Didik Khusnul Arif

Identification and estimation of state variables on reduced model using balanced truncation method

In this paper, we study the identification of variables on a model reduction process and estimation of variables on reduced system. We aim to relate variables on reduced and original system, so that we can compare the estimation accuracy of the original system and reduced system. As such, the objective of this paper is to discuss identification and estimation of variables on reduced model. First, model order reduction is done by using balanced truncation method. This process begins with the construction of balanced system. After that, we identify the relationship between variables of the balanced system and the original system. Then, we eliminate variables of the balanced system that have a small influence on the system. Furthermore, we estimate state variables on the original system and reduced system using a Kalman Filter algorithm. Finally, we compare the estimation result of the identified reduced and original system.

Estimation of three-dimensional radar tracking using modified extended kalman filter

Kalman filter is an estimation method by combining data and mathematical models then developed be extended Kalman filter to handle nonlinear systems. Three-dimensional radar tracking is one of example of nonlinear system. In this paper developed a modification method of extended Kalman filter from the direct decline of the three-dimensional radar tracking case. The development of this filter algorithm can solve the three-dimensional radar measurements in the case proposed in this case the target measured by radar with distance r, azimuth angle θ, and the elevation angle . Artificial covariance and mean adjusted directly on the three-dimensional radar system. Simulations result show that the proposed formulation is effective in the calculation of nonlinear measurement compared with extended Kalman filter with the value error at 0.77% until 1.15%.

Fractional kalman filter to estimate the concentration of air pollution

Air pollution problem gives important effect in quality environment and quality of humans life. Air pollution can be caused by nature sources or human activities. Pollutant for example Ozone, a harmful gas formed by NOx and volatile organic compounds (VOCs) emitted from various sources. The air pollution problem can be modeled by TAPM-CTM (The Air Pollution Model with Chemical Transport Model). The model shows concentration of pollutant in the air. Therefore, it is important to estimate concentration of air pollutant. Estimation method can be used for forecast pollutant concentration in future and keep stability of air quality. In this research, an algorithm is developed, based on Fractional Kalman Filter to solve the model of air pollutions problem. The model will be discretized first and then it will be estimated by the method. The result shows that estimation of Fractional Kalman Filter has better accuracy than estimation of Kalman Filter. The accuracy was tested by applying RMSE (Root Mean Square Error).

Accelerating simulation time of unstable discrete-time systems using Singular Perturbation Approximation

In the natural phenomenon, many systems are unstable. Moreover, the systems in the universe often have large order. The system that has a large order is more complicated than the system that has a small order. Therefore, we need to simplify the order of the system without any significant errors. Simplification of the system can be done using the reduction of the model. Model reduction can only be done on the stable system, so that the unstable system needs to be decomposed to obtain a stable subsystem that can be reduced. Singular Perturbation Approximation (SPA) method is one of the model reduction method. The reduced models are obtained by taking the speed of fast mode equal to zero. According to our simulation result using MATLAB, for reduced model having a small order (many state variables are removed) in low frequency, the model reduced using SPA is closer to original model compared with the model reduced using Balanced Truncation (BT). The time needed to simulate the reduced model is smaller than the time needed to simulate the original model. However, when the order of reduced model is small, then the error is big.