Transcription of Chapter utorial: The Kalman Filter
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Chapter utorial: The Kalman Filter
Chapter11 lter[1]haslongbeenregardedastheoptimalso lutiontomanytrackinganddatapredictiontas ks,[2]. lterisconstructedasameansquarederrormini miser,butanalternativederivationofthe lterisalsoprovidedshowinghowthe lteringistoextracttherequiredinformation fromasignal, nethegoalofthe ;yk=akxk+nk( )where;ykisthetimedependentobservedsigna l,akisagainterm, erencebetweentheestimateof^xkandxkitself istermedtheerror;f(ek)=f(xk ^xk)( )Theparticularshapeoff(ek)isdependentupo ntheapplication,howeveritisclearthatthef unctionshouldbebothpositiveandincreasemo notonically[3].
implemen tation of the lter in the discrete domain, another reason for its widespread app eal. 11.5 State space deriv ation Assume that w ew an ttokno w the v alue of a v ariable within a pro cess of the form; x k +1 = + w (11.10) where; x k is the state v ector of the pro cess at time k, (nx1); is the state transition matrix of the pro cess ...
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