Wigner-Hough/Radon Transform for GPS Post-Correlation Integration (Preprint)

Abstract : A new approach to weak GPS signal acquisition is presented in this paper. It belongs to the category of approaches that aim at enhancing the sensitivity of standalone GPS receivers without network assistance, which is also called unaided GPS receivers. Acquisition and ultimate tracking of a weak GPS signal (e.g., in an in-door environment) faces several technical challenges, notably, possible data bit sign reversal every 20 ms and tolerable frequency error inversely proportional to the integration interval. Brute force search over all possible combinations of the unknown values is prohibitive computationally. Aided GPS relying on external infrastructure for timing, data bit, and frequency error information is costly. Coherent techniques such as the block accumulating coherent integration over extended interval (BACIX) have recently been proposed to extend coherent integration. Although efficient, such coherent methods may still be too expensive except for high-end receivers and may not maintain the SNR performance when there are large frequency changes over the intended integration interval. In this paper, we set forth a novel method that utilizes the semi-coherent scheme for post-correlation integration, which is named as "block accumulating semi-coherent integration of correlations" or BASIC. It can be viewed as an extension of the BACIX algorithm. Although less sensitive than coherent integration, semi-coherent integration based on inter-block conjugate products is computationally more efficient. In addition, it can handle large frequency changes. The BASIC algorithm is first formulated in the paper. Computer simulation results are then presented to illustrate operation and performance of the BASIC algorithm for joint estimation of the initial frequency, chirping rate (frequency rate), bit sync, and bit sign pattern.