This paper investigates a distributed recursive projection identification problem with binaryvalued observations built on a sensor network, where each sensor in the sensor network measures partial information of the unknown parameter only, but each sensor is allowed to communicate with its neighbors. A distributed recursive projection algorithm is proposed based on a specific projection operator and a diffusion strategy. The authors establish the upper bound of the accumulated regrets of the adaptive predictor without any requirement of excitation conditions. Moreover, the convergence of the algorithm is given under the bounded cooperative excitation condition, which is more general than the previously imposed independence or persistent excitations on the system regressors and maybe the weakest one under binary observations. A numerical example is supplied to demonstrate the theoretical results and the cooperative effect of the sensors, which shows that the whole network can still fulfill the estimation task through exchanging information between sensors even if any individual sensor cannot.