A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.

A generalised background correction algorithm for a Halo Doppler lidar and its application to data from Finland

Current commercially available Doppler lidars provide an economical and robust solution for measuring vertical and horizontal wind velocities, together with the ability to provide co- and cross-polarised backscatter profiles. The high temporal resolution of these instruments allows turbulent properties to be obtained from studying the variation in radial velocities. However, the instrument specifications mean that certain characteristics, especially the background noise behaviour, become a limiting factor for the instrument sensitivity in regions where the aerosol load is low. Turbulent calculations require an accurate estimate of the contribution from velocity uncertainty estimates, which are directly related to the signal-to-noise ratio. Any bias in the signal-to-noise ratio will propagate through as a bias in turbulent properties. In this paper we present a method to correct for artefacts in the background noise behaviour of commercially available Doppler lidars and reduce the signal-to-noise ratio threshold used to discriminate between noise, and cloud or aerosol signals. We show that, for Doppler lidars operating continuously at a number of locations in Finland, the data availability can be increased by as much as 50 % after performing this background correction and subsequent reduction in the threshold. The reduction in bias also greatly improves subsequent calculations of turbulent properties in weak signal regimes.