The monitoring of GPS integrity is critical for preventing Harzardously Misleading Information (HMI) in safety-of-life applications. We propose an integrity monitoring algorithm based on Direct Position Estimation (DPE), an unconventional GPS receiver architecture. Without the need for intermediate pseudorange models, which are essential under conventional schemes, we are able to account for all sources of error collectively in the position domain, enabling more thorough protection against different modes of integrity threats. Using the correlation manifold provided by a generic DPE receiver, our algorithm characterizes the deformation of the manifold with a Gaussian distribution, which reflects the trust-worthiness of the DPE navigation solution. In this paper, we focus on the vertical aspect of our DPE-based integrity monitoring algorithm. This proposed algorithm was verified with live data to be able to provide indication for the presence of integrity threats, such as a degrading signal environment.