Summary: This paper proposes an optimal design of the general distributed nonlinear Kalman-based filtering algorithm to tackle the discrete-time estimation problem with noisy communication networks. The algorithm extends the Kalman filter by enabling it to predict the noisy communication data and fuse it with the received neighboring information to produce a posterior estimate value. In the prediction step, the unscented transformations of the estimate values and covariances originated in the unscented Kalman filter (UKF) are exploited. In the update step, a communication protocol is appended to the posterior estimator, which consequently leads to a modified posterior error covariance containing the covariance of the communication term with its communication gain. Both Kalman and communication gains are then optimised to collectively minimise the mean-squared estimation error. Afterwards, stochastic stability analysis is performed to guarantee its exponential boundedness. To exemplify the performance, this algorithm is applied to a group of robots in a sensor network assigned to estimate an unknown information distribution over an area in the optimal coverage control problem. Comparative numerical experiments finally verify the effectiveness of our design.