The global economic situation under open macroeconomic conditions is treacherous, and China’s development is inevitably in a more complex environment, both internally and externally, in which there are closely interacting external correlations and chain shocks arising from various economic changes. It faces the constraints of several factors, such as economic cycle fluctuations, the impact of the financial crisis, the role of technological innovation, human capital, etc. Therefore, the shift from a low level of labour resources to high-quality innovative human capital has become the primary consideration for China to complete the transformation of its economic growth mode.

Forrester et al. [1] proposed the human capital theory, and since then the impact on human capital has started to attract attention from various countries. Clark et al. [2] defines and characterises innovative human capital as the ability to innovate with social scarcity, i.e. the ability to unbalance the market and restore it to equilibrium. Bayon et al. [3] proposes an extended Solow model that includes human capital as one of the factors influencing economic growth, after it has been measured and in what form it is introduced into the model to establish its relationship with economic growth. This allows for the classification of three types of human capital: general, professional and innovative [4]. US technology and innovation leadership depends on a dynamic and vibrant innovation ecosystem, and the health of an innovation ecosystem depends on the educational status of a country’s workforce, its R&D capabilities, its entrepreneurial climate and its improved infrastructure. They need access to a global network of knowledge; and in this respect, Willie et al. [5] even compares Silicon Valley to a rainforest that is constantly generating and evolving new technologies and business models, and the innovation in Silicon Valley is due to its unique ecology [6–9].

Based on the research on innovative human resources, this paper finds that the previous literature has two main shortcomings: Firstly, most of the literature now focuses on human capital as the main object of research or systematic research [10–13]. Secondly, there are not enough studies at the regional level and most of them use provincial data to analyse, and thus the sample size is small and the reliability of the empirical results is low [13–16]. This paper analyses the impact of innovative human capital on China’s economic development based on the STI model, which expands the sample size of the study and takes the nationwide innovative human capital as the research object, and improves the credibility of the research purpose.

This paper empirically analyses the relationship by using Kalman filter algorithm model with innovative human capital as the core explanatory variable and labour force quantity, physical capital, trade openness and industrial structure as control variables.

The basic Kalman filter is restricted to the assumption of linearity. The ‘nonlinear nature’ of these systems may be present. The extended Kalman filter solves the problem of nonlinear non-Gaussian application scenarios [17–20]. Extended Kalman filtering is currently one of the mainstream algorithms in the field of state estimation and data fusion.

Let the nonlinear state space model be as shown in Formula (1):

Using the system model, the probability density function of the previous state predicts the next state, and using the Chapman-Kolmogorov formula, the prior probability

In Formula (2), it is assumed that the state transfer model conforms to a first-order Markov process.

Using the latest observations, the predicted probability density function is modified. The posterior probability _{k}

The above recursive relationship between prediction and update needs to be approximated in practical applications in nonlinear, non-Gaussian systems using Monte Carlo methods.

In sequential importance sampling (SIS), the posterior probability

SIS is a way to perform importance sampling recursively, for example, the expectation of a function

In each recursive process, the weights of the next sampling are calculated from the weights of the previous sampling, and assuming that the importance density function applies, the weights can be expressed as Formula (6):

The posterior probability is then expressed as the formula:

After SIS has undergone several recursions, many small weight particles can be neglected, leaving only particles with relatively large weights, which will waste a lot of computation on negligible small weight particles and reduce the estimation performance [21–25]. In the recursive process, the transformation of weights will only become increasingly larger, and thus the degradation problem is inevitable.

In the SIS process, if the number of effective particles is less than a certain threshold, the particles are resampled to avoid degradation problems. To perform resampling, a new set of particles

The core idea of the Kalman filter-STI model is to estimate the joint post-talent density function based on information about its observations, where the observations refer to points in time. The time density function of innovative talents can be derived, which is computationally complex and does not converge easily [26]. And the RBPF algorithm decomposes the joint probability density function using Formula (9).

The SIR algorithm presented in the previous section requires evaluating the weights of the particles from scratch. Doucet obtains a recursive formula to calculate the importance weights by restricting the importance probability density function to Formula (11).

