Estimation of aerosol particle number distributions with Kalman Filtering – Part 1: Theory, general aspects and statistical validity

TLDR: In this paper, Extended Kalman Filter (EKF) is introduced as a method to estimate aerosol particle number size distributions from multiple simultaneous observations and validated by calculating the bias and the standard deviation for the estimated size distributions with respect to the raw measurements.

Abstract: . Aerosol characteristics can be measured with different instruments providing observations that are not trivially inter-comparable. Extended Kalman Filter (EKF) is introduced here as a method to estimate aerosol particle number size distributions from multiple simultaneous observations. The focus here in Part 1 of the work was on general aspects of EKF in the context of Differential Mobility Particle Sizer (DMPS) measurements. Additional instruments and their implementations are discussed in Part 2 of the work. University of Helsinki Multi-component Aerosol model (UHMA) is used to propagate the size distribution in time. At each observation time (10 min apart), the time evolved state is updated with the raw particle mobility distributions, measured with two DMPS systems. EKF approach was validated by calculating the bias and the standard deviation for the estimated size distributions with respect to the raw measurements. These were compared to corresponding bias and standard deviation values for particle number size distributions obtained from raw measurements by a inversion of the instrument kernel matrix method. Despite the assumptions made in the EKF implementation, EKF was found to be more accurate than the inversion of the instrument kernel matrix in terms of bias, and compatible in terms of standard deviation. Potential further improvements of the EKF implementation are discussed.