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Total Propagated Uncertainty (TPU) has been a very important topic of research and developments in the last five years in the bathymetric lidar community.
To date, two models coexist to estimate the TPU of a bathymetric lidar system. One would rely on an analytical approach based on the General Law Of Propagation Of Variance (GLOPOV) whereas the other relies on a probabilistic and modeling approach based on water surface simulation, Monte Carlo and Ray-tracing principles. We propose a new hybrid method that is based on the GLOPOV and the Law of Large Number (LLN). This new approach includes several innovative mathematical concepts and computational tools that help to overcome known challenges and limitations whilst improving the computation speed.
For instance, an analytical TPU estimation relies on the Jacobian and Covariance matrices associated to the LiDAR system. The estimation the Jacobian matrix, i.e. the partial derivatives of the LiDAR equation’s vector function, remains a difficult task. Therefore, we’ve developed an equation parser and a code generator tool that evaluate the partial derivatives of any equation system and produce the GPU code for its evaluation. The Covariance matrix also has its own challenges and we propose new approaches to estimate some of the sigma values.
The probabilistic model based on Monte Carlo simulation and ray tracing is inherently intensive in terms of computation and therefore slow. The use of the LLN offers a scalable and robust approach to estimate parameters and coefficients of the model.
Finally, we will present an attempt to adapt the Quality Factor introduce by Lurton and Augustin in 2009 for the Multibeam echosounder systems. This factor has the potential to deliver an objective way to assess the bathymetric performance of any Airborne Bathymetric Lidar based on waveform analysis.
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