Recursive Algorithms for the Estimation of Multiple Superimposed Undamped Tones and Their Application to Radar Systems

Abstract

In this article, two recursive algorithms for the detection of multiple superimposed tones in noise and the estimation of their parameters are derived. They are based on a maximum likelihood approach and combine an innovative single-tone estimator with a serial cancellation procedure. Our numerical results lead to the conclusion that the developed methods can achieve a substantially better accuracy-complexity tradeoff than various related techniques in the presence of multiple closely spaced tones. Moreover, they can be exploited to detect multiple closely spaced targets and estimate their spatial coordinates in multiple-input multiple-output frequency-modulated continuous wave radar systems.

Novel Movement-Based Methods for the Calibration of Colocated Multiple-Input Multiple-Output Radars

“…In this section, various numerical results, obtained for the TC, FF-MBC and NF-MBC of the radar device described in Subsection V-A, are analysed. In generating these results, the following choices have been made for the considered calibration methods: TC -The complex single frequency estimation and cancellation (CSFEC) algorithm developed in [29] has been used for estimating the frequency and the complex amplitude (and, consequently, the phase) of the complex tone associated with the employed reference target in place of the periodogram method; this choice has allowed us to achieve a better accuracy. Moreover, the following parameters have been selected for the CSFEC: 1) FFT order N 0 = 8192 (corresponding to an oversampling factor L equal to 16, since N = 512); 2) number of iterations N it = 8.…”

“…Moreover, in our experiments, since the reference target adopted for NF-MBC was close to the radar, it was easy to measure its distance with sufficient accuracy and validate the effectiveness of target range estimation through (89). In this case, since we were able to reliably estimate the reference tar-get position, the absolute range bias can be trivially assessed by evaluating (78) and (29).…”

“…8 Note that a more accurate algorithm for the estimation of both parameters can be adopted in place of that proposed here (e.g., see [29] and references therein). (see (25) and ( 26), with Z = RX), respectively, are evaluated for the mth RX antenna (for any m).…”