Department of Electrical & Computer Engineering ECE 240AUniversity of California, Santa Barb ara Winter 2010ShynkH.O. #2ECE 240A OPTIMAL ESTIMATION AND FILTERINGTENTATIVE COURSE OUTLINELINEAR MODEL (Lesson 2)State-space formulationRandom and deterministic signalsAutoregressive modelMoving average modelFiltering, smoothing, and predictionLEAST-SQUARES ESTIMATION (Lessons 3, 4, and 5)Batch processingOrthogonality cond itionSingular value decompositionRecursive processingInformation and covariance formsInitial conditionsPROPERTIES OF ESTIMATORS (Lessons 6, 7, 8, and 9)Small-sample propertiesUnbiasedness an d efficiencyCramer-Rao inequality and Fisher’s informationLarge-sample p ropertiesStochastic convergence and consistencyProperties of least-squares estimatorsBest linear unbiased estimationSUFFICIENT STATISTICS (Lesson A)Factorization theoremExponential families of distributionsComplete and sufficient statisticsUniformly minimum-variance unbiased estimation1MAXIMUM LIKELIHOOD (ML) ESTIMATION (Lessons 10, 11, and 12)Likelihood ratioMultiple hyp othesesMaximum-likelihood methodLog-likelihood functionMultivariate Gaussian random variablesMEAN-SQUARED (MS) ESTIMATION (Lesson 13)Mean-square errorOrthogonality principleConditional mean estimatorNonlinear estimationMAXIMUM A POSTERIORI (MAP) ESTIMATION (Lesson 14)Bayesian estimationConditional likelihood functionDetection theoryComparison of ML, MS, and MAP estimationSTATE ESTIMATION (Lessons 15 and 16)Gauss-Markov random sequencesState-variable modelSingle-stage predictorInnovations processState prediction, filtering, and smoothingKALMAN FILTE R (Lessons 17, 18, 19, 20, and 21)Recursive estimationProperties of Kalman filterWhitening filterSteady-state Kalman filterRelationship to Wiener filterSmoothing: fixed interval, fixed point, and fixed