Chengfang Ren

Performance bounds under misspecification model for MIMO radar application

Recent tools established on misspecified lower bound on the mean square error allow to predict more accurately the mean square error behavior than the classical lower bounds in presence of model. errors. These bounds are helpful since model errors exist in practice due to system imperfections. In this paper, we are interested in the direction of arrival and direction of departure estimation in MIMO radar context with array elements position error. A closed-form expression is derived for the misspecified Cramér-Rao bound (or Huber limit) for any antennas geometry. A comparison of the misspecified Cramér-Rao bound with the classical Cramér-Rao bound and with the maximum likelihood estimator mean square error highlights the tightness improvement resulting from the use of the proposed bound.

Hybrid lower bound on the MSE based on the Barankin and Weiss-Weinstein bounds

This article investigates hybrid lower bounds in order to predict the estimators mean square error threshold effect. A tractable and computationally efficient form is derived. This form combines the Barankin and the Weiss-Weinstein bounds. This bound is applied to a frequency estimation problem for which a closed-form expression is provided. A comparison with results on the hybrid Barankin bound shows the superiority of this new bound to predict the mean square error threshold.

A Ziv-Zakaï type bound for hybrid parameter estimation

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. In this communication, we propose a new hybrid lower bound which, for the first time, includes the Ziv-Zakaï bound well known for its tightness in the Bayesian context (random parameters only). For the general case of parameterized mean model with Gaussian noise, closed-form expressions of the proposed bound are provided.

Hybrid Barankin–Weiss–Weinstein Bounds

This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay-Seidman bound and the Weiss-Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound.

Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér-Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified.

On the Accuracy and Resolvability of Vector Parameter Estimates

In this paper we address the problem of fundamental limitations on resolution in deterministic parameters estimation. We introduce a definition of resolvability based on probability and incorporating a requirement for accuracy unlike most existing definitions. Indeed in many application the key problem is to obtain distributions of estimates that are not only distinguishable but also accurate and compliant with a required precision. We exemplify the proposed definition with estimators that produce normal estimates, as in the conditional model for which the Gaussianity and efficiency of maximum likelihood estimators (MLEs) in the asymptotic region of operation (in terms of signal-to-noise ratio and/or in large number of snapshots) is well established, even for a single snapshot. In order to measure the convergence in distribution, we derive a simple test allowing to check whether the conditional MLEs operate in the asymptotic region of operation. Last, we discuss the resolution of two complex exponentials with closely spaced frequencies and compare the results obtained with the ones provided by the various statistical resolution limit released in the open literature.

Information–Estimation Relationship in Mismatched Gaussian Channels

In this letter, we investigated the connection between information and estimation measures for mismatched Gaussian models. In addition to the input prior mismatch, we take into account the noise mismatch and establish a new relation between relative entropy and excess mean square error. The derived formula shows that the input prior mismatch may be canceled by the noise mismatch. Finally, an example illustrates the impact of model mismatches on estimation accuracy.

Performance bounds for coupled models

Two models are called “coupled” when a non empty set of the underlying parameters are related through a differentiable implicit function. The goal is to estimate the parameters of both models by merging all datasets, that is, by processing them jointly. In this context, we show that the parameter estimation accuracy under a general class of dataset distributions always improves when compared to an equivalent uncoupled model. We eventually illustrate our results with the fusion of multiple tensor data.

A constrained hybrid Cramér-Rao bound for parameter estimation

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. However in many systems both random and non-random parameters may occur simultaneously. In this communication, we propose a constrained hybrid lower bound which take into account of equality constraint on deterministic parameters. The usefulness of the proposed bound is illustrated with an application to radar Doppler estimation.