A distributed Kalman smoother

Kalman smoothers obtain state estimates in a system with stochastic dynamics and measurement noise. We consider the smoothing problem in a distributed setting, present a cooperative smoothing algorithm for Gauss-Markov linear models, and provide a convergence analysis for the algorithm. An extension of the algorithm that maximizes the likelihood with respect to a sequence of state vectors subject to inequality constraints, e.g. positivity conditions, is also described. Finally, a numerical experiment regarding cubic spline regression is included to test the new approach.