# An Indirect Identification Method for Train Basic Resistance Parameters
## 1 Introduction  
Automatic Train Operation (ATO) technology plays a key role in the Intelligent Railway System, which executes the control of automatic train operation process and determines the quality of train operation [1]. The train basic resistance is an important component of train dynamics, which consists of axle bearing friction, rolling, and sliding friction between wheels and rails, impact resistance and air resistance. Its value accuracy affects the control performance of ATO system, but itself is affected by train formation, geometry, weight, wheel rail, climatic conditions, train running speed [2], etc. These factors have complex high-order coupling characteristics, making it difficult to directly calculate accurate resistance value using mechanism models. As a consequence, TBRPs are usually measured under experimental conditions to obtain a set of empirical parameters [3]. However, due to environmental conditions, such as wind speed, weather, air humidity, altitude, and air pressure, as well as the body wear and replacement of vehicle components, the TBRP change both fast and slowly over time. This leads to a deviation between the empirical parameters and the actual parameters, which may cause severe overshoot and oscillation of the model-based controller. In addition, basic resistance measurement techniques based on sensors are difficult to develop and costly. In response to this issue, researchers mainly approach it from two aspects: Basic resistance modeling and TBRPs identification. The first basic resistance formula was determined by [PERSON] [4], as shown in Equation (1):  
\[w(v)=a+bv+cv^{2} \tag{1}\]  
where \(v\) is running speed of train. The parameters \(a\), \(b\), \(c\) are resistance characteristic parameters. \(a\) is related to wheel rolling friction and bearing friction, \(b\) is related to wheelrail sliding friction, \(c\) is related to air resistance. Parameters \(a\), \(b\), \(c\) can be confirmed in the official train parameter specification when vehicle category has been determined. Subsequently, [PERSON] [5] built models for freight train and rolling resistance, and proposed introducing suspension resistance in the Davis formula. [PERSON] [6] analyzed the influence of air pressure and temperature change on the basic resistance of locomotive and vehicle operation by studying the data of the Sichuan-Tibet Railway. [PERSON] [7] analyzed the composition of high-speed train basic resistance and its relationship with train weight, achieving the decoupling of air resistance and other resistances. The above research has achieved significant results in basic resistance modeling. However, the high-order and complex basic resistance models are not suitable for the design of some linear controllers. The ever-changing operating environment and vehicle mechanical wear still cause basic resistance uncertainty. These factors led to some identification methods being proposed. One of the identification methods is the basic resistance characteristics identification method [8; 9; 10; 11; 12]. This method uses speed differences to calculate acceleration, then obtain the calculated basic resistance by [PERSON]'s second law. The objective function is to minimize the deviation between the characteristic curve of a set of TBRPs and the calculated basic resistance, as shown in Equation (2):  
\[\min_{\theta\in\Theta}\mathbf{O}_{LS}=\|\mathbf{Y}-\Phi\mathbf{\theta}\| \tag{2}\]  
where \(\mathbf{Y}\) is the calculated basic resistance, \(\mathbf{\theta}\) is basic resistance parameters, \(\mathbf{\Phi}=[1\), \(\mathbf{v}\), \(\mathbf{v}^{2}]\) is the input-output data information vector, \(\Theta\) is the definition domain of \(\mathbf{\theta}\). The objective function is greatly affected by the accuracy and precision of data acquisition. When data shaping or high amplitude sporadic noise exists, the error of basic resistance is large.