On Bayesian Fixed-Interval Smoothing Algorithms

Fixed-Interval Kalman Smoothing Algorithms in Singular State-Space Systems

Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far : the regular case, i.e. with positive definite covariance matrix; and the perfect measurement case, i.e. with zero measurement noise. In this paper we address the smoothing problem in the intermediate case ...

Nonparametric fixed-interval smoothing with vector splines

Fixed Interval Smoothing for Nonlinear Continuous Time Systems

Here, dr~dr and dw/dt are independent, zero mean, ganssian white noise processes, with covariances I 3 ( t r ) and R ( t ) 8 ( t T), respectively. The matrix R(t) is positive definite for all t. An a priori distribution for the density of x 0 is assumed known, and it is assumed that f , G, h and R all have sufficient smoothness properties to guarantee the usual existence and uniqueness requirem...

Nonparametric fixed-interval smoothing of nonlinear vector-valued measurements

This paper addresses the problem of estimating a smooth vector-valued function given noisy nonlinear vector-valued measurements of that function. We present a nonparametric optimality criterion for this estimation problem, and develop a computationally eficient iterative algorithm for its solution. The new criterion is the natural generalization of our earlier work on vector splines with linear...

The Fixed-Interval Smoothing Problem for Continuous Systems

The smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques. The smoothing problem is introduced in an criterion by means of an artificial discontinuity that splits the problem in term of forward and backward filtering problems. Hence, the smoother design is realized in three steps. First, a forward filter is developed. Sec...