The Chemical Phy.dcs of Solvation Part A Theory of Solvation R. R. Dogonadze, E. Kalman, a. A. Koiiiyshev, J. Ulstrup, Eds., Elsevier, Amsterdam (1985). [Pg.214]

Other chemometrics methods to improve caUbration have been advanced. The method of partial least squares has been usehil in multicomponent cahbration (48—51). In this approach the concentrations are related to latent variables in the block of observed instmment responses. Thus PLS regression can solve the colinearity problem and provide all of the advantages discussed earlier. Principal components analysis coupled with multiple regression, often called Principal Component Regression (PCR), is another cahbration approach that has been compared and contrasted to PLS (52—54). Cahbration problems can also be approached using the Kalman filter as discussed (43). [Pg.429]

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]

Kalman demonstrated that as integration in reverse time proeeeds, the solutions of F t) eonverge to eonstant values. Should t be infinite, or far removed from to, the matrix Rieeati equations reduee to a set of simultaneous equations [Pg.276]

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]

K is the Kalman gain and the total error varianee expeeted is [Pg.286]

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]

Before equations (9.99) can be run, and initial value of P(/c//c) is required. Ideally, they should not be close to the final value, so that convergence can be seen to have taken place. In this instance, P(/c//c) was set to an identity matrix. Figure 9.16 shows the diagonal elements of the Kalman gain matrix during the first 20 steps of the recursive equation (9.99). [Pg.297]

Fig. 9.16 Convergence of diagonal elements of Kalman gain matrix. |

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]

Disturbance noise covariance matrix %Kalman gain matrix [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]

© 2019 chempedia.info