For geometric analysis of side-looking SAR image, it is frequently of interest to determine the time-varying radar antenna's position parameters along a flight path. This paper employs converging higher (fourth)-order time polynomials to model the position/orientation parameters; and the polynomials are incorporated into the basic ranging/Doppler (radargrammetric) conditions. As usual, an iterative least-squares adjustment yields both polynomial parameter corrections and measurement residuals. The estimated corrections and their statistical variances can be used to investigate their respective parametric significance. Equally essential are the estimated measurement residuals because the corresponding residual quadratic-form should theoretically reflect a minimum value. Explicitly, the paper expresses the parameter significance testing and the model optimization criteria. The results of an experimental airborne SAR slant-range image indicate that the proposed methodology satisfactorily works.