As bias estimation methods are developed, it becomes necessary to obtain the bound on bias estimation for more complex bias and sensor models. Three-dimensional (3-D) sensors, such as radars commonly used in applications, contain both scale and additive biases in sine space which result in a nonlinear estimation problem that may have poor observability and accuracy depending on the geometry of the sensors. By converting the sine space and range measurements to Cartesian using an unbiased conversion, it is possible, via creation of pseudomeasurements, to eliminate the need to estimate the target's state thereby reducing the sensor bias estimator complexity. The present paper evaluates the Cramér–Rao lower bound (CRLB) for estimating scale and additive biases in sine space for 3-D sensors and compares it with a maximum likelihood formulation implemented via iterated least squares, which is thereby shown to be statistically efficient. Additionally, the importance of measurement diversity is investigated with respect to the CRLB.

中文翻译：

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用于 3 维传感器的正弦空间中的偏置 CRLB

随着偏差估计方法的发展，有必要为更复杂的偏差和传感器模型获得偏差估计的界限。三维 (3-D) 传感器，例如应用中常用的雷达，在正弦空间中包含尺度和附加偏差，这会导致非线性估计问题，根据传感器的几何形状，该问题可能具有较差的可观察性和准确性。通过使用无偏转换将正弦空间和距离测量转换为笛卡尔，可以通过创建伪测量来消除估计目标状态的需要，从而降低传感器偏差估计器的复杂性。本论文评估了 Cramér-Rao 下限 (CRLB)，用于估计 3-D 传感器正弦空间中的尺度和加性偏差，并将其与通过迭代最小二乘法实现的最大似然公式进行比较，从而证明其在统计上是有效的。此外，还针对 CRLB 研究了测量多样性的重要性。