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This paper focuses on Sequential Monte Carlo approximations of smoothingdistributions in conditionally linear and Gaussian state spaces. To reduceMonte Carlo variance of smoothers, it is typical in these models to useRao-Blackwellization: particle approximation is used to sample sequences ofhidden regimes while the Gaussian states are explicitly integrated conditionalon the sequence of regimes and observations, using variants of the Kalmanfilter / smoother. The first successful attempt to use Rao-Blackwellization forsmoothing extends the Bryson-Frazier smoother for Gaussian linear state spacemodels using the generalized two-filter formula together with Kalman filters /smoothers. More recently, a forward backward decomposition of smoothingdistributions mimicking the Rauch-Tung-Striebel smoother for the regimescombined with backward Kalman updates has been introduced. This paperinvestigates the benefit of introducing additional rejuvenation steps in allthese algorithms to sample at each time instant new regimes conditional on theforward and backward particles. This defines particle based approximations ofthe smoothing distributions whose support is not restricted to the set ofparticles sampled in the forward or backward filter. These procedures areapplied to commodity markets which are described using a two factor model basedon the spot price and a convenience yield for crude oil data.

Particle rejuvenation of Rao-Blackwellized Sequential Monte Carlo smoothers for Conditionally Linear and Gaussian models