Estimating Wideband Polynomial Phase Signals in Sensor Arrays Using the Extended Kalman Filter

In the present paper, we consider the problem of parameter estimation of wideband polynomial phase signals (PPS) impinging on a uniform linear array antenna. The parameters of interest are the polynomial phase coefficients and the direction of arrival of the signal. The principle of estimation is based on the introduction of an exact but unfortunately nonlinear state space modelization, of the wideband PPS, which compels us to use the extended Kalman filter (EKF) instead of the usual Kalman filter. Furthermore, we propose a solution to the problem of initialization of the EKF since the initial conditions are assumed to be unavailable. The proposed solution is based on the use of the high-order ambiguity function, generally used to estimate PPS, and the CramerRao bounds. Under this solution, the numerical simulations show that the use of the EKF improves existing methods in terms of statistical performances since the EKF-based estimators exhibit high performances. Keywords—Cramer-Rao bound, direction of arrival, Extended Kalman filter, high-order ambiguity function, parameter estimation, wideband polynomial phase signal.