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To solve the problem of Doppler radar rignal detection, the discrete Fourier transform is re-examined based on the geometric algebra tool. The Doppler radar geometric detector is designed with the projection angle as a new geometric test statistic. Compared with the traditional power/envelope detector, the performance of dynamic compression and constant false alarm of the proposed detector are excellent. Through several comparative experiments with existing constant false alarm rate detectors using power or envelope detection as its input, the excellent constant faise alarm performance of the geometric detector and its ability to adapt to clutter and strong interference signals are illustrated. It provides a new perspective and a new tool for radar detection. [ABSTRACT FROM AUTHOR]

Geographic information space is a high-dimensional space combining virtual and real. Geographic information system (GIS) based on European geometry plays an important role in the development of geographic information science. However, because the expression of GIS geographic objects and phenomena in European-style space depends on object coordinates and the adopted coordinate system, it is difficult for the expression, calculation and analysis of geographic objects to form a multi-dimensional unified operation rule and framework, which increases the algorithm’s complexity and reduces the efficiency of algorithm analysis. Geometric algebra is a kind of combination algebra based on dimensional operation. Space can be defined as the operation between vector sets. The dimension of space is directly determined by the algorithm, which realizes the unification of high - dimensional geometric calculation and analysis. Based on the unified calculation and analysis framework of geometric algebra, GIS can better express and analyze high - dimensional objects, and then improve the ability of expressing complex geographical objects and dynamic geographical phenomena, analyzing spatiotemporal multi - scale objects and integration of different scale geographical models. This lays the theoretical foundation for the development of GIS towards holographic maps with real-time dynamics,virtual-real fusion,full perspective, full elements and full content expression. [ABSTRACT FROM AUTHOR]

Based on the multi-dimensional unified geometric algebra, this paper discussed the multi-vector expression and computation of multi-dimensional vector filed. The vector differentiations are computed by template convolution. With the help of the unified expression of inner and outer product of geometric product, the unified calculation method of divergence and curl and the implementation algorithm are proposed. This method can not only reproduce the geometric association between vector field divergence and rotation parameters as well as their differential geometry characteristics, but also achieve a unified and multi-dimensional coordinate-free calculation. Simulation experimental results based on the wind fields of North American suggest that our method has much better performance of contrast and smoothness against the gradient-based algorithm. It also has strong ability to deal with vector fields of high noise and provide new insights and method foundations for vector field data analysis. [ABSTRACT FROM AUTHOR]