Due to the existence of various uncertainties, the design of distributed estimation algorithms with robustness and high accuracy is an urgent demand for sensor network applications. This paper is aimed at investigating the design of distributed parameter estimation algorithms and the analysis of their convergence properties in uncertain sensing and communication environments. Consensus-based distributed parameter estimation algorithms for both discrete-time and continuous-time cases are established, which are suitable for unreliable communication networks with stochastic communication noises, random link gains and Markovian signal losses. Under mild conditions on stochastic noises, gain function and topology-switching Markov chain, we establish both the mean square and almost sure convergence of the designed algorithms by use of probability limit theory, algebraic graph theory, stochastic differential equation theory and Markov chain theory. The effect of sensor-dependent gain functions on the convergence of the algorithm is also analyzed.