Description
Electrical impedance tomography (EIT) is typically treated as a minimization problem bridging the gap between predicted data from an idealized model and real measurements from an imperfect system. This process results in a map of an object’s internal conductivity distribution which can be used to detect irregularities or inclusions not visible from the object’s surface. EIT is non-invasive, cost-effective, and also unstable in the presence of noise. Due to this instability, EIT requires the use of prior system knowledge and constraints to produce a reasonable output. One method used to solve this problem is the nonlinear Kalman filter that assumes variables are drawn from Gaussian distributions. Kalman filters use an iterative prediction-correction approach incorporating data into a model using parameters of the Gaussian distribution as constraints. Though applications of standard nonlinear Kalman filters in EIT have proven successful, the assumption of Gaussian errors can prove untrue for cases with an extreme degree of nonlinearity. In these cases, the conductivity approximation can diverge from the truth producing unrealistic internal distributions. The particle filter makes fewer assumptions on the shape of error distributions but is also prone to divergence in high dimensions. Combining the Kalman and particle filter methods allows application of the particle filter to systems with many unknowns such as a mesh of conductivities. To observe potential improvements, six methods are analyzed within the context of EIT including the extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, extended Kalman particle filter, unscented particle filter, and the ensemble Kalman particle filter. These techniques are applied to an artificial scenario and experimental data from the Finish Inverse Problems Society. For the artificial conductivity model with Gaussian noise, the EKF produces a decent conductivity approximation within seconds outperforming the other methods. For the experimental cases, the EKF reasonably predicts the locations of conductivity inclusions. However, multiple iterations of either the UKF or EKPF with a large number of particles appear to more accurately represent the shape of inclusions compared to the standard EKF for some of the cases. The UPF, EnKF, and EnKPF reconstructions yield poor approximations of the experimental conductivity distributions.
