## 1 Introduction  
Accurate measurement of running parameters such as the step length (\(SL\)), step frequency (\(SF\)), and _running velocity_ is crucial for analyzing performance in sprinting events [1, 2]. These parameters provide valuable insights for training optimization [3]. Traditionally, they have been obtained using two-dimensional (2D) video analysis [4]. However, 2D analysis typically offers only segment-based averages (e.g., every 10-20 m in a 100 m sprint [5] or every 50 m in a 400 m sprint [6]) and fails to capture detailed, step-by-step variations, limiting assessment of fluctuations in acceleration, peak velocity,and asymmetries. Three-dimensional (3D) motion capture is more precise but expensive, complex, and less practical [7]. Wearable sensors overcome these limitations, enabling detailed per-step analysis [8]. For example, studies utilizing smart socks [9] and insole sensors [10; 11] have confirmed their ability to accurately capture foot contact timing. However, while these sensors can determine contact timing and estimate the \(SL\) based on averaged values, they are not capable of conducting a detailed step-by-step analysis. Furthermore, inertial measurement units (IMUs), widely used as wearable sensors [12], effectively detect initial contact (IC) timings and provide continuous temporal data [13]. However, estimating the \(SL\) from IMUs is difficult due to cumulative errors and drift [14; 15], especially at higher speeds [16], and requires complex calibration and data processing [17]. To our knowledge, no prior research has presented a single-sensor wearable solution which reliably captures step-by-step \(SL\) data throughout a full 400 m sprint. Real-time kinematic global navigation satellite systems (RTK GNSSs) overcome IMU-related drift issues by providing centimeter-level positional accuracy [18]. Unlike IMUs, which accumulate drift over time, an RTK GNSS directly measures absolute positions in real time, preventing drift-related errors even during extended runs. Previous studies have shown that low-cost RTK GNSS modules, when mounted on the head and operating at 1-5 Hz, improve distance accuracy over standard GPS watches [19]. However, such low sampling rates limit the ability to capture stride-to-stride variations in sprinting. With recent developments enabling sampling rates up to 100 Hz--well above the conventional 10-15 Hz [14]--RTK GNSSs may now allow precise detection of the \(SF\) and accurate estimation of the \(SL\). As the \(SL\) and \(SF\) define the _running velocity_ (_velocity_ = \(SF\times SL\)), all key parameters can be derived directly outdoors, free from the constraints of 3D motion capture systems. In this study, we propose a novel approach to estimating the running parameters for every step across an entire 400 m sprint using a 100 Hz RTK GNSS receiver. This approach enables the calculation of running parameters on a per-step basis, offering a drift-free, single-sensor solution which eliminates the need for additional devices such as IMUs. We explored two theoretical methods for extracting running parameters from the RTK GNSS data, with both grounded in the spring-mass model of running mechanics [20; 21]. The first method (Method 1: vertical position minima) leverages the concept of the spring-mass model [20; 21], in which the center of mass (CoM) reaches its lowest point mid-stance. Such a head-mounted GNSS approach has been used in other cyclical sports, such as cross-country skiing, to capture precise kinematic patterns [22; 23]. These minima can be used to estimate running parameters such as the \(SF\) and \(SL\). This method relies solely on position data--direct outputs from GNSS--making it computationally straightforward. However, left-right asymmetries in sprint running [24; 25] may distort vertical displacement patterns, potentially introducing timing errors. Therefore, we propose the second method (Method 2: vertical velocity minima) as an alternative to the first method.