Target Doppler Rate Estimation Based on the Complex Phase of STFT in Passive Forward Scattering Radar

Abstract

This article presents a novel approach to the estimation of motion parameters of objects in passive forward scattering radars (PFSR). In such systems, most frequency modulated signals which are used have parameters that depend on the geometry of a radar scene and an object’s motion. Worth noting is that in bistatic (or multistatic) radars forward scattering geometry is present thus in this case only Doppler measurements are available while the range measurement is unambiguous. In this article the modulation factor, also called the Doppler rate, was determined based on the chirp rate (equivalent Doppler rate) estimation concept in the time-frequency (TF) domain. This approach utilizes the idea of the complex phase of the short-time Fourier transform (STFT) and its modification known from the literature. Mathematical dependencies were implemented and verified and the simulation results were described. The accuracy of the considered estimators were also verified using the Cramer-Rao lower bound (CRLB) to which simulated data for the considered estimators was compared. The proposed method was validated using a real-life signal collected from a radar operating in PFSR geometry. The Doppler rate provided by a car crossing the baseline between the receiver and the GSM transmitter was estimated. Finally, the concept of using CR estimation, which in the case of PFSR can be understood as Doppler rate, was confirmed on the basis of both simulated and real-life data.

Detection of LFM Radar Signals and Chirp Rate Estimation Based on Time-Frequency Rate Distribution

“…Next, the STFT for the optimal window is performed to obtain rough estimates of parameters (including the parameter) [ 25 ], which are used as initial conditions in the ML procedure. The concept of the complex phase of the STFT results in additional new structures of instantaneous estimators for LFM signals [ 26 ].…”

Double‐adaptive chirplet transform for radar signature extraction

“…In (5)–(7) is the real part and is the imaginary part. Extended equations, as well as the interpretation and limitations of these tools, are widely described in [27, 29–35], so the considerations will not be duplicated in this paper and the author will focus only on their applications. In fact, the method provides calculation of the instantaneous frequency rate for each coordinate of the two‐dimensional signal distribution, and in most practical aspects, they can be used interchangeably, giving similar outcomes.…”

“…The signal was analysed using one of the estimators and then processed using adaptive algorithms using the same estimator. The analysis window width determines the Cramer‐Rao lower bound [35] and was samples during the simulations.…”

The Use of the Reassignment Technique in the Time-Frequency Analysis Applied in VHF-Based Passive Forward Scattering Radar

“…Thus, any additional characterization of the target movement is significant in this case. In the literature, different approaches are proposed in order to estimate motion parameters, such as spectrogram analysis [ 22 ], chirp rate estimation in the time-frequency (TF) domain [ 23 ], or the Radon transform [ 20 ]. This paper refers to the latter example, and the authors of this work proposed the method known from the literature to improve the resolution of the TF distribution using the TF reassignment technique in order to distinguish the kinematic parameter of the cooperative target using the Hough transform, which can be interpreted as a discrete realization of the Radon transform [ 24 , 25 ].…”