MATLAB CONTROL SYSTEM TOOLBOX 9 Guia do Utilizador descarregar pdf (Página 498)

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101

kalman

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11kalman

Purpose Design continuous- or discrete-time Kalman estimator

Syntax [kest,L,P] = kalman(sys,Qn,Rn,Nn)

[kest,L,P,M,Z] = kalman(sys,Qn,Rn,Nn) % discrete time only

[kest,L,P] = kalman(sys,Qn,Rn,Nn,sensors,known)

Description kalman designs a Kalman state estimator given a state-space model of the

plant and the process and measurement noise covariance data. The Kalman

estimator is the optimal solution to the following continuous or discrete

estimation problems.

Continuous-Time Estimation

Given the continuous plant

with known inputs and process and measurement white noise

satisfying

construct a state estimate that minimizes the steady-state error

covariance

The optimal solution is the Kalman filter with equations

where thefilter gain is determined by solving an algebraic Riccati equation.

Thisestimator uses theknown inputs and the measurements togenerate

Ax Bu Gw++= (state equation)

Cx Du Hw v++ += (measurement equation)

Ew() Ev() 0, Eww

()Q,= Evv

()R=,Ewv

()N===

t()

PExx

–{}xx

–{}

()

t∞→

lim=

Bu L y

– Du–()++=

u+=

1 2 ... 493 494 495 496 497 498 499 500 501 502 503 ... 648 649

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