In order to derive domain-independent heuristics from the specification of a planning problem, it is required to relax the given problem and then solve the relaxed one. In this paper, we present a new planning graph, Merged Planning Graph(MPG), and GD heuristics for solving contingent planning problems with both uncertainty about the initial state and non-deterministic action effects. The merged planning graph is an extended one to be applied to the contingent planning problems from the relaxed planning graph, which is a common means to get effective heuristics for solving the classical planning problems. In order to get heuristics for solving the contingent planning problems with sensing actions and non-deterministic actions, the new graph utilizes additionally the effect-merge relaxations of these actions as well as the traditional delete relaxations. Proceeding parallel to the forward expansion of the merged planning graph, the computation of GD heuristic excludes the unnecessary redundant cost from estimating the minimal reachability cost to achieve the overall set of goals by analyzing interdependencies among goals or subgoals. Therefore, GD heuristics have the advantage that they usually require less computation time than the overlap heuristics, but are more informative than the max and the additive heuristics. In this paper, we explain the experimental analysis to show the accuracy and the search efficiency of the GD heuristics.