Basics of parametric estimation All parametric estimation methods can be broken into a few main steps Observation equations: equations that relate the arameters to be estimated to the observed quantities(observables). Mathematical model position sat elite position (implicit in po clocks receiver Stochastic model: Statistical description that describes the random fluctuations in the measurements and maybe the parameters Inversion that determines the parameters values from the mathematical model consistent with the statistical mode 03/1203 12540Lec10 Observation model Observation model are equations relating observables to parameters of model Observable= function(parameters) Observables should not appear on right-hand-side of equation Often function is non-linear and most common method is linearization of function using Taylor senes expansion Sometimes log linearization for f=a bc ie Products fo parameters03/12/03 12.540 Lec 10 5 Basics of parametric estimation – Observation equations: equations that relate the parameters to be estimated to the observed position, satellite position (implicit in r), clocks, atmospheric and ionosphere delays – Stochastic model: Statistical description that describes the random fluctuations in the measurements and maybe the parameters – Inversion that determines the parameters values from the mathematical model consistent with the statistical model. 03/12/03 12.540 Lec 10 6 Observation model – – of equation • All parametric estimation methods can be broken into a few main steps: quantities (observables). Mathematical model. • Example: Relationship between pseudorange, receiver • Observation model are equations relating observables to parameters of model: Observable = function (parameters) Observables should not appear on right-hand-side • Often function is non-linear and most common method is linearization of function using Taylor series expansion. • Sometimes log linearization for f=a.b.c ie. Products fo parameters 3