a simple straight line model which is estimated by recursive regression. Firstly, the measurement model has to be specified, which describes the relationship between the independent variable x, e.g., the concentrations of a series of standard solutions, and the dependent variable, y, the measured response. If we assume a straight line model, any response is described by [Pg.577]

Kalman filter algorithm equations for time-invariant system states [Pg.585]

Equations (41.15) and (41.19) for the extrapolation and update of system states form the so-called state-space model. The solution of the state-space model has been derived by Kalman and is known as the Kalman filter. Assumptions are that the measurement noise v(j) and the system noise w(/) are random and independent, normally distributed, white and uncorrelated. This leads to the general formulation of a Kalman filter given in Table 41.10. Equations (41.15) and (41.19) account for the time dependence of the system. Eq. (41.15) is the system equation which tells us how the system behaves in time (here in j units). Equation (41.16) expresses how the uncertainty in the system state grows as a function of time (here in j units) if no observations would be made. Q(j - 1) is the variance-covariance matrix of the system noise which contains the variance of w. [Pg.595]

See also in sourсe #XX -- [ Pg.575 , Pg.576 , Pg.594 , Pg.596 ]

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