Digital Signal Processing 16 (2006) 369–388 www.elsevier.com/locate/dsp A general smoothing equation for signal estimation using randomly delayed observations in the correlated signal-noise case S. Nakamori a,∗ , A. Hermoso-Carazo b , J. Linares-Pérez b a Department of Technology, Faculty of Education, Kagoshima University, 1-20-6, Kohrimoto, Kagoshima 890-0065, Japan b Departamento de Estadística e Investigación Operativa, Universidad de Granada, Campus Fuentenueva, s/n, 18071 Granada, Spain Available online 16 June 2005 Abstract This paper treats the least-squares linear smoothing problem for signal estimation using measure- ments 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 smooth- ing. 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.  2005 Elsevier Inc. All rights reserved. Keywords: Fixed-point smoothing; Fixed-interval smoothing; Fixed-lag smoothing; Covariance information; Delayed observations * Corresponding author. E-mail addresses: nakamori@edu.kagoshima-u.ac.jp (S. Nakamori), ahermoso@ugr.es (A. Hermoso-Carazo), jlinares@ugr.es (J. Linares-Pérez). 1051-2004/$ – see front matter  2005 Elsevier Inc. All rights reserved. doi:10.1016/j.dsp.2005.04.013