KONSTRUKSI DAN IMPLEMENTASI ALGORITMA FILTER KALMAN PADA MODEL TEREDUKSI; CONSTRUCTION AND IMPLEMENTATION OF THE KALMAN FILTER ALGORITHM ON REDUCED MODELS

Arif, Didik K, Widodo

2015 | Tesis | FMIPA

Filter Kalman is an estimation method of state variable from a stochastic dynamic system. Estimation of state variable on a system is needed to be carried out since not all of state variable can be directly measured from available data. Kalman filter has two main basic filtering namely Kalman and Information filters. Estimation using Kalman filter, in fact, has some major disadvantages, e.g. numerically filtering unstable and high computational time. In order to maintain filtering stability numerically, the covariance matrices have been written on the Kalman filter and the information matrix of Information filter in square root form. The algorithms are known as Square Root Covariance Filter (SRCF) and Square Root Information Filter (SRIF). The SRCF and SRIF filters are much more numerically stable than Kalman or Information filters. However, it needs more computational time. Subsequently, to reduce computational time in the SRCF and SRIF filters, it requires a rank reduction of its square root matrices. These methods are known as the Square Root Covariant Filter with Reduced Rank (SRCFRR) and the Square Root Information Filter with Reduced Rank (SRIFRR). In this present study, a combination of estimation method between the Kalman filter and the reduced model has been performed. Method of reduced model to be applied is the balanced cut method. Combination of the two methods formed the Kalman filter algorithm on reduced system. Formation of the Kalman filter algorithm on reduced system has been started with forming the Kalman filter algorithm on balanced system. Then, the Kalman filter algorithm on balanced system has been given the properties that apply to the reduction process model. In this present study, it also analyzed the existence requirements and the Kalman filter stability on reduced system. Finally, the implementation the Kalman filter algorithm on reduced system has been employed in the case of thermal conductive distribution. Estimation of thermal conductive distribution on the one dimensional of metal wire is a good example of the high order system. Simulation results show that the estimation of the Kalman filter on reduced system has more accurate results and less computational time compared with Kalman filter on initial system.

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