Sequential Bayesian Estimation While Drilling

Drilling systems and related methods are disclosed. A drilling system may include a drill bit positioned at an end of a drill string, and one or more sources and receivers positioned on the drill string behind the drill bit. The sources may be configured to emit signals into a medium surrounding a borehole in which the drill string extends, and the signals may cause a response in the medium at one or more predetermined positions ahead of the drill bit, and response signals may be measured by the one or more receivers. A processor may use the measured response signals to iteratively update an estimate of a property of the medium at the predetermined position, which in some embodiments, may be done using a sequential estimation process, as the drill string is advanced into the medium.