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In this paper, we consider the problem of the performance bound of a nonlinear filtering problem corresponding to tracking an extended target in cluttered environments (i.e., with false alarms and missed detections). The high resolution sensor obtains the measurements of the position and the extent of the extended target whose shape is modeled by an ellipse. The posterior Cramer-Rao lower bound (PCRLB) provides a useful tool to evaluate the best achievable performance of the nonlinear filtering problem. The bounds of the traditional kinematic state estimation are calculated using the point and the extended target model. It is shown in this paper that the bound of extended target tracking is smaller than that of point model because more information is utilized. The bounds are calculated to examine the influence of the measuring accuracy, the geometry between the sensor and the target, the prior knowledge of the target, and the environmental circumstance. In a cluttered environment, the PCRLB is calculated by IRF (information reduction factor), MSC (measurement sequence conditioning), and MESC (measurement existence sequence conditioning) approaches. The simulation results also illustrate the relationship of the three methods. [ABSTRACT FROM AUTHOR]

This paper presents recursive performance bounds for dynamic estimation and tracking problems in both single and multiple target cases within the framework of finite set statistics. Because the targets can appear and disappear when the detection probability of a sensor is less than unity (P_d < 1), we must determine the existence or nonexistence of the state as well as its value. Following the possible detection/miss sequences within the framework of a random vector, possible observation sets sequences are first defined. Based on these sequences, the performance bounds can be represented by a multivariate function of some time-based auxiliary elements. Recursive relations for all the auxiliary elements are derived rigorously. For the multitarget case, this recursive estimated bound can be applied without data association. Applications are analyzed through simulations to verify our theoretical results and show that our bounds are tighter than all other bounds for the case where detection probability P_d < 1. [ABSTRACT FROM PUBLISHER]

Trans-jurisdictional conflict in both water quantity and quality is a general concern in large river basins. In this paper, the relative utility function combined with the asymmetric Nash bargaining method was established to analyze the trans-jurisdictional conflict between water quantity and water quality in the Zhangweinan Canal Basin in China. The basin was divided into four conflict stakeholders, namely, Shanxi, Hebei, Henan, and Shandong Provinces, based on administrative unit. The water usage and pollutant discharge scheme for multiple stakeholders was optimized using the established model to satisfy the environmental flow and water quality objectives at the identified conflict sections. The results indicated that the total water consumption was reduced from 4.38 × 10 m in 2007 to 1.97 × 10 m, and that the allowable COD and NH-N discharged into the river was less than 3.8 × 10 t and 4.3 × 10 t, respectively. About 81.1 % of COD and 76.1 % of NH-N should be further reduced compared with the values in 2007. [ABSTRACT FROM AUTHOR]