In order to study and forecast extreme weather, a comprehensive and systematic analysis of the spatial and temporal relationship between Precipitable Water Vapor (PWV), predicted by Numerical Weather Predication (NWP) data, and precipitation, is necessary. The goal of this paper was to study the temporal and spatial relationship between PWV and precipitation during the so-called ‘July 20’ (18–21 July 2021) heavy rainstorm in Zhengzhou. Firstly, the PWV data provided by 120 radiosonde stations uniformly distributed throughout the world, and two IGS stations in China, in 2020, was used to evaluate the accuracy of PWV estimation by ERA5 and MERRA-2 data, and the factors affecting the accuracy of NWP PWV were explored. Secondly, ERA5 PWV and the precipitation data of six meteorological stations were used to qualitatively analyze the relationship between PWV and precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou. Finally, a quantitative study was conducted by an eigenvalue matching method. The main experimental results were as follows. Compared with MERRA-2 PWV, the accuracy of ERA5 PWV was slightly higher. Latitude, altitude and season were the influencing factors of the NWP PWV estimation accuracy. The change trend of ERA5 PWV was consistent with both 24 h cumulative precipitation and surface precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou. The average optimal matching degree and optimal matching time between NWP PWV and surface precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou was 56.6% and 3.68 h, respectively. The maximum optimal matching degree was 80.3%. The spatial–temporal relationship between NWP PWV and surface precipitation was strong.

Step detection for smartphones plays an important role in the pedestrian dead reckoning (PDR) for indoor positioning. Aiming at the problem of low step detection accuracy of smartphones in complex unconstrained states in PDR, smartphone-based unconstrained step detection method fusing a variable sliding window and an adaptive threshold is proposed. In this method, the dynamic updating algorithm of a peak threshold is developed, and the minimum peak value filtered after a sliding window filter is used as the adaptive peak threshold, which solves the problem that the peak threshold of different motion states is difficult to update adaptively. Then, a variable sliding window collaborative time threshold method is proposed, which solves the problem that the adjacent windows cannot be contacted, and the initial peak and the end peak are difficult to accurately identify. To evaluate the performance of the proposed unconstrained step detection algorithm, 50 experiments in constrained and unconstrained states are conducted by 25 volunteers holding 21 different types of smartphones. Experimental results show: The average step counting accuracy of the proposed unconstrained step detection algorithm is over 98%. Compared with the open source program Stepcount, the average step counting accuracy of the proposed algorithm is improved by 10.0%. The smartphone-based unconstrained step detection fusing a variable sliding window and an adaptive threshold has a strong ability to adapt to complex unconstrained states, and the average step counting accuracy rate is only 0.6% lower than that of constrained states. This algorithm has a wide audience and is friendly for different genders and smartphones with different prices.