Estimation of non-stationary aerosol size distributions using the state-space approach

All algorithms proposed for the reconstruction of aerosol size distributions are based on the assumption that the size distribution to be determined is time invariant during each measurement cycle. However, this assumption does not hold true in the general case. In this paper we consider the problem of estimating time-varying aerosol size distributions from DMPS measurements. The problem is formulated as a discrete-time state estimation problem and the reconstruction approach is based on the use of the Kalman filter and fixed-interval smoother algorithms. Temporal changes in the size distribution function are assumed to occur between DMA voltage changes and the observation errors are assumed to be Gaussian with zero mean. We also exploit additional information on the solution to prevent non-physical features. The performance of the proposed method is evaluated with synthetic measurement data and it is shown that the temporal resolution and the accuracy of the estimates can be considerably enhanced with the proposed approach when compared to traditional approaches.