Cramer-Rao Lower Bounds of Parameter Estimation for Frequency-Modulated Continuous Wave Lidar
Z. Fan, Q. Sun, L. Du and J. Bai
Signal processing is the key for frequency-modulated continuous–wave (FMCW) lidar, and the accuracy limits of parameters estimation are given by Cramer-Rao lower bound (CRLB). The aim for this work is to gain CRLB and evaluate the estimation algorithm by using CRLB. By introducing the generation of beat signal and the working principles of velocity and distance measurement, the joint probability density function (PDF) of sample parameter vector of intermediate frequency (IF) signal with Gaussian noise is established, then the CRLBs of velocity and distance estimation are obtained from the conversion of Fisher information matrix. It can be found from the theoretical analysis and simulation results that the CRLB can be effectively reduced by increasing the length of sampling data, decreasing the sampling frequency and improving the signal-to-noise ratio (SNR) of the system. A frequency offset correction (FOC) algorithm is discussed as well compared with CRLB. The difference between CRLB of velocity estimation and error of FOC algorithm is small and reduces from 3.5 × 10-5 to 3.5 × 10-7 m/s, as the SNR increases from -10.00 to 30.00 dB. The difference between CRLB of range estimation and error of FOC algorithm is large and constantly equals to 53.00 dB. It means FOC algorithm is suitable for velocity estimation of FMCW lidar, but there is a lot of room for improvement for range estimation. For having higher precise range estimation for FMCW lidar, the phase-based estimator is considered. The comparisons with CRLB show that the phase-based estimator could achieve high precise speed and range estimation. It is proven that the comparison of estimator and CRLB gives the basis for algorithm choice and improvement.
Keywords: Lidar, frequency-modulated continuous-wave (FMCW), Cramer-Rao lower bound, laser measurement, frequency offset correction algorithm, probability density function, analytical model, parameter estimation