Cramer-Rao bounds for estimating range, velocity, and direction with an active array
Cramer-Rao bounds for estimating range, velocity, and direction with an active array
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DOI：
10.1109/78.923295
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发表时间：
2001-06-01
影响因子：
5.4
通讯作者：
Nehorai, A
中科院分区：
文献类型：
--
作者：
Dogandzic, A;Nehorai, A
我们推导出Cramer-Rao界（CRB）表达式的距离（时间延迟），速度（多普勒频移），和使用主动雷达或声纳阵列的点目标的方向。首先，一般CRB表达式推导出窄带信号和阵列模型和时空可分离的噪声模型，允许空间和时间相关。我们讨论了该模型的CRB和模糊函数之间的关系，然后，我们专门的情况下，时间白色噪声和实际重要的信号形状的线性调频脉冲序列的CRB结果。我们计算CRB的三维（3-D）阵列与各向同性传感器在空间白色噪声，并表明，它是一个函数的阵列几何形状，只有通过“转动惯量”的阵列。提出了用目标位置置信域的体积作为精度的度量，证明了目标沿着阵列的惯性主轴之一来达到最高（和最低）的定位精度。最后，比较了几种阵列的定位精度。
We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array, First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model, Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional (3-D) array with isotropic sensors in spatially white noise and show that it is a function of the array geometry only through the "moments of inertia" of the array. The volume of the confidence region for the target's location is proposed as a measure of accuracy, For this measure, we show that the highest (and lowest) target location accuracy is achieved if the target lies along one of the principal axes of inertia of the array, Finally, we compare the location accuracies of several array geometries.