Modeling of observability during in-drilling alignment for horizontal directional drilling

Navigation performance is an important factor in horizontal directional drilling. In-drilling alignment (IDA) was previously suggested to improve downhole navigation performance when utilizing an inertial navigation system (INS). It was shown that the IDA process enhances the ability to estimate INS bias and drift errors and, particularly, their azimuth-related components. It was suggested that this improvement was related to a better observability that is achieved with the help of the induced dynamics during the IDA phase. The observability of a system is an important parameter that facilitates the estimation of the state parameters and the achievable accuracy of the system. However, observability models that are related to the IDA technique are lacking. This paper presents observability modeling of the newly suggested IDA process to aid horizontal drilling. The presented methodology clearly demonstrates that an induced motion during the IDA process increases system observability and converts the azimuth angle into an observable system state. Adequate system modeling profoundly influences the overall system observability. The utilization of the vertical damped model with a reduced state order is preferable for a faster and more efficient performance due to a decreased computational load but remains inferior when compared to a full system model.