The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase

Peleg, Shir; Porat, B.

doi:10.1109/78.80864

Cited by 236 publications

(95 citation statements)

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“…Existing motion parameter estimation techniques (e.g., [13][14][15]) are based on time-frequency analysis of Doppler signatures of received signals, which are commonly modeled as general-order polynomials [16]. For a moderately long coherent processing interval (CPI), it suffices to model the target motion by a second-order polynomial or a linear frequency-modulated signal.…”

Section: Introductionmentioning

confidence: 99%

Motion parameter estimation of multiple ground moving targets in multi-static passive radar systems

Subedi

Zhang

Amin

et al. 2014

EURASIP J. Adv. Signal Process.

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Multi-static passive radar (MPR) systems typically use narrowband signals and operate under weak signal conditions, making them difficult to reliably estimate motion parameters of ground moving targets. On the other hand, the availability of multiple spatially separated illuminators of opportunity provides a means to achieve multi-static diversity and overall signal enhancement. In this paper, we consider the problem of estimating motion parameters, including velocity and acceleration, of multiple closely located ground moving targets in a typical MPR platform with focus on weak signal conditions, where traditional time-frequency analysis-based methods become unreliable or infeasible. The underlying problem is reformulated as a sparse signal reconstruction problem in a discretized parameter search space. While the different bistatic links have distinct Doppler signatures, they share the same set of motion parameters of the ground moving targets. Therefore, such motion parameters act as a common sparse support to enable the exploitation of group sparsity-based methods for robust motion parameter estimation. This provides a means of combining signal energy from all available illuminators of opportunity and, thereby, obtaining a reliable estimation even when each individual signal is weak. Because the maximum likelihood (ML) estimation of motion parameters involves a multi-dimensional search and its performance is sensitive to target position errors, we also propose a technique that decouples the target motion parameters, yielding a two-step process that sequentially estimates the acceleration and velocity vectors with a reduced dimensionality of the parameter search space. We compare the performance of the sequential method against the ML estimation with the consideration of imperfect knowledge of the initial target positions. The Cramér-Rao bound (CRB) of the underlying parameter estimation problem is derived for a general multiple-target scenario in an MPR system. Simulation results are provided to compare the performance of the sparse signal reconstruction-based methods against the traditional time-frequency-based methods as well as the CRB.

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Section: Introductionmentioning

confidence: 99%

Motion parameter estimation of multiple ground moving targets in multi-static passive radar systems

Subedi

Zhang

Amin

et al. 2014

EURASIP J. Adv. Signal Process.

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“…Figure 4 plots the performance of the proposed algorithm for different signal lengths, 256, 512 and 1024 samples, and compares our results with Cramer-Rao lower bound (CRLB) [26] and Zheng and Shi's MACF algorithm given in [16]. The results show that the proposed method nearly achieves the CRLB for SNR values as low as −7dB.…”

Section: Estimating Chirp-rate Using Fractional Fourier Transformentioning

confidence: 70%

A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform

Serbes

Aldimashki

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this work, a fast and accurate chirp-rate estimation algorithm is presented. The algorithm is based on the fractional Fourier transform. It is shown that utilization of the golden section search algorithm to find the maximum magnitude of the fractional Fourier transform domains not only accelerates the process, but also increases the accuracy in a noisy environment. Simulation results validate the proposed algorithm and show that the accuracy of parameter estimation nearly achieves the Cramer-Rao lower bound for SNR values as low as −7dB.

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“…A general bound, even if approximate, will be practically useful. This can be done by extending the analysis in [32] to yield a large sample approximation on any IF estimator as CRB (18) where is the observed data size, and is the order of the IP. , where !…”

Section: A Polynomial Modelmentioning

confidence: 99%

Auditory motivated level-crossing approach to instantaneous frequency estimation

Sekhar

Sreenivas

2005

IEEE Trans. Signal Process.

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Abstract-We address the problem of estimating the instantaneous frequency (IF) of a phase signal using its level-crossing (LC) information based on front-end auditory processing motivation. We show that the problem of IF estimation using LC information can be cast in the framework of estimation from irregularly sampled data. The formulation has the generality of estimating different types of IF without the need for a quasistationary assumption. We consider two types of IF-polynomial and bandlimited; we use polynomial interpolating functions for the former, and for the latter, we propose a novel "line plus sum of sines" model.

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The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase

Cited by 236 publications

References 1 publication

Motion parameter estimation of multiple ground moving targets in multi-static passive radar systems

Motion parameter estimation of multiple ground moving targets in multi-static passive radar systems

A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform

Auditory motivated level-crossing approach to instantaneous frequency estimation

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