A square-root-free matrix decomposition method for energy-efficient least square computation on embedded systems

QR decomposition (QRD) is used to solve least-squares (LS) problems for a wide range of applications. However, traditional QR decomposition methods, such as Gram-Schmidt (GS), require high computational complexity and nonlinear operations to achieve high throughput, limiting their usage on resource-limited platforms. To enable efficient LS computation on embedded systems for real-time applications, this paper presents an alternative decomposition method, called QDRD, which relaxes system requirements while maintaining the same level of performance. Specifically, QDRD eliminates both the square-root operations in the normalization step and the divisions in the subsequent backward substitution. Simulation results show that the accuracy and reliability of factorization matrices can be significantly improved by QDRD, especially when executed on precision-limited platforms. Furthermore, benchmarking results on an embedded platform show that QDRD provides constantly better energy-efficiency and higher throughput than GS-QRD in solving LS problems. Up to 4 and 6.5 times improvement in energy-efficiency and throughput, respectively, can be achieved for small-size problems.