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Article
Cramér-Rao bounds for estimating range, velocity, and direction with an active array
IEEE Transactions on Signal Processing (2001)
  • Aleksandar Dogandžić, University of Illinois at Chicago
  • Arye Nehorai, University of Illinois at Chicago
Abstract
We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional (3-D) array with isotropic sensors in spatially white noise and show that it is a function of the array geometry only through the “moments of inertia” of the array. The volume of the confidence region for the target's location is proposed as a measure of accuracy. For this measure, we show that the highest (and lowest) target location accuracy is achieved if the target lies along one of the principal axes of inertia of the array. Finally, we compare the location accuracies of several array geometries
Keywords
  • Doppler shift,
  • FM radar,
  • Array signal processing,
  • Chirp modulation,
  • Delay estimation,
  • Direction-of-arrival estimation,
  • Radar signal processing,
  • Sequences,
  • Sonar signal processing,
  • White noise
Disciplines
Publication Date
2001
Publisher Statement
© 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Citation Information
Aleksandar Dogandžić and Arye Nehorai. "Cramér-Rao bounds for estimating range, velocity, and direction with an active array" IEEE Transactions on Signal Processing Vol. 49 Iss. 6 (2001)
Available at: http://works.bepress.com/aleksandar_dogandzic/17/