In this paper, to enhance the spectrum utilization in cognitive unmanned aerial vehicle networks (CUAVNs), we propose a cooperative spectrum sensing scheme based on a continuous hidden Markov model (CHMM) with a novel signal-to-noise ratio (SNR) estimation method. First, to exploit the Markov property in the spectrum state, we model the spectrum states and the corresponding fusion values as a hidden Markov model. A spectrum prediction is obtained by combining the parameters of CHMM and a preliminary sensing result (obtained from a clustered heterogeneous two-stage-fusion scheme), and this prediction can further guide the sensing detection procedure. Then, we analyze the detection performance of the proposed scheme by deriving its closed-formed expressions. Furthermore, considering imperfect SNR estimation in practical applications, we design a novel SNR estimation scheme which is inspired by the reconstruction of the signal on graphs to enhance the proposed CHMM-based sensing scheme with practical SNR estimation. Simulation results demonstrate the proposed CHMM-based cooperative spectrum sensing scheme outperforms the ones without CHMM, and the CHMM-based sensing scheme with the proposed SNR estimator can outperform the existing algorithm considerably.