Abstract
This paper presents a methodology to design a sparse multiband ranging signal with a large virtual bandwidth, from which time delay and carrier phase are estimated by a low complexity multivariate maximum likelihood (ML) method. In the estimation model for a multipath channel, not all reflected paths are considered, and time delay and carrier phase are estimated in a step-wise manner to further reduce the computational load. By introducing a measure of dependence and a measure of bias for a multipath reflection, we analyse the bias, precision and accuracy of time delay and carrier phase estimation. Since these two indicators are determined by the signal spectrum pattern, they are used to formulate an optimization for signal design. By solving the optimization problem, only a few bands from the available signal spectrum are selected for ranging. Consequently, the designed signal only occupies a small amount of signal spectrum but has a large virtual bandwidth and can thereby still offer a high ranging precision with only a small bias, based on the low-complexity simplified ML method. Numerical and laboratory experiments are carried out to evaluate the ranging performance of the proposed estimation method based on sparsely selected signal bands. Relative positioning, in which we only measure a change in position, based on either the time delay estimates or the carrier phase estimates, is presented as a proof-of-concept for precise positioning. The results show that positioning based on only 7 out of 16 signal bands, sparsely placed in the available spectrum, achieves a decimeter level accuracy when using time delay estimates, and a millimeter level accuracy when using carrier phase estimates. Compared with the case of using all available bands, and without largely decreasing the positioning performance, the computational complexity when using the sparse multiband signal can be reduced by about 80%.
Highlights
A CCURATE positioning is in high demand for various emerging applications and vehicular systems
We analyse the performance of time delay estimation using both the full model and the simplified model, as well as the performance of estimating the complex gain and its corresponding carrier phase
We consider the following signal patterns to evaluate the performance of time delay and carrier phase estimation: two edge signal bands, a sparse multi-band signal, all M = 16 signal bands, and 7 contiguous signal bands which provides less virtual signal bandwidth than the other three patterns
Summary
A CCURATE positioning is in high demand for various emerging applications and vehicular systems. Considering the LoS path and all reflections in the model, results in significant computational complexity, and becomes less attractive in practice This raises the question of how to design a ranging signal which enables time delay and carrier phase estimation, and satisfies the requirement on both precision and bias, when not all reflections are considered in the model in order to reduce the computational complexity. The time delay and carrier phase will be jointly estimated based on the maximum likelihood method only for the LoS path and a few reflections, as a compromise between the computational complexity and the overall performance.
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