Propagation Basics: - Signal, tagged with time from satellite clock, transmitted. - About66msec(20,000km) later the signal arrives at GPS receiver. Satellite has moved about 66 m during the time it takes signal to propagate to receiver

Specific common processes White-noise: Autocorrelation is Dirac-delta function; PSD is flat; integral of power under PSD is variance of process(true in general) First-order Gauss-Markov process (one of most models common in Kalman filtering)

Estimation · Summary Examine correlations -Process noise · White noise · Random walk First-order Gauss Markov Processes Kalman filters Estimation in which the parameters to be estimated are changing with time

Statistical approach to estimation Examine the multivariate Gaussian distribution: (x-)\v-(x-) Multivariant f(x)= Minimize (x-u)'v(x-u) gives largest probability density By minimizing the argument of the exponential in the probability density function, we maximize the likelihood of the estimates(MLE)

Basic concepts Basic problem: We measure range and phase data that are related to the positions of the ground receiver, satellites and other quantities How do we determine the \ best position for the receiver and other quantities What do we mean by best \ estimate?

Summary · Review: -Examined definitions of pseudorange and carrier phase Looked at some actual raw measurements from a RINEX file Today we look at:

Examined methods for measuring distances Examined GPS codes that allow a type of distance measurement and phase to be measured Examine how the range measurements are defined Use of carrier phase measurements Examine rinEx format and look at some \raw data

Today's Lecture Examine specifics of GPS signals Multiple modulations on same carrier signal Structure of signals GPS receiver operation and satellite acquistion

GPS Observables Today's class we start discussing the nature of GPS observables and the methods used to make range and phase measurements Start with idea of remotely measuring distances

Treat the basic description and dynamics of satellite orbits Major perturbations on GPS satellite orbits · Sources of orbit information: -SP3 format from the International GPS service Broadcast ephemeris message