The asymptotic normality for the least squares estimator of parameters in a two dimensional sinusoidal model of observations

Consistency of the LSE for Chirp Signal Parameters in the Models with Strongly and Weakly Dependent Noise

“…Over the last decades trigonometric models on the plane, where under the signs of cosines and sines are linear forms of two variables with unknown frequencies as coefficients, have received special attention in the literature on signal and image processing due to their wide applications in the analysis of symmetrical textured surfaces. See, for example, Rao, Zhao, and Zhou (1994), Kundu and Mitra (1996), Zhang and Mandrekar (2001), Kundu and Nandi (2003), Nandi, Kundu, and Srivastava (2013), Ivanov and Malyar (2018), Ivanov and Lymar (2020).…”

Asymptotic normality of the LSE for chirp signal parameters

“…Since the Taylor formula for vectors does not exist, equality (11) needs clarification. We write 4N Taylor formulas for coordinates of the vector Q T (θ T ) and obtain for each such expansion its own intermediate value θ i depending on T , which has the property θ i − θ 0 ≤ θ T − θ 0 , i = 1, 4N .…”

“…Over the past decades, in the literature on signal and image processing sinusoidal statistical models on the plane have been intensively studied due to their multiple applications in the analysis of the symmetrical textured surfaces. See, for example, [27,16,28,17,25,12,11]. Some of scalar and 2D results are generalized to trigonometric regression models on R M , M ≥ 3, in the papers [3,13,10].…”