We present a short overview of applications of estimation theory in atmospheric chemistry and discuss some common methods of gridding and mapping of irregular satellite observations of chemical constituents. It is shown that these methods are unable to produce truly synoptic maps of short-lived photochemically active species due to insufficient temporal and spatial density of satellite observations. The only way to overcome this limitation is to supplement observations with prior independent information given, for instance, by atmospheric numerical models and/or climatologies. Objective approaches to combining such prior information with observations are commonly referred to as data assimilation. Mathematical basis of data assimilation known as optimal estimation equations is presented following Lorenc <1986>. Two particular techniques of data assimilation, the variational method and the extended Kalman filter, are briefly described, and their applications to time-dependent numerical photochemical models are discussed. We investigate validity of the linear approximation which is utilized in both methods, present time evolution of the linearization and covariance matrices, and discuss some of their properties. On the basis of ideas of Fisher and Lary <1995> we then employ a trajectory model and a photochemical box model for assimilation and mapping of the Upper Atmosphere Research Satellite (UARS) measurements of chemical species. The assimilation is performed using the variational technique and the extended Kalman filter, and results of both methods are presented and discussed. ¿ 1999 American Geophysical Union