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Abstract This paper considers a class of nonlinear filtering algorithms based on variational Bayesian (VB) theory to settle the unknown measurement noise problem in target tracking system. When the unknown measurement noise is conditionally independent of states, based on the variational idea, estimate of probability density function of state is converted into approximation two probability density functions for both unknown noise and nonlinear states. Then, an iterative algorithm is established to jointly estimate the state and the unknown measurement noise using variational Bayesian inference. Thus, the unknown measurement noise could be estimated as hidden state. The convergence result of the proposed nonlinear probability density function approximation algorithm is also given. The simulation results of typical examples show that the proposed VB based methods have superior performance to these classic algorithms in target tracking problems. [ABSTRACT FROM AUTHOR]

It usually suffers from long observing time and interference sensitivity when a radar transmits the high-range-resolution stepped-frequency chirp signal. Motivated by this, only partial pulses of the stepped-frequency chirp are utilized. For the obtained incomplete frequency data, a Bayesian model based on transfer learning is proposed to reconstruct the corresponding full-band frequency data. In the training phase, a complex beta process factor analysis (CBPFA) model is utilized to statistically model each aspect-frame from a set of given full-band frequency data, whose probability density function (pdf) can be learned from this CBPFA model. It is important to note that the numbers of factors and dictionaries are automatically learned from the data. The inference of CBPFA can be performed via the variational Bayesian (VB) method. In the reconstruction phase for the incomplete frequency data that “related” to the training samples, its corresponding full-band frequency data can be analytically reconstructed via the compressive sensing (CS) method and Bayesian criterion based on the transfer knowledge of the previous pdfs learned from the training phase. About the “relatedness” between each training frame and the incomplete test frequency data, we utilize the frame condition distribution of incomplete test frequency data to represent. The proposed method is validated on the measured high range resolution (HRR) data. [ABSTRACT FROM PUBLISHER]

In an uncertain ocean environment, the environmental model used by matched field processing (MFP) is different from the real world. As a result of the environmental mismatch, the performance of MFP deceases largely. In order to improve its robustness to the environmental mismatch, a posterior probability constraint matched field processing (MFP-PPC) is proposed. The algorithm derives the posterior probability density (PPD) of the source locations from Bayesian criterion, then the main lobe of AMFP is protected by PPD, so MFP-PPC has not only the merit of high resolution as AMFP, but also the advantage of robustness. To evaluate the algorithm, the simulated and experimental data in an uncertain shallow ocean environment are used. The results show that MFP-PPC is robust not only to the moored source in the uncertain ocean environment, but also to the moving source. The tracking curve is consistent with the trajectory of the moving source. [ABSTRACT FROM AUTHOR]

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration. [ABSTRACT FROM AUTHOR]