On InSAR AMBIGUITY RESOLUTION FOR DEFORMATION MONITORING

Integer carrier phase ambiguity resolution is the key to fast and highprecision satellite positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. It also applies to stacked radar interferometry for deformation monitoring, see e.g. [Hanssen, et al, 2001]. In this contribution we apply the integer least-squares’ principle to the rank defect model of stacked InSAR carrier phase data. We discuss two ways of dealing with the rank defect for ambiguity resolution. One is based on the use of a priori data, the other is based on the use of an interval constraint on the deformation rate. 1 INTEGER LEAST-SQUARES (ILS) Consider the system of observation equations y = Ax+Bz + e (1) where y ∈ R is the vector of observations, x ∈ R and z ∈ Z are the vectors of unknown parameters and e ∈ R is the noise vector. Matrix (A,B) is given and assumed to be of full column rank. The structure of the system (1) is typical for carrier phase GPS applications. In that case y consists of the carrier phase and pseudo range data, z consists of the integer double difference ambiguities and x consists of the baseline components and possibly other real-valued parameters (e.g. atmospheric delay parameters). The model is however also applicable to radar interferometric phase ambiguity resolution problems, see e.g. [Bamler and Hartl, 1998], [Hanssen, 2001], [Hanssen et al, 2001], [Kampes and Hanssen, 2004], [Kampes, 2005]. In order to solve (1) in a least-squares sense, we follow the approach of [Teunissen, 1993]. Let Qy be the variance matrix of y and let ||.||Q−1 y = (.) TQ−1 y (.). We first decompose ||e||2 Q−1 y into a sum of three quadratic terms: ||e||2 Q−1 y = ||y − Ax−Bz||2 Q−1 y = ||ê||2 Q−1 y + ||ẑ − z||2 Q−1 ẑ + ||x̂(z)− x||2 Q−1 x̂|z (2) ARTIFICIAL SATELLITES, Vol. 41, No. 1 2006 DOI: 10.2478/v10018-007-0002-8