Lidar Doppler Tomography Focusing Error Analysis and Focusing Method for Targets with Unknown Rotational Speed

Abstract

Lidar Doppler tomography (LDT) is a significant method for imaging rotating targets in long-distance air and space applications. Typically, these targets are non-cooperative and exhibit unknown rotational speeds. Inferring the rotational speed from observational data is essential for effective imaging. However, existing research predominantly emphasizes the development of imaging algorithms and interference suppression, often neglecting the analysis of rotational speed estimation. This paper examines the impact of errors in rotational speed estimation on imaging quality and proposes a robust method for accurate speed estimation that yields focused imaging results. We developed a specialized measurement matrix to characterize the imaging process, which effectively captures the variations in measurement matrices resulting from different rotational speed estimates. We refer to this variation as the law of spatiotemporal propagation of errors, indicating that both the imaging accumulation time and the spatial distribution of the target influence the error distribution of the measurement matrix. Furthermore, we validated this principle through imaging simulations of point and spatial targets. Additionally, we present a method for estimating rotational speed, which includes a coarse estimation phase, image filtering, and a fine estimation phase utilizing Rényi entropy minimization. The initial rough estimate is derived from the periodicity observed in the echo time-frequency distribution. The image filtering process leverages the spatial regularity of the measurement matrix’s error distribution. The precise estimation of rotational speed employs Rényi entropy to assess image quality, thereby enhancing estimation accuracy. We constructed a Lidar Doppler tomography system and validated the effectiveness of the proposed method through close-range experiments. The system achieved a rotational speed estimation accuracy of 97.81%, enabling well-focused imaging with a spatial resolution better than 1 mm.

Keywords

• Lidar Doppler tomography (LDT)
• measurement matrix
• error analysis
• rotational speed estimation
• Rényi entropy
• long-distance imaging