A convex optimization based approach is presented to perform model-data assimilation of spatial temporal dynamical systems where sensor error characteristics are not available. The key idea of the proposed technique is that one should not make any assumption regarding the statistical properties of sensor data when they are not available. Recently developed quadrature scheme, Conjugate Unscented Transformation in conjunction with convex optimization tools is used to obtain an approximation of posterior density function. The proposed approach is validated by considering the problem of source parameter estimation for toxic material release in the atmosphere. The numerical experiments provides a basis for optimism for the robustness of the proposed methodology.