Novel High-Precision Simulation Technology for High-Dynamics Signal Simulators Based on Piecewise Hermite Cubic Interpolation

This paper proposes novel high-precision simulation technology for high-dynamics signal simulators used for performance validation in high-speed application environments, such as the global navigation satellite system or telemetry, tracking, and command systems. The proposed method is based on piecewise Hermite cubic interpolation, and regenerates the satellite-to-earth distance from the available sparse motion data. A convolution equation is derived to implement the interpolation using an interpolation filter. Therefore, distance interpolation can be performed with digital circuitry without having to explicitly solve for the interpolation polynomial using floating-point calculations. The Hermite interpolator design is based on polyphase or Farrow structures, depending on whether the required sample rate conversion (SRC) ratio is integer or fractional, respectively. The implementation complexities of both structures are shown to be acceptable. The proposed technology is validated and compared with existing methods. It is shown that the proposed approach is applicable to arbitrary SRC ratios, maintains the continuity of both distance and velocity, and improves their simulation precision by up to 98.5% and 95.7%, respectively. Additionally, it reduces the computation complexity (additions and multiplications) by up to 90.4% and 87.5%, respectively.