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Abstract: This paper treats the least-squares linear smoothing problem for signal estimation using measurements contaminated by additive white noise correlated with the signal, with stochastic delays. We derive a general smoothing equation which is applied to obtain specific smoothing algorithms, which are referred in the signal estimation literature as fixed-point, fixed-interval, and fixed-lag smoothing. Using an innovation approach, the general smoothing equation is derived without requiring the whole knowledge of the state-space model generating the signal, but only covariance information of the signal and the observation noise, as well as the delay probabilities. [Copyright &y& Elsevier]