Energy-Efficient State Estimation with 1-Bit Sensing: A Bussgang-Kalman Framework for Internet of Things

Accurate state estimation from heavily quantized measurements is a key challenge in resource-constrained Internet of Things (IoT) sensing and tracking, where battery-powered devices may employ low-resolution analog-to-digital converters (ADCs) to simplify sensor hardware and reduce the amount of data. Existing model-based and hybrid learning-based estimators, however, typically assume high-resolution observations and therefore degrade severely under 1-bit quantization. In this paper, we study nonlinear state estimation with 1-bit observations and develop a Bussgang-aided filtering framework for IoT sensing front-ends with 1-bit quantization. For fully known system models, we propose a Bussgang-aided Kalman Filter (BKF) that explicitly incorporates quantization distortion into recursive estimation, together with a reduced-complexity variant (reduced-BKF) for computationally efficient implementation. For partially known models, we further propose Bussgang-aided KalmanNet (BKNet), a model-based deep learning architecture that combines adaptive dithering with gated recurrent units (GRUs) to mitigate severe quantization effects and model mismatch. Experiments on the Lorenz attractor and the Michigan NCLT dataset, both under 1-bit front-end quantization, demonstrate accurate and robust state estimation under highly nonlinear dynamics, imperfect models, and extreme quantization. These results support the potential of the proposed framework for reliable state estimation in resource-constrained IoT sensing and tracking applications with low-resolution front-ends.