## A Noniterative Maximum Likelihood Parameter Estimator of Superimposed Chirp Signals

Citations: | 6 - 0 self |

### BibTeX

@MISC{Saha_anoniterative,

author = {Supratim Saha and Steven Kay},

title = {A Noniterative Maximum Likelihood Parameter Estimator of Superimposed Chirp Signals},

year = {}

}

### OpenURL

### Abstract

We address the problem of parameter estimation of superimposed chirp signals in noise. The approach used here is a computationally modest implementation of a maximum likelihood (ML) technique. The ML technique for estimating the complex amplitudes, chirping rates and frequencies reduces to a separable optimization problem where the chirping rates and frequencies are determined by maximizing a compressed likelihood function which is a function of only the chirping rates and frequencies. Since the compressed likelihood function is multidimensional, its maximization via grid search is impractical. We propose a non-iterative maximization of the compressed likelihood function using importance sampling. Simulation results are presented for a scenario involving closely spaced parameters for the individual signals.

### Citations

801 |
Fundamentals of Statistical Signal Processing: Estimation Theory
- Kay
- 1993
(Show Context)
Citation Context ...of a ML estimator for the chirp signal parameters. To develop the estimator, we first show that the data model involves estimation of linear and nonlinear parameters of a partial general linear model =-=[1]-=-. The complex amplitudes form the linear parameter vector and the chirp rates and frequencies form the nonlinear parameter vector. The parameter estimation gets decoupled, where the nonlinear paramete... |

12 |
Hierarchical Bayesian Analysis Using Monte Carlo Integration: Computing Posterior Distributions When There are Many Possible Models
- Stewart
- 1987
(Show Context)
Citation Context ...mber of signals. To carry out this maximization non-iteratively we use a global optimization theorem proposed in [2]. To efficiently implement the optimization, we use Monte Carlo Importance Sampling =-=[4]-=-. It is observed that the technique produces good estimates for the unknown parameters even in cases where the individual parameters are closely spaced. Furthermore, the computational burden is quite ... |

9 | The circular nature of discrete-time frequency estimates
- Lovell, Kootsookos, et al.
- 1991
(Show Context)
Citation Context ...her use � and� of the limited ranges of ¢ and � £ in reducing the computations. and � ¢ , they posses � £ the properties of a circular ranSince��� dom variable. Circular mean also =-=alleviates the bias [7]. We thus compute th-=-e circular means and obtain the angle of the circular means to compute . ��� The expressions for the � � � � estimates based on the circular mean � definition are � given by, and� ... |

3 |
Parameter estimation for superimposed chirp signals
- Liang, Arun
- 1992
(Show Context)
Citation Context ... shown in [6] that the problem of range and direction of arrival estimation for moderately far, broadside targets reduces to that of estimating the parameters of sums of chirp signals. Liang and Arun =-=[5]-=- have also addressed an iterative maximum likelihood (ML) approach to this problem. Rank reduction techniques were used to get good initial parameter estimates, which were then used in a maximum likel... |

1 |
A Closed Form Solution for Certain Programming
- Pincus
- 1962
(Show Context)
Citation Context ...id search which is impractical and whose computational complexity increases with the number of signals. To carry out this maximization non-iteratively we use a global optimization theorem proposed in =-=[2]-=-. To efficiently implement the optimization, we use Monte Carlo Importance Sampling [4]. It is observed that the technique produces good estimates for the unknown parameters even in cases where the in... |

1 |
Nonstationary Signal Analysis”, Chapter 2
- Ramalingam
- 1995
(Show Context)
Citation Context ...ntered in many different engineering applications including radar, active sonar and passive sonar systems. The problem of parameter estimation of chirp signals has received a great deal of attention, =-=[3]-=-. These approaches have been proven to be effective in the sense that they achieve the Cramer Rao Lower Bound (CRLB). However most of these approaches are designed for a single chirp signal. Parameter... |

1 |
A Closed Form Solution for Instantaneous Amplitude and Frequency Estimation: Performance Bounds and applications to source localization
- Arun, Liang
- 1991
(Show Context)
Citation Context ...mposed chirp signals is a difficult signal processing problem. The need for determining the parameters of superimposed chirp signals arises in passive sensor array systems, where it has been shown in =-=[6]-=- that the problem of range and direction of arrival estimation for moderately far, broadside targets reduces to that of estimating the parameters of sums of chirp signals. Liang and Arun [5] have also... |