Sensor Query Schedule and Sensor Noise Covariances for Accuracy-Constrained Trajectory Estimation

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">specific estimation accuracy</i>. Concretely, we focus on estimating: (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i>) the rate or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">schedule</i> with which a sensor of known covariance must generate measurements to achieve specific estimation accuracy, and alternatively, (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i>) 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.