Square-root unscented Kalman filter (SRUKF) is a widely used state estimator for several state of-the-art, highly nonlinear, and critical applications. It improves the stability and numerical accuracy of the system compared to the non-square root formulation, the unscented Kalman filter (UKF). At the same time, SRUKF is less computationally intensive compared to UKF, making it suitable for portable and battery-powered applications. This paper proposes a low-complexity and power-efficient architecture design methodology for SRUKF presented with a use case of the simultaneous localization and mapping (SLAM) problem. Implementation results show that the proposed SRUKF methodology is highly stable and achieves higher accuracy than the extensively used extended Kalman filter and UKF when developed for highly critical nonlinear applications such as SLAM. The design is synthesized and implemented on resource constraint Zynq-7000 XC7Z020 FPGA-based Zedboard development kit and compared with the state-of-the-art Kalman filter-based FPGA designs. Synthesis results show that the architecture is highly stable and has significant computation savings in DSP cores and clock cycles. The power consumption was reduced by 64 % compared to the state-of-the-art UKF design methodology. ASIC design was synthesized using UMC 90-nm technology, and the results for on-chip area and power consumption results have been discussed. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.