1 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Kalman Filter Techniques J.Narendra Babu 1 , Dr.Chandan Majumdar 2 1 myece88@gmail.com __________________________________________________________________ Abstract This paper answers several questions of centralized Kalman-Filters in multi-sensor fusion, fault detection and isolation in sensors, optimal control in linear-quadratic Gaussian problem, an algorithm in fuzzy based approach to adaptive Kalman-Filtering additionally in multi-state multi-sensor fusion. Generally, Kalman-Filters comprise a number of types and topologies depending on use and computing complexity of applied processors. State estimation provided by a Kalman-Filter is crucial in this thesis. Kalman-Filter performs optimal estimation of an unknown system state through filters behavior. This thesis supposes some models of promising linear Kalman- Filter simulated beyond MATLAB and Simulink program especially utilized in the fields of steering-controls or navigations, etc. Index Terms — Kalman-Filter, multi-sensorfusion, Fuzzy-Logic, Gaussian, Optimal estimate ______________________________________________________________________________________ 1. Introduction In this paper, we dedicate the effort to introduce Kalman filter - KF techniques with 2 models of conventional Kalman filter, CoKF, mainly. Although there is no difference between centralized Kalman filter CKF and CoKF, we like to show the CoKF as an estimator structure in single-sensor systems First of all, we will assume a mathematical model of a plant defined by equations of discrete system dynamics. To get the equations of the optimum estimator, i.e., the KF, suppose that the plant of system dynamics are designed by the (possibly time-varying) general model of linear finite- dimensional stochastic system, see below; [1], [2]. x(n + 1)= Ax (n )+ Bw(n ) (1-1) y v (n )= Cx (n )+ v(n ) , n ≥ n 0 ( 1-2 2. Model 1 of Kalman filter In this part, investigates a timing diagram of KF In order to get a control program flow with applied equations in Table 2-1 below. This will be also introduced briefly in next model. The model refers to [1 - 2]. The table deals with two programs, i.e. initial program and main iterative program. The Initial time n 0 is the formal time when processor does not process Table 2-1 first sample but starts an initial program Intional Program Initial Time n=0 P(n|n-1) = B Q d B T , where Q d is defaulted Q(0) > 0 (2-1) x(n|n-1) = 0 (2-2) y e (n) = 0 (2-3) Iteration Time n = 1,2,3,… M(n) = P(n|n-1) C T / (C P(n|n-1) C T + R(n)) (2-4) r(n) = y v (n) – C x(n|n-1) (2-5) x(n|n) = x(n|n-1) + M(n) r(n ) (2-6) P(n|n) = [I - M(n) C] P(n|n-1) (2-7) y e (n) = C x(n|n) (2-8) error cov = C P(n|n) C T (2-9) x(n+1|n) = A x(n|n) + B u(n ) ( