Optimization of an unscented Kalman filter for an embedded platform

The unscented Kalman filter (UKF) is finding increased application in biological fields. While realizing a complex UKF system in a low-power embedded platform offers many potential benefits including wearability, it also poses significant design challenges. Here we present a method for optimizing a UKF system for realization in an embedded platform. The method seeks to minimize both computation time and error in UKF state reconstruction and forecasting. As a case study, we applied the method to a model for the rat sleep-wake regulatory system in which 432 variants of the UKF over six different variables are considered. The optimization method is divided into three stages that assess computation time, state forecast error, and state reconstruction error. We apply a cost function to variants that pass all three stages to identify a variant that computes 27 times faster than the reference variant and maintains required levels of state estimation and forecasting accuracy. We draw the following insights: 1) process noise provides leeway for simplifying the model and its integration in ways that speed computation time while maintaining state forecasting accuracy, 2) the assimilation of observed data during the UKF correction step provides leeway for simplifying the UKF structure in ways that speed computation time while maintaining state reconstruction accuracy, and 3) the optimization process can be accelerated by decoupling variables that directly impact the underlying model from variables that impact the UKF structure. Author summaryPowerful statistical tools can be used to estimate unmeasured information in biological systems and predict the systems future state. Translating these tools from a desktop computer to small, wearable or implantable platforms can unlock many benefits, but presents many design challenges, because tradeoffs between computational simplicity and system accuracy must be balanced. We present an approach to translating one such widely used statistical tool, the unscented Kalman filter, from a desktop computer to a miniature device. We demonstrate the approach with a case study centering on the neural circuits governing the mammalian sleep-wake cycle. By exploiting uncertainty in the biology being estimated and the corrective influence of biological measurements, we arrive at a design that is easily computable on the miniature device and maintains a high level of accuracy. We anticipate that our approach will aid others in designing such miniaturized systems for a broad range of applications.