Robust Indoor Localization Methods With Anchor Position Uncertainty

The demand of the indoor positioning will continue to increase in the future, and for the improvement of positioning accuracy has been an important objective of the research. There are many factors that affect the positioning accuracy, whether it is to consider environmental factors of non-line-of sight(NLOS) propagation, multipath propagation, or the measurement error caused by noise, these all will lead to positioning error. Aim at the indoor positioning, in consideration of the positioning error caused by anchor uncertainty, so we also need to pay more attention to it.Refer to common positioning model, this paper take anchor position uncertainty into consideration, and re-establish positioning model used in this paper, and then mathematical modeling, for the purpose of simulation and analysis. Usually, we often think that in simulation and application of the anchor location is its true position, but it is actually not the case, in the model of anchor uncertainty, we need to get the position of the anchor, by many position obtained manner, because of various reasons, making the so-called known anchor position relative to its real position is with errors.Refer to analytical methods of the range measurement error impact on positioning, start from the range measurement error obey Gaussian distribution, and then change it into actual measure results; and there are many references have made a detailed research and analysis of positioning error. We refer to some method that can be applied to the problems that the article needs to solve, which is divided into two parts: non-Bayesian estimation method and Bayesian estimation method.The purpose of using these two methods is because there are a lot of algorithm of non-Bayesian method can apply to the analysis of the anchor position uncertainty, the algorithm is common, and very easy to understand, and the error distribution assumed is also common Gaussian form. If it is needed to consider the actual situation of anchor error, we can start from the Bayesian approach, which is more common, and in order to facilitate the follow-up research.In this paper, on the one hand, through the non-Bayesian estimation methods, we take four linear algorithms into account, simulate and analysis the anchor uncertainty impact on positioning accuracy, consider the magnitude of error and location area size, obtained different algorithms have positioning performance difference under different conditions, intuitive reflect the positioning error brought by anchor uncertainty, and using different algorithms characteristic to guide practical applications. Solved the singular solution problem caused by anchor position uncertainty, guarantee the localization algorithm robustness. On the other hand, we bring in belief propagation though Bayesian estimation methods, through the prior knowledge of anchor to obtain the posterior probability distribution, from parametric form to the nonparametric form, using particle-based of message-passing and distribution of Gaussian approximation, so that make it possible to solve the problem of anchor position error obey the actual distribution, it is more versatile compared to non-Bayesian approach, and apply belief propagation for the improvement of anchor accuracy by iterative itself, and the following research on cooperative localization.