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MEMS accelerometers are miniature integrated systems widely utilized for measuring carrier acceleration in various industrial and domestic applications. However, these devices are susceptible to faults due to internal and external factors during operation. Failure to promptly detect and correct these faults may lead to inaccurate perception of the external environment, resulting in control deviations. Hence, timely detection and correction of MEMS accelerometer faults are crucial for enhancing system robustness, measurement accuracy, and control stability. Existing detection and calibration methods often rely on establishing the accelerometer"s physical model or constructing redundant sensor networks, which suffer from complexities in modeling and introduce additional errors or high hardware resource requirements. To mitigate inaccuracies introduced by modeling and reduce algorithmic hardware demands, a lightweight, data-driven self-testing and self-calibration algorithm for MEMS accelerometers is proposed based on the notion of proximal sensor computation. Test results demonstrate that the algorithm achieves a detection rate of 90% for four types of faults: shock, bias, signal loss, and constant output. The average absolute error between calibrated data and normal data is less than 0.15 g, with the ability to process accelerometer response data within 2.55 ms.