Signal estimation with binary-valued sensors

This paper introduces several algorithms for signal estimation using binary-valued output sensing. The main idea is derived from the empirical measure approach for quantized identification, which has been shown to be convergent and asymptotically efficient when the unknown parameters are constants. Signal estimation under binary-valued observations must take into consideration of time varying variables. Typical empirical measure based algorithms are modified with exponential weighting and threshold adaptation to accommodate time-varying natures of the signals. Without any information on signal generators, the authors establish estimation algorithms, interaction between noise reduction by averaging and signal tracking, convergence rates, and asymptotic efficiency. A threshold adaptation algorithm is introduced. Its convergence and convergence rates are analyzed by using the ODE method for stochastic approximation problems.