Finite Horizon Maximum Likelihood Estimation for Integrated Navigation with RF Beacon Measurements

We develop a Finite Horizon Maximum Likelihood Estimator (FHMLE) that fuses Inertial Measurement Unit (IMU) and radio frequency (RF) measurements over a sliding window of finite length for three-dimensional navigation. Available RF data includes pseudo-ranges, angles of transmission (AoT), and Doppler shift measurements. The navigation estimates are obtained by solving a finite-dimensional nonlinear optimization using a primal-dual interior point algorithm (PDIP). The benefits of the proposed estimation method are highlighted using simulations results comparing the FHMLE approach with an Unscented Kalman Filter (UKF), in a scenario where an aircraft approaches a carrier, with RF measurements from beacons aboard the carrier, and low-cost IMU measurements aboard the aircraft. When the Geometric Dilution of Precision is large, we found that the FHMLE is able to achieve smaller estimation errors than the UKF, which tends to carry a bias throughout the trajectory.