Asymptotically Tight Bayesian Cramér-Rao Bound

Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB (BCRB) in the Bayesian framework. However, unlike the CRB, the BCRB is asymptotically unattainable in general, and its equality condition is restrictive. This paper introduces an extension of the Bobrovsky--Mayer-Wolf--Zakai class of bounds, also known as the weighted BCRB (WBCRB). The WBCRB is optimized by tuning the weighting function in the scalar case. Based on this result, we propose an asymptotically tight version of the bound called AT-BCRB. We prove that the AT-BCRB is asymptotically attained by the maximum {\it a-posteriori} probability (MAP) estimator. Furthermore, we extend the WBCRB and the AT-BCRB to the case of vector parameters. The proposed bounds are evaluated in several fundamental signal processing examples, such as variance estimation of white Gaussian process, direction-of-arrival estimation, and mean estimation of Gaussian process with unknown variance and prior statistical information. It is shown that unlike the BCRB, the proposed bounds are asymptotically attainable and coincide with the expected CRB (ECRB). The ECRB, which imposes uniformly unbiasedness, cannot serve as a valid lower bound in the Bayesian framework, while the proposed bounds are valid for any estimator.

MCRB on DOA Estimation for Automotive MIMO Radar in the Presence of Multipath

Autonomous driving and advanced active safety features require accurate high-resolution sensing capabilities. Automotive radars are the key component of the vehicle sensing suit. However, when these radars operate in proximity to flat surfaces, such as roads and guardrails, they experience a multipath phenomenon that can degrade the accuracy of the direction-of-arrival (DOA) estimation. Presence of multipath leads to misspecification in the radar data model, resulting in estimation performance degradation, which cannot be reliably predicted by conventional performance bounds. In this paper, the misspecified Cram\'er-Rao bound (MCRB), which accounts for model misspecification, is derived for the problem of DOA estimation in the presence of multipath which is ignored by the estimator. Analytical relations between the MCRB and the Cram\'er-Rao bound are established, and the DOA estimation performance degradation due to multipath is investigated. The results show that the MCRB reliably predicts the asymptotic performance of the misspecified maximum-likelihood estimator and therefore, can serve as an efficient tool for automotive radar performance evaluation and system design.

Barankin-Type Bound for Constrained Parameter Estimation

In constrained parameter estimation, the classical constrained Cramer-Rao bound (CCRB) and the recent Lehmann-unbiased CCRB (LU-CCRB) are lower bounds on the performance of mean-unbiased and Lehmann-unbiased estimators, respectively. Both the CCRB and the LU-CCRB require differentiability of the likelihood function, which can be a restrictive assumption. Additionally, these bounds are local bounds that are inappropriate for predicting the threshold phenomena of the constrained maximum likelihood (CML) estimator. The constrained Barankin-type bound (CBTB) is a nonlocal mean-squared-error (MSE) lower bound for constrained parameter estimation that does not require differentiability of the likelihood function. However, this bound requires a restrictive mean-unbiasedness condition in the constrained set. In this work, we propose the Lehmann-unbiased CBTB (LU-CBTB) on the weighted MSE. This bound does not require differentiability of the likelihood function and assumes Lehmann-unbiasedness, which is less restrictive than the CBTB mean-unbiasedness. We show that the LU-CBTB is tighter than or equal to the LU-CCRB and coincides with the CBTB for linear constraints. For nonlinear constraints the LU-CBTB and the CBTB are different and the LU-CBTB can be a lower bound on the WMSE of constrained estimators in cases, where the CBTB is not. In the simulations, we consider direction-of-arrival estimation of an unknown constant modulus discrete signal. In this case, the likelihood function is not differentiable and constrained Cramer-Rao-type bounds do not exist, while CBTBs exist. It is shown that the LU-CBTB better predicts the CML estimator performance than the CBTB, since the CML estimator is Lehmann-unbiased but not mean-unbiased.

Neural Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with a-priori unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.