A J Gasiewski statistical signal processing notes2 PDF
Preview A J Gasiewski statistical signal processing notes2
EECCEENN 55000044 Environmental Signal Processing Professor Albin J. Gasiewski Lecture #2 – August 26, 2011 EECCOOTT 224466 303-492-9688 (O) [email protected] Classes: ECCS 1B14 MF 2:00-3:15 PM 1 ECEN 5004 Environmental Signal Processing Fall 2011 University of Colorado at Boulder Last Lecture • AApplliicattiions off EEnvSSPP • Forward and inverse problems 4 ECEN 5004 Environmental Signal Processing Fall 2011 University of Colorado at Boulder Today’s Lecture Model Based Parameter Identification: • Review of Gaussian random variables • LLeeaasstt ssqquuaarree eerrrroorr ffiittttiinngg • Pseudoinversion • CChhii-square ffiittttiing 5 Model-Based Parameter Estimation 6 Forward and Inverse – Remote Sensing AAccttiivvee ccaassee – FFoorrwwaarrdd pprroobblleemm:: WWeeaatthheerr rraaddaarr θ <P > 3dB R Inverse problem: Nonlinear mapping ΔR › RR (mm/hr) R 7 Rain Rate (RR) vs. Reflectivity (Z) SSiizzee ddiissttrriibbuuttiioonnss vvaarryy depending on phase of hydrometeor (i.e., rain, clloudd lliiquiidd, snow graupel, ice) and evolution of pprecippitation event. A common distribution for rain is from Marshall and Palmer*: Using Rayleigh scattering theory: * Marshall and Palmer, 1948 8 Radiometric Brightness vs. Water Vapor * Westwater et al., 2007 9 Review of Gaussian RVs 10 Brief Review of Gaussian Random Variables 11 Brief Review of Gaussian Random Variables (cont’d) 12
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