High-Speed Strassen Matrix Multiplication Accelerators for 2D Kalman Filter

Abstract

High-speed and low-area Kalman filter (KF) algorithms are critical in autonomous vehicles, robotics, military, target tracking, and other applications. KF requires a large number of matrix multiplications (complexity of order O(n<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>)), which increases the number of cycles needed to process data. There is a vital requirement to develop a matrix multiplication accelerator module to enhance the efficiency of the entire Kalman Filter (KF) process. This paper proposes two accelerator models for KF, namely pipelined Strassen matrix multiplication and hybrid Strassen matrix multiplication. We propose pipelining the existing Strassen matrix multiplication architecture to reduce critical time to a single multiplication operation. To accelerate the KF and target the low area, we present a hybrid Strassen matrix multiplication architecture that reduces higher dimensions using the Strassen algorithm and computes the 2 × 2 matrix using standard matrix multiplication. The Strassen algorithm, pipelined Strassen algorithm, and hybrid Strassen algorithm-based accelerators are designed for the Vertix-7 FPGA to determine the maximum possible frequency and space limitations. For demonstration purposes, a 2D-KF is studied with a four-dimensional state vector.