Binder1 - 167-Prove the conditionin the .9...

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Unformatted text preview: 167-Prove the conditionin the discussionfollowingEquation4.9 thatEWkZT=fori=1, ...kwhenWkandVkare uncorrelatedand white.rIn Example4:4,use whitenoiseas a drivinginputto rangerate(i'k)andbearing rate(8k)equationsinsteadof colorednoise. This reducesthe dimen-sion of the state vectorfrom 6 x 1 to 4 x 1. Formulatethe new observationequation.Generatethe covarianceand Kalmangain plots for the same valuesofPo,Q,R,(J~, (J~, (J~,and(J~.For the same problemas Problem 4.6, obtain values of the plant covarianceQfor the four-statemodelsuch the associatedmean-squaredestimationuncer-taintiesfor range, range rate, bearing,and bearingrate are within5-10 % ofthose for the six-state model.(Hint:This should be possible because the plantnoise is used to model the effects of linearizationerrors, discretizationerrors,,---.andotherunmodeledeffectsorapproximations.Thistypeofsuboptimalfiltering will be discussedfurther in Chapter7.).8For the estimationproblemmodeledby the equationsXk=xk-l+wk-l,tJ----( < - - -wk ~ N(O,...
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Binder1 - 167-Prove the conditionin the .9...

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