This article concerns the problem of the estimation bound for tracking an extended target observed by a high resolution sensor. Two types of commonly used models for extended targets and the corresponding posterior Cramer-Rao lower bound (PCRLB) are discussed. The first type is the equation-extension model which extends the state space to include parameters such as target size and shape. Thus, the extended state vector can be estimated through the measurements obtained by a high resolution sensor. The measurement vector is also an expansion of the conventional one, and the additional measurements such as target extent can provide extra information for the estimation. The second model is based on multiple target measurements, each of which is an independent random draw from a spatial probability distribution. As the number of measurements per frame is unknown and random, the general form of the measurement contribution to the Fisher information matrix (FIM) conditional on the number of measurements is presented, and an extended information reduction factor (EIRF) approach is proposed to calculate the overall FIM and, therefore, the PCRLB. The bound of the second extended target model is also less than that of the point model, on condition that the average number of measurements is greater than one. Illustrative simulation examples of the two models are discussed and demonstrated.
Keywords: Fisher information matrix (FIM); extended information reduction factor (EIRF); extended target tracking; posterior Cramer-Rao lower bound (PCRLB).