Statistics and Probability, Modeling and Simulation
3
Scopus Publications
10
Scholar Citations
2
Scholar h-index
Scopus Publications
On Weighted Least Squares Estimation of Elementary Chirp Model Anjali Mittal, Debasis Kundu, Amit Mitra IEEE Transactions on Aerospace and Electronic Systems, 2025 In this article, we consider the estimation of the parameters of a multiple-component elementary chirp model based on weighted least squares estimators (WLSEs). Recently, Mittal et al. (2023) have proposed least squares estimators (LSEs) to estimate the parameters of the elementary chirp model. However, it has been observed that LSEs are quite sensitive to outliers. The least absolute deviation estimators and Huber's M-estimators are robust estimators for estimation in the presence of outliers. However, computing these robust estimators is numerically challenging, and deriving their statistical properties is not straightforward under the same error assumption as LSEs. We prove the strong consistency and asymptotic normality of WLSEs under the same error assumptions as those of LSEs. We have also considered sequential WLSEs to estimate the parameters, which are less computationally involved and have the same asymptotic properties as WLSEs. Based on extensive numerical studies, it has been observed that the behavior of the proposed estimators is better than that of LSEs in the presence of outliers. We also discuss the choice of weight function, as the performance of the proposed estimators depends on the weight function. For illustration, we have presented a simulation study, where outliers are present anywhere in the data, not only in a specific portion. We have also analyzed a synthetic dataset and a real dataset. The performance is quite satisfactory.
Estimation of the Elementary Chirp Model Parameters Anjali Mittal, Rhythm Grover, Debasis Kundu, Amit Mitra IEEE Transactions on Aerospace and Electronic Systems, 2023 In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one component elementary chirp model. It is proved that the proposed estimators are strongly consistent and follow the normal distribution asymptotically. We also suggest how to obtain proper initial values for these methods. The problem of finding initial values is a difficult problem when the number of components in the model is large, or when the signal-to-noise ratio is low, or when two frequency rates are close to each other. We propose sequential procedures to estimate the multiple component elementary chirp model parameters. We prove that the theoretical properties of sequential least squares estimators and sequential approximate least squares estimators coincide with those of least squares estimators and approximate least squares estimators, respectively. Further, the asymptotic variances of the proposed estimators attain the Cramér-Rao lower bounds asymptotically when errors are normal random variables and independently and identically distributed. To evaluate the performance of the proposed estimators, numerical experiments are performed. It is observed that the proposed sequential estimators perform well even in situations where least squares estimators do not perform well. We illustrate the performance of the proposed sequential algorithm on a bat data.
On Efficient Parameter Estimation of Elementary Chirp Model Anjali Mittal, Rhythm Grover, Debasis Kundu, Amit Mitra IEEE Transactions on Signal Processing, 2023 Elementary chirp signals can be found in various fields of science and engineering. We propose two computationally efficient algorithms based on the choice of two different initial estimators to estimate the parameters of the elementary chirp model. It is observed that the proposed efficient estimators are consistent; they have the identical asymptotic distribution as that of the least squares estimators and they are also less computationally intensive. We also propose sequential efficient procedures to estimate the parameters of the multi-component elementary chirp model. The asymptotic properties of the sequential efficient estimators coincide with the least squares estimators. The important point about the efficient and sequential efficient algorithms is that these algorithms produce efficient frequency rate estimators in a fixed number of iterations. Another important point is that the under normal error assumption the theoretical variances of the proposed estimators achieve the Cramér-Rao lower bounds asymptotically. Simulation experiments are performed to see the performance of the proposed estimators, and it is observed that they are computationally efficient, take less time in computation than the other existing methods and perform well when two frequency rates are close to each other upto a reasonably low degree of separation. On an EEG dataset, we demonstrate the performance of the proposed algorithm.
RECENT SCHOLAR PUBLICATIONS
On Weighted Least Squares Estimation of Elementary Chirp Model A Mittal, D Kundu, A Mitra IEEE Transactions on Aerospace and Electronic Systems , 2025 2025 Citations: 1
On efficient parameter estimation of elementary chirp model A Mittal, R Grover, D Kundu, A Mitra IEEE Transactions on Signal Processing 71, 2352-2365 , 2023 2023 Citations: 3
Estimation of the elementary chirp model parameters A Mittal, R Grover, D Kundu, A Mitra IEEE Transactions on Aerospace and Electronic Systems 59 (5), 5218-5234 , 2023 2023 Citations: 6
MOST CITED SCHOLAR PUBLICATIONS
Estimation of the elementary chirp model parameters A Mittal, R Grover, D Kundu, A Mitra IEEE Transactions on Aerospace and Electronic Systems 59 (5), 5218-5234 , 2023 2023 Citations: 6
On efficient parameter estimation of elementary chirp model A Mittal, R Grover, D Kundu, A Mitra IEEE Transactions on Signal Processing 71, 2352-2365 , 2023 2023 Citations: 3
On Weighted Least Squares Estimation of Elementary Chirp Model A Mittal, D Kundu, A Mitra IEEE Transactions on Aerospace and Electronic Systems , 2025 2025 Citations: 1
