Conventional methods such as matched filtering, fractional lower order statistics cross ambiguity function, and recent methods such as compressed sensing and track-before-detect are used for target detection by passive radars. Target detection using these algorithms usually assumes that the background noise is Gaussian. However, non-Gaussian impulsive noise is inherent in real world radar problems. In this paper, a new optimization based algorithm that uses weighted l 1 and l 2 norms is proposed as an alternative to the existing algorithms whose performance degrades in the presence of impulsive noise. To determine the weights of these norms, the parameter that quantifies the impulsiveness level of the noise is estimated. In the proposed algorithm, the aim is to increase the target detection performance of a universal mobile telecommunication system (UMTS) based passive radars by facilitating higher resolution with better suppression of the sidelobes in both range and Doppler. The results obtained from both simulated data with α stable distribution, and real data recorded by a UMTS based passive radar platform are presented to demonstrate the superiority of the proposed algorithm. The results show that the proposed algorithm provides more robust and accurate detection performance for noise models with different impulsiveness levels compared to the conventional methods.