A Low Complexity Blind Estimator of Narrowband Polynomial Phase Signals

Abstract

Abstract-Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio.Index Terms-Algebraic constant modulus algorithm, blind estimation, maximum likelihood estimation, polynomial phase signals, synthetic aperture radar.

A Novel Parameter Estimation Method Based on LSU-EKF for Polynomial Phase Signal

“…Therefore, precise estimations of range, velocity, and acceleration obtained from the echoes of high-speed targets, such as rockets and missiles, are of great importance for radar detection and imaging [9,10]. In recent years, parameter estimation of PPS has attracted considerable attention and many methods have been proposed [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Among these methods, a typical estimator of the unknown coefficients is the least squares estimator [11,12], which is an effective approach, being both computationally efficient and statistically accurate when the noise is white and Gaussian.…”

An efficient joint estimation of wideband polynomial-phase signal parameters and direction-of-arrival in sensor array

“…Numerous publications address the problem of estimating the PPS parameters along with the direction-of-arrival (DOA) [7][8][9][10][11][12]. Gershman et al [9], consider the joint estimation of DOA and PPS parameters using a technique called the polynomial-phase beamformer.…”

“…The EKF can also be used with multicomponent PPSs [11]. An important recent advance has been proposed in [12], where multiple PPSs impinging on non-calibrated arrays, common for practical trials, are considered. The effects of non-calibration are avoided and signal components are separated using a blind separation technique [7,12,13].…”

“…An important recent advance has been proposed in [12], where multiple PPSs impinging on non-calibrated arrays, common for practical trials, are considered. The effects of non-calibration are avoided and signal components are separated using a blind separation technique [7,12,13]. In [12], the precise estimation is performed by means of the phase unwrapping for each component separately under the assumption that the considered signal is narrowband.…”

“…We consider monocomponent PPSs impinging on a uniform linear array (ULA) of omnidirectional sensors, assuming that advanced techniques can be used for components separation and array calibration [7,12,13]. Furthermore, we do not introduce a restriction that the considered signal is narrowband as in [12] since such a restriction is hard to be satisfied in underwater systems [2]. The main tools used in the proposed technique are the HAF [14] and the cubic phase function (CPF) [15].…”