Comparison of numerical integration methods in strapdown inertial navigation algorithm

Abstract

The numerical mathematical theory provides a few ways of numerical integration with different errors. It is necessary to make use of the most exact method with respect to the computing power for a majority of microprocessors, because errors are integrated within them due to the algorithm. In our contribution, trapezoidal rule and Romberg's method of numerical integration are compared in the velocity calculation algorithm of the strapdown inertial navigation. The sample frequency of acceleration and angular velocity measurement was 816.6599 Hz. Inertial navigation velocity was compared with precise incremental encoder data. Trapezoidal method velocity error in this example was 1.23 × 10-3 m/s in the fifteenth-second measurement. Romberg's method velocity error was 0.16 × 10-3 m/s for the same input data. The numerical mathematical theory provides a few ways of numerical integration with different errors. It is necessary to make use of the most exact method with respect to the computing power for a majority of microprocessors, because errors are integrated within them due to the algorithm. In our contribution, trapezoidal rule and Romberg's method of numerical integration are compared in the velocity calculation algorithm of the strapdown inertial navigation. The sample frequency of acceleration and angular velocity measurement was 816.6599 Hz. Inertial navigation velocity was compared with precise incremental encoder data. Trapezoidal method velocity error in this example was 1.23 × 10-3 m/s in the fifteenth-second measurement. Romberg's method velocity error was 0.16 × 10-3 m/s for the same input data.

Keywords

• romberg's method
• trapezoidal rule
• accelerometer
• gyroscope
• micro electro-mechanical system (mems)