Trajectory estimation involves determining the trajectory of a mobile robot by combining prior knowledge about its dynamic model with noisy observations of its state obtained using sensors. The accuracy of such a procedure is dictated by the system model fidelity and the sensor parameters, such as the accuracy of the sensor (as represented by its noise covariance) and the rate at which it can generate observations, referred to as the sensor query schedule. Intuitively, high-rate measurements from accurate sensors lead to accurate trajectory estimation. However, cost and resource constraints limit the sensor accuracy and its measurement rate. Our work's novel contribution is the estimation of sensor schedules and sensor covariances necessary to achieve a specific estimation accuracy. Concretely, we focus on estimating: (i) the rate or schedule with which a sensor of known covariance must generate measurements to achieve specific estimation accuracy, and alternatively, (ii) the sensor covariance necessary to achieve specific estimation accuracy for a given sensor update rate. We formulate the problem of estimating these sensor parameters as semidefinite programs, which can be solved by off-the-shelf solvers. We validate our approach in simulation and real experiments by showing that the sensor schedules and the sensor covariances calculated using our proposed method achieve the desired trajectory estimation accuracy. Our method also identifies scenarios where certain estimation accuracy is unachievable with the given system and sensor characteristics.

翻译：轨迹估计涉及通过结合移动机器人动态模型的先验知识与使用传感器获取的状态噪声观测，来确定其运动轨迹。该过程的精度由系统模型保真度和传感器参数决定，例如传感器的精度（由其噪声协方差表示）以及传感器生成观测的速率（称为传感器查询调度）。直观而言，来自高精度传感器的高频测量可实现精确的轨迹估计。然而，成本和资源约束限制了传感器的精度及其测量速率。本工作的创新贡献在于估计实现特定估计精度所需的传感器调度方案和传感器协方差。具体而言，我们重点研究：（i）已知协方差的传感器为达到特定估计精度所需生成测量的速率或调度方案；以及（ii）在给定传感器更新速率下，为达到特定估计精度所需的传感器协方差。我们将这些传感器参数的估计问题构建为半定规划，可通过现成求解器进行求解。通过仿真和真实实验验证，我们证明采用所提方法计算的传感器调度方案和传感器协方差能够实现期望的轨迹估计精度。该方法还能识别在给定系统和传感器特性下无法达到特定估计精度的场景。