Abstract We consider the tracking problem of a point moving in a three-dimensional space using only measurements of distance from a set of reference points. The approach followed in this paper is to derive a linear map with multiplicative noise through a quadratic transformation of the distance measurements. A suitable rewriting by means of an output injection term makes the multiplicative noise of the linear map amenable to be processed by recursive estimators. These estimators are guaranteed to be internally stable and the variance of the estimation error is estimated. We compare the performance of the resulting algorithm for the linear and quadratic case with standard alternatives.

中文翻译：

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用于从距离测量进行跟踪的最佳线性和二次估计器

摘要 我们仅使用距一组参考点的距离测量值来考虑在三维空间中移动的点的跟踪问题。本文采用的方法是通过距离测量值的二次变换来导出带有乘性噪声的线性地图。通过输出注入项的适当重写使得线性映射的乘法噪声易于由递归估计器处理。这些估计量保证是内部稳定的，估计误差的方差是估计的。我们将所得算法在线性和二次情况下的性能与标准替代方案进行比较。