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Sequential detection and robust estimation of vapor concentration using frequency-agile lidar time series data

This paper extends an earlier optimal approach for frequency-agile lidar using fixed-size samples of data to include the time series aspect of data collection. The likelihood ratio test methodology for deterministic but unknown vapor concentration is replaced by a Bayesian formalism in which the path integral of vapor concentration CL evolves in time through a random walk model. The fixed- sample maximum likelihood estimates of CL derived earlier are replaced by Kalman filter estimates, and the log- likelihood ratio is generalized to a sequential test statistic written in terms of the Kalman estimates. In addition to the time series aspect, the earlier approach is generalized by (1) including the transmitted energy on a short-by-shot basis in a statistically optimum manner, (2) adding a linear slope component to the transmitter and received data models, and (3) replacing the nominal multivariate normal statistical assumption by a robust model in the Huber sensor for mitigating the effects of occasional data spikes caused by laser misfiring or EMI. The estimation and detection algorithms are compared with fixed-sample processing by the DIAL method on FAL data collected by ERDEC during vapor chamber testing at Dugway, Utah.