Performance bounds under misspecification model for MIMO radar application

IEEE Signal Process. Mag.

Gini

Greco

et al. 2017

117

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few.Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf), which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest.Motivated by the widespread and practical need to assess the performance of a "mismatched" estimator, the goal of this paper is to help to bring attention to the main theoretical

Section: Some Historical Backgroundmentioning

confidence: 99%

Section: A Covariance Inequality In the Presence Of Misspecified Modelsmentioning

confidence: 99%

Section: Examples Of Applicationsmentioning

confidence: 99%

See 1 more Smart Citation

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications

IEEE Signal Process. Mag.

Gini

Greco

et al. 2017

117

“…Regarding the Gaussian model assumption, large-scale measurement campaigns and the subsequent statistical analysis of the data gathered from a plethora of engineering applications, e.g. outdoor/indoor mobile communications, radar/sonar systems or magnetic resonance imag-riety of well-known engineering problems: to Direction-of-Arrival (DoA) estimation in array and MIMO processing [7,10] , to covariance/scatter matrix estimation in CES distributed data [8,11,12] , to radar-communication systems coexistence [13] and to waveform parameter estimation in the presence of uncertainty in the propagation model [14] , just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Slepian-Bangs-type formulas and the related Misspecified Cramér-Rao Bounds for Complex Elliptically Symmetric distributions

Mennad

Korso³

et al. 2018

Signal Processing

S. Fortunati). ing (MRI), have highlighted the impulsive, heavy-tailed behaviour of the observations [1] . These experimental evidences have motivated the need to go beyond the Gaussian model and develop new statistical models able to better characterize the data. One of the more flexible and general non-Gaussian model is represented by the set of the Complex Elliptically Symmetric (CES) distributions [2] , also called Multivariate Elliptically Contoured distributions [3] . CES distributions encompasses the complex Gaussian, the Generalized Gaussian and all the Compound Gaussian (CG) distributions, such as the complex t -distribution and the K -distribution, as special cases. The pdf of a CES distributed N -dimensional random vector x l ∈ C N is completely characterized by the mean value γ, the scatter (or shape) matrix and by a real valued function w (t) : R + → R , called the density generator , i.e. x l ∼ CES N ( γ, , w ) [2,3] . The CES distributions have been used in a variety of applications, in particular in the radar and array signal processing fields.Other experimental evidences reveal recurring violations of the matched model assumption, that is the claim of a perfect match between the assumed and the true data model. The mathematical bases of a formal theory of the parameter estimation under model misspecification has been firstly developed by statisticians as Huber [4] , White [5] and Vuong [6] and recently rediscovered by the Signal Processing (SP) community [7-9] and applied to a va-

“…More recently, a different proof of the same MCRB has been proposed by Richmond and Horowitz in [1], where an extension of this bound to complex parameter vectors has been also provided and applied to the DOA estimation problem. In [5], the MCRB for the joint DOA-DOD estimation in MIMO radars has been obtained by stacking the real and the imaginary parts of the complex parameters. In this paper, we provide a general expression of the MCRB for complex unconstrained (Theorem 1) and constrained (Theorem 2) parameter vectors that can be applied to both circular and non-circular (i.e.…”

Section: Introductionmentioning

confidence: 99%

Misspecified Cramér-rao bounds for complex unconstrained and constrained parameters

2017 25th European Signal Processing Conference (EUSIPCO)

2017