Abstract: In detection of Bernoulli-Gaussian processes for Kalman filtering and optimal smoothing with jumping input sequences, two main traditional difficulties are the interference from adjacent signals and the infinite increase of the number of detected signals. To solve these problems, a new detection method based on optimal deconvolution and a new modeling strategy for the multi-valued input signals are proposed. Then, based on the frequency-do- main properties of fixed-interval optimal smoothing and maximum-likelihood principle, an optimal likelihood-ratio detection index is derived. Simulation shows that the proposed method has high resolution and is a good candidate for the detection of signals with intersymbol interference.