Design and Application of Programmable Analog Computing Circuit for Kalman Filter Algorithm Based on Memristive Array

Kalman Filter algorithm is a crucial tool for estimating the state of dynamic systems in the presence of numerous uncertainties, which plays a pivotal role in various application scenarios such as information fusion and deep learning. However, current accelerators and hardware face limitations in terms of both latency and performance overhead when executing the Kalman Filter algorithm. Aiming at the above problem, we firstly propose a programmable circuits based on memristors for full process of Kalman Filter algorithm, which can efficiently run Kalman Filter algorithm with the advantage of analog circuits in parallel and fast computing, which achieve computing speed increasing in order of magnitude. Moreover, the empowerment of programmability from memristors avoid intensive memory access. For the problem how to linearly adjust weight for the memristor, we propose a new memristor-based programmable unit, the corresponding crossbar and method in order to achieve linear weight adjustment. The evaluation shows that the proposed circuits not only has over 95<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> accuracy for 32-th order parameter matrix in Kalman Filter algorithm, but also has good robustness against some non-ideal factors it can still achieve 90<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> accuracy under 10<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> noise interference. The evaluating results of performance also show that it reduces energy consumption by 3.1<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times$</tex-math></inline-formula> and 8.9<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times$</tex-math></inline-formula>, compared with corresponding VLSI and FPGA accelerator, respectively. Moreover, an improved image fusion algorithm and circuit based on the proposed Kalman Filter circuits is proposed, which achieve good image fusion and speedup in computing time by 82.6<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times$</tex-math></inline-formula> and 121.3<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times$</tex-math></inline-formula>, compared with corresponding ASIC and FPGA, respectively.