  This paper is concerned with the linear/nonlinear Kalman-like filtering
problem under binary sensors. Since innovation represents new information in
the sensor measurement and serves to correct the prediction for the Kalman-like
filter (KLF), a novel uncertain measurement model is proposed such that the
innovation generated from binary sensor can be captured. When considering
linear dynamic systems, a conservative estimation error covariance with
adjustable parameters is constructed by matrix inequality, and then an optimal
filter gain is derived by minimizing its trace. Meanwhile, the optimal
selection criterion of an adjustable parameter is developed by minimizing the
upper bound of the conservative estimation error covariance. When considering
nonlinear dynamic systems, a conservative estimation error covariance with
adjustable parameters is also constructed via unscented transform and matrix
inequalities. Then, following the idea of designing KLF in linear dynamic
systems, the nonlinear filter gain and the optimal adjustable parameter are
designed. Finally, $O_2$ content estimation and nonlinear numerical system are
employed to show the effectiveness and advantages of the proposed methods.
