Abstract
The theoretical and practical performance limits of a 2D ultra-wideband impulse-radio localization system operating in the far field are studied under the assumption that estimates of location are based on time-difference-of-arrival (TDOA) measurements. Performance is evaluated in the presence of errors in both the TDOA measurements and the sensor locations. The performance of both optimal (maximum-likelihood) and suboptimal location estimation algorithms is studied and compared with the theoretical performance limit defined by the Cramer-Rao lower bound on the variance of unbiased TDOA location estimates. A novel weighted total-least-squares algorithm is introduced that compensates somewhat for errors in sensor positions and reduces the bias in location estimation compared with a widely used weighted least-squares approach. In addition, although target tracking per se is not considered in this paper, performance is evaluated both under the assumption that sequential location estimates are not aggregated as well as under the assumption that some sort of tracker is available to aggregate a sequence of estimates.
Highlights
Ultra-wideband (UWB) impulse radio (IR) technology is a high-bandwidth communication scheme that offers several advantages for location estimation of targets based on radiofrequency emissions
The results presented in this paper provide a comprehensive evaluation of the theoretical and practical performance characteristics of UWB-IR TDOA localization systems operating in the far field
The increase in mean-squared error (MSE) is quite dramatic for a very small increase in sensor position error. We have explored both the theoretical and practical performance limits of long-range UWB-IR TDOA location and tracking systems
Summary
Ultra-wideband (UWB) impulse radio (IR) technology is a high-bandwidth communication scheme that offers several advantages for location estimation of targets based on radiofrequency emissions. The CRLB for unbiased estimates of location in 2D based on inaccurate TDOA measurements has been derived under the assumption that the sensor positions are known precisely and that the TDOA measurement errors are independent identically distributed (i.i.d.) zero-mean Gaussian random variables with variance determined by the CRLB for TDOA estimation Taken in conjunction, these two bounds provide a lower bound on the achievable performance of a 2D UWBIR TDOA localization and tracking system in the absence of errors in sensor position measurements, subject to the constraints imposed by other system parameters such as SNR, number of receiving sensors, target range, and sensor geometry.. We show that the relatively small one-shot bias present in the most commonly used constrained least-squares TDOA algorithm rapidly dominates the overall MSE of the location estimates in the low-SNR regime when a moderate amount of block-averaging is performed on the sequence of estimates.
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