According to Formula (11), the formula for calculating the weight can be obtained as:

By integrating the observations into the probability distribution, sampling can be concentrated in regions where the observation likelihood is meaningful. Doucet proposed the optimal importance probability density function, and Formula (13) is the optimal distribution of the particle weights.

The Kalman filter-STI model relies on a high-resolution, high scan frequency SLAM algorithm that ignores the information of labour-based talents. Since the Hector SLAM algorithm for 3D motion estimation is based on 2D planar localisation information, it can be easily extended to a common planar Kalman filter-STI model.

The optimal density _{t}

The first-order Taylor expansion of

The solution of Formula (17) can be derived by making Formula (16) obtain a value of 0, as shown in Formula (18) below:

Where

_{m}

By taking the partial derivatives of

The optimal estimate of can be obtained by the above steps, the matched Chinese economic development data are stored in multiple layers by borrowing the idea of innovative human capital pyramid, and the layers are arranged in descending order of raster precision [27–29]. When searching the STI model, the optimal solution is obtained by starting from the one with the lowest raster precision, the optimal solution is used as the initial estimate of the probability function of innovative human capital in the previous layer, and the search is carried out layer by layer. Also, for computational efficiency, the Gaussian filtering and down-sampling methods are avoided, and the innovative human capital density data are directly used to generate multiple economic development tables with different probability distributions.

Based on the innovative human capital stock measured by the Kalman filter algorithm model, this section measures the innovative human capital of each province in China from 2005 to 2021, and selects typical years to analyse the evolution of innovative human capital in China’s regions (Figure 1).

The only region with a high value of innovative human capital stock in 2005 is Beijing. Beijing accounts for the largest share of innovative human capital in China, with a share of about 34.59% [30]. The top six include Beijing, Shanghai, Jiangsu, Shaanxi, Sichuan and Hubei, all of which have a share of >13.4%. Among them, four regions, namely Tibet, Ningxia, Hainan and Qinghai, all have a share of <13%. In 2001, China joined the WTO, and in the context of economic globalisation, the CPC Central Committee and the State Council jointly formulated and issued the ‘2002–2005 China Talent Team Construction Planning Outline’, proposing the implementation of ‘Talent Power Occupation Rate’, through the vigorous development of education and science and technology, in order to promote China’s economic development, and to meet the opportunities and challenges brought by economic globalisation. Compared with 2005, the total innovative human capital of all regions increased by 27.41% in 2010, and the innovative human capital stock of central and eastern provinces and major cities has increased substantially. The stock of human capital in Beijing remains number one, while the human capital in Jiangsu has increased from third in 2005 to second in 2010, with a share of 44.15% and a 14.4% increase. The stock of human capital in Ningxia, Hainan, Tibet and Qinghai also shows a certain degree of growth, but its share decreases nationwide, accounting for <2.8%. By 2015, the sum of innovative human capital across regions increased by 6.15% compared to 2010. Beijing remains in first place with a share of about 55.98%. This is followed by Jiangsu, which has >43.6% of the innovative human capital stock, significantly ahead of other provinces. Although the innovative human capital stock of Ningxia, Hainan, Tibet and Qinghai has increased, its share in the national stock has further decreased, accounting for <22.6%, and the location factor is the direct reason limiting the growth [31]. By 2021, these four regions still have the lowest share of innovative human capital stock, and their ability to attract human capital is low.

The map of the sub-spatial distribution of innovative human capital reveals that most of China’s innovative human capital is mainly concentrated. In order to further investigate the deep-seated reasons for the uneven distribution, we analysed the impact of the International Three Systems.

As can be seen from Figure 2, the number steadily ranks among the top three in China in all years. Beijing has a good environment and resources for science and technology innovation. In 2017, the number of scientific and technical papers indexed by the International Three Systems in Beijing was more than twice higher than that of Shanghai [32, 33]. In terms of the proportion of China’s share of the number of scientific and technical papers included in the International Three Systems by provinces and major cities from 2005 to 2021, Beijing’s share decreased from 45% to 31%, Shanghai’s share decreased from 34% to 21%, and Jilin and Gansu’s shares decreased. In 2021, Shanghai, in third place, similar to Beijing, is the place where the world’s information technology exchange is gathered and has earlier access to the frontier of science and technology, which can effectively place Shanghai’s science and technology scholarly research output ahead of other provinces. Jiangsu Province, in second place, has a large number of industrial talents and is a major manufacturing province, which provides a driving force for China’s economic growth.

Figure 3 shows the spatial distribution. The number generally showed a steady increasing trend during the period 2005–2018. Among them, Guangdong, Zhejiang and Jiangsu Provinces steadily ranked the top three in the country, and the numbers in these three provinces in 2005 were 72,520, 47,111 and 29,911, respectively. By 2021, the numbers in Guangdong, Zhejiang and Jiangsu Provinces were 803,214, 501,250 and 700,123, respectively, and the activities connected with patent development and application far exceeded those of other provinces [34]. From the perspective of regional rise, the number in Anhui Province in 2018 is nearly 54 times higher than that in 2005. Fujian Province, driven by some high-tech enterprises, has seen a significant increase and has been among the top 10 in the country since 2015.

The economic development plays a transitional role in catching up with the east and taking over the west, and the central region is in the middle of the pack, both in terms of total volume and growth rate. The central region is an important undertaking area in the process of industrial transfer from the eastern region. As there is an obvious economic gradient between the eastern and central regions, the resulting gradient difference provides sufficient preconditions for industrial transfer. At present, the factor payoffs have not yet entered the bottleneck period of significant decreasing [35]. Therefore, for the central region, expanding the investment of capital is the key layout to achieve economic development and human capital layout.

The contribution can be divided into direct contribution and indirect contribution. The direct contribution is an indication of innovative human capital, i.e. the attribute of production factor, which is the most basic attribute of innovative human capital; contrastingly, the indirect effect refers to the fact that the input of scientific knowledge and professional skills of innovative human capital in the production process will have a significant promotion effect on the regional economy; in most cases, the technological progress is distributed in the society as a kind of public information, and thus the generation of new technologies in one region will have technological spillover effects on the technological progress in other regions, i.e. innovative human capital has knowledge effects and external effects.

When the stock is high in a region, it can not only contribute to the technological growth directly through the technological development of innovative human capital, but also make the region have enough technological absorption capacity to absorb the technological spillover from other regions.

In 2005, the only region with a high value of innovative human capital stock was Beijing, with a share of about 34.59%. In 2015, the sum of innovative human capital in each region increased by 6.15% compared to 2010. Beijing’s share remains in first place, at about 55.98%. By 2021, these four regions still have the lowest share of innovative human capital stock, and their ability to attract human capital is low.

From 2005 to 2021, the proportion of scientific and technical papers included in the International Three Systems in China decreases from 45% to 31% in Beijing, from 34% to 21% in Shanghai, and decreases in Jilin and Gansu. Jiangsu Province is the province with the largest increase in the proportion, from 13% to 26%, and the other provinces all remain within the 4% increase range.

As of 2021, the numbers in Guangdong, Zhejiang and Jiangsu Provinces are 803,214, 501,250 and 700,123, respectively, and the activities connected with patent development and application far exceed those of other provinces. From the perspective of regional rise, the number in Anhui Province in 2018 is nearly 54 times of that in 2005.

The following thoughtful countermeasure suggestions are made accordingly, taking into account the actual situation in China in recent years.

The first measure is to increase the investment in higher education research funds and pay attention to the cultivation of innovative talents in higher education. The original power source of innovative human capital is talents with higher education, and therefore, education is an important means to improve the quantity and quality of human capital.

The second is to guide the positive flow of innovative talents. The economically developed regions in the east are more capable of attracting innovative talents. The economy is more backward and the type of industry is mostly traditional, and thus the ability to attract innovative talents is poor. The central and western regions with high potential for innovative talents need to establish and improve various incentive mechanisms to increase the employment opportunities for innovative talents and ensure the retention of human capital for local use. In addition, some studies have shown that increasing workers’ compensation helps to increase the number of years of education, which releases the ‘force capital dividend’ and has a significant effect on economic growth. Finally, it is important to strengthen holistic thinking. At present, China still suffers from unfair allocation of educational resources and barriers to talent mobility, which leads to insufficient human capital mobility between economically developed regions and less developed regions. The country should take effective measures to strengthen the learning collaboration between innovative talents from different regions.

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prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network