A Modified Strassen Algorithm based DSP Accelerated 3D Kalman Filter

Abstract

The high-speed Kalman filter (KF) algorithms are essential for robotics, autonomous vehicle, target tracking, and other applications. The dimensions of the state vector and traditional matrix multiplication (complexity of order $\mathcal{O}\left(n^{3}\right)$) are the two main reasons for the computational time of the $K F$ algorithm. Hence, a matrix multiplication accelerator module is needed to accelerate the KF algorithm for higher dimensions of the state vector. In this paper, modified Strassen matrix multiplication (complexity of order $\mathcal{O}\left(n^{2.80}\right)$) is utilized to increase the computational efficiency of the KF algorithm. The number of cycles is evaluated against the dimensions of the KF algorithm to illustrate the proposed methodology. After that, 2D-KF and 3D-KF algorithms targeted on DSP processor TMS320C6678 using C language to ensure real-time processing. The $3 D-K F$ with a state of nine consumes $19.962 \mathrm{~ms}, 30.47 \mathrm{~ms}$, and $40.04 \mathrm{~ms}$ of time by employing the hybrid Strassen, Strassen, and conventional matrix multiplication. It is observed that the usage of hybrid Strassen takes only half of the time provided by conventional multiplications.