A Closed-Form Estimator Based on Array Invariant for Estimating the Initial State of Constant Velocity Target in Shallow Water

In this paper, we derive an improved instrumental variable estimator (IIVE) to estimate the initial state (position and velocity) of a constant velocity target in two-dimensional (2D) shallow water environment, based on azimuths and array invariant (AI) measurements collected by a moving horizontal linear array (HLA). Unlike the traditional instrumental variable estimator (IVE) based on azimuths measurements only, the proposed IIVE additionally exploits the characteristics of the waveguide by incorporating the AI measurements into the estimation process. The system of pseudolinear equations between the target initial state and the observer state is firstly derived based on the azimuths and AI measurements, with a rough estimation being derived from it. Then, the instrumental variable (IV) matrix, based on this rough solution, is applied for the bias reduction. Simulation results show that, the proposed IIVE based on azimuths and AI measurements outperforms its azimuths-only counterpart, providing a more reliable estimation of the target initial position and velocity.