Nonparametric fixed-interval smoothing of nonlinear vector-valued measurements

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...

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...

Fixed Interval Smoothing of Nonlinear/Non-Gaussian Dynamic Systems in Cell Space

State estimation problems such as optimal filtering and smoothing do not lend themselves to analytical treatment in general nonlinear/non-Gaussian dynamic systems. The fixed interval smoothing problem aims to construct the marginal conditional probability density function of the state given past and future measurements relative to the state. For linear Gaussian systems it is derived as the Rauc...

Holt’s exponential smoothing model for interval-valued time series

Interval-valued time series are interval-valued data that are collected in a chronological sequence through time. This paper adapts an approach to forecasting interval valued-time series based on Holt’s exponential smoothing method. In the adapted Holt’s method for interval-valued time series, the smoothing parameters are estimated by using techniques for non-linear optimization problems with b...