Modeling Behavior of Sensors Using a Novel β-Divergence-Based Adaptive Filter

Sensors are widely used in many applications, acting as a link between the physical and digital domains. However, the sensor output is often affected by external factors, such as noise, interference, drifts, and nonlinearities, making it challenging for accurate signal and event detection. To address this issue, a novel approach to model a sensor using an adaptive filter based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>-divergence-inspired cost function is proposed to make the sensor robust against changing environmental conditions over time. The proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>-divergence-based least mean-square (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>LMS) algorithm can effectively analyze and compensate for external influences in sensor output, leading to a more dependable and precise representation of sensor behavior while maintaining computational efficiency. In addition, the mean and mean-square stability bounds are determined to establish the acceptable range of learning rates for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>LMS algorithm. Furthermore, this article examines the transient, steady-state, tracking performance, and robustness of the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>LMS algorithm. Moreover, the performance of the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>LMS algorithm is assessed through simulation study, demonstrating its efficacy in various real-world applications of sensors, such as system identification, missile tracking, and active noise cancellation (ANC). The hardware implementation is also carried out to validate the performance of the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>LMS algorithm in real-time scenario to model high-cost sensor behavior using low-cost sensors. The results indicate that the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>LMS algorithm significantly enhances the performance of the sensors in practical applications.