  The paper investigates the distributed estimation problem under low bit rate
communications. Based on the signal-comparison (SC) consensus protocol under
binary-valued communications, a new consensus+innovations type distributed
estimation algorithm is proposed. Firstly, the high-dimensional estimates are
compressed into binary-valued messages by using a periodic compressive
strategy, dithered noises and a sign function. Next, based on the dithered
noises and expanding triggering thresholds, a new stochastic event-triggered
mechanism is proposed to reduce the communication frequency. Then, a modified
SC consensus protocol is applied to fuse the neighborhood information. Finally,
a stochastic approximation estimation algorithm is used to process innovations.
The proposed SC-based algorithm has the advantages of high effectiveness and
low communication cost. For the effectiveness, the estimates of the SC-based
algorithm converge to the true value in the almost sure and mean square sense.
A polynomial almost sure convergence rate is also obtained. For the
communication cost, the local and global average bit rates for communications
decay to zero at a polynomial rate. The trade-off between the convergence rate
and the communication cost is established through event-triggered coefficients.
A better convergence rate can be achieved by decreasing event-triggered
coefficients, while lower communication cost can be achieved by increasing
event-triggered coefficients. A simulation example is given to demonstrate the
theoretical results.
