利用距离、距离变化率及距离变化率导数求解运动车辆速度与加速度的闭式解
Closed-form Solutions for Velocity and Acceleration of a Moving Vehicle Using Range, Range Rate, and Derivative of Range Rate
AI总结：
针对运动目标运动学参数估计问题，提出结合距离、距离变化率及其导数的方法，推导速度与加速度的闭式LS和WLS解，仿真验证其性能优于现有方法。
摘要：
本信函提出了一种利用基于距离的测量值估计运动目标位置、速度与加速度的新方法。现有研究大多聚焦于位置与速度估计，本文将研究框架拓展至加速度估计。为此，本文提出除距离与距离变化率测量值外，还引入距离变化率的导数进行估计。该方法首先利用基于到达时间（Time-of-Arrival, TOA）的技术估计位置；随后构建重构的最小二乘（least squares, LS）与加权最小二乘（weighted least squares, WLS）方法用于速度估计；最后结合已得到的位置与速度估计结果，利用距离变化率的导数估计加速度。此外，本文还推导了速度与加速度估计的闭式LS和WLS解。仿真结果表明，与现有方法相比，所提方法在运动目标运动学参数估计方面性能更优。
英文摘要：
This letter presents a novel method for estimating the position, velocity, and acceleration of a moving target using range-based measurements. Although most existing studies focus on position and velocity estimation, the framework of this letter is extended to include acceleration. To achieve this, we propose using the derivative of the range rate, in addition to the range and range rate measurements. The proposed method estimates the position at first using Time-of-Arrival (TOA)-based techniques; then, develops a reformulated least squares (LS) and weighted least squares (WLS) approaches for velocity estimation; and finally, employs the derivative of the range rate to estimate the acceleration using previous position and velocity estimates. On the other hand, closed-form LS and WLS solutions are derived for both velocity and acceleration. The simulation results show that the proposed approach provides improved performance in estimating moving target kinematics compared to existing methods.
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