Cramer-Rao Bounds for Target Tracking Problems Involving Colored Measurement Noise

2012 ◽  
Vol 48 (1) ◽  
pp. 620-636 ◽  
Author(s):  
H. C. Lambert
Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3611
Author(s):  
Yang Gong ◽  
Chen Cui

In multi-target tracking, the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter is a practical algorithm. Influenced by outliers under unknown heavy-tailed measurement noise, the SMC-PHD filter suffers severe performance degradation. In this paper, a robust SMC-PHD (RSMC-PHD) filter is proposed. In the proposed filter, Student-t distribution is introduced to describe the unknown heavy-tailed measurement noise where the degrees of freedom (DOF) and the scale matrix of the Student-t distribution are respectively modeled as a Gamma distribution and an inverse Wishart distribution. Furthermore, the variational Bayesian (VB) technique is employed to infer the unknown DOF and scale matrix parameters while the recursion estimation framework of the RSMC-PHD filter is derived. In addition, considering that the introduced Student- t distribution might lead to an overestimation of the target number, a strategy is applied to modify the updated weight of each particle. Simulation results demonstrate that the proposed filter is effective with unknown heavy-tailed measurement noise.


Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 907
Author(s):  
Xianghao Hou ◽  
Jianbo Zhou ◽  
Yixin Yang ◽  
Long Yang ◽  
Gang Qiao

The bearing-only tracking of an underwater uncooperative target can protect maritime territories and allows for the utilization of sea resources. Considering the influences of an unknown underwater environment, this work aimed to estimate 2-D locations and velocities of an underwater target with uncertain underwater disturbances. In this paper, an adaptive two-step bearing-only underwater uncooperative target tracking filter (ATSF) for uncertain underwater disturbances is proposed. Considering the nonlinearities of the target’s kinematics and the bearing-only measurements, in addition to the uncertain noise caused by an unknown underwater environment, the proposed ATSF consists of two major components, namely, an online noise estimator and a robust extended two-step filter. First, using a modified Sage-Husa online noise estimator, the uncertain process and measurement noise are estimated at each tracking step. Then, by adopting an extended state and by using a robust negative matrix-correcting method in conjunction with a regularized Newton-Gauss iteration scheme, the current state of the underwater uncooperative target is estimated. Finally, the proposed ATSF was tested via simulations of a 2-D underwater uncooperative target tracking scenario. The Monte Carlo simulation results demonstrated the reliability and accuracy of the proposed ATSF in bearing-only underwater uncooperative tracking missions.


2021 ◽  
Vol 54 (3-4) ◽  
pp. 279-291
Author(s):  
Weijun Xu

Under the Gaussian noise assumption, the probability hypothesis density (PHD) filter represents a promising tool for tracking a group of moving targets with a time-varying number. However, inaccurate prior statistics of the random noise will degrade the performance of the PHD filter in many practical applications. This paper presents an adaptive Gaussian mixture PHD (AGM-PHD) filter for the multi-target tracking (MTT) problem in the scenario where both the mean and covariance of measurement noise sequences are unknown. The conventional PHD filters are extended to jointly estimate both the multi-target state and the aforementioned measurement noise statistics. In particular, the Normal-inverse-Wishart and Gaussian distributions are first integrated to represent the joint posterior intensity by transforming the measurement model into a new formulation. Then, the updating rule for the hyperparameters of the model is derived in closed form based on variational Bayesian (VB) approximation and Bayesian conjugate prior heuristics. Finally, the dynamic system state and the noise statistics are updated sequentially in an iterative manner. Simulations results with both constant velocity and constant turn model demonstrate that the AGM-PHD filter achieves comparable performance as the ideal PHD filter with true measurement noise statistics.


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