Chapter utorial: The Kalman Filter

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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].

h (x ^)() i (11.15) Assuming the prior estimate of ^ x k is called ^ 0 k, and w as gained b y kno wledge of the system. It p osible to write an up date equation for the new estimate, com bing the old estimate with measuremen t data th us; ^ x k = 0 + K (z H) (11.16) where; K k is the Kalman gain, whic h will b e deriv ed shortly. The term z H ...