Together with Peter Gerstoft and William S. Hodgkiss, we are currently working on the inversion of the electromagnetic signals, specifically the Refractivity From Clutter (RFC) problem. The main purpose of RFC is trying to infer the environment in which a sea-borne low altitude radar operates (where it is very common to have non-standard atmospheric propagation due to atmospheric phenomenon like the ducting). Then it is possible to estimate the effects of the environment on the radar performance and take necessary precautions to mitigate the adverse effects.

    An accurate knowledge of radio refractivity is essential in many radar and propagation applications. Especially at low altitudes, radio refractivity can vary considerably with both height and range, heavily affecting the propagation characteristics. One important example is the formation of an electromagnetic duct. A signal sent from a surface or low altitude source, such as a ship or low-flying object, can be totally trapped inside the duct. This will result in multiple reflections from the surface and they will appear as clutter rings in the radar plan position indicator (PPI) screen. In such cases, a standard atmospheric assumption may not give reliable predictions for a radar system operating in such an environment.

    Ducting is a phenomenon that is encountered mostly in sea-borne applications due to the abrupt changes in the vertical temperature and humidity profiles just above large water masses, which may result in an sharp decrease in the modified refractivity (M-profile) with increasing altitude. This will, in turn, cause the electromagnetic signal to bend downward, effectively trapping the signal within the duct. It is frequently encountered in many regions of the world such as the Persian Gulf, the Mediterranean, and California.

    RFC uses the clutter received by the radar to find the environmental parameters. The main advantage of RFC is its ability to estimate the M-profile using only the radar clutter return, which can readily be obtained during the normal radar operation, without requiring any additional measurements or hardware. A near-real-time estimation can be achieved with a sufficiently fast optimizer. Electromagnetic split-step FFT parabolic equation approximation to Maxwell's equations is used to propagate the signal. Various techniques are used to analyze/solve the problem (genetic algorithms-GA, Markov chain Monte Carlo-MCMC methods, hybrid GA-MCMC methods, extended and unscented  Kalman, particle and multiple model particle filters).

    Acoustic research focuses on the application of tracking techniques such as the extended Kalman (EKF), unscented Kalman (UKF), and particle (PF) filters into geoacoustic inversion problems. This enables spatial and temporal tracking of environmental parameters and their underlying probability densities, making geoacoustic tracking a natural extension to geoacoustic inversion techniques. Filter performances are compared in terms of filter efficiencies using the posterior Cramér-Rao lower bound. Tracking capabilities of the geoacoustic filters under slowly and quickly changing environments are studied in terms of divergence statistics. Geoacoustic tracking can provide continuously environmental estimates and their uncertainties using only a fraction of the computational power of classical geoacoustic inversion schemes. Inter-filter comparison show that, while a high-particle-number PF outperform the Kalman filters, there are many cases where all three filters perform equally well depending on the inversion configuration (such as the HLA vs. VLA and frequency) and the tracked parameters.

    We also work on the tracking of acoustic source parameters such as depth, range and speed in spatially and temporally changing ocean acoustic environments. Conventional matched-field processing requires an accurate knowledge of environmental parameters (e.g. sound speed profile (SSP), water depth, sediment and bottom parameters) for source localization. Since environmental mismatch may result in significant errors in source parameters, algorithms that minimize this mismatch should be employed. For this purpose, a particle filtering (PF) approach is adopted here where the geoacoustic parameters are tracked simultaneously with the source location and ship speed in a range-dependent environment. This allows real-time updating of the environment and accurate tracking of the moving source. As a sequential Monte Carlo technique that operates on nonlinear systems with non-Gaussian probability densities, the PF is an ideal algorithm to perform tracking of source and environmental parameters, and their uncertainties via the evolving posterior probability densities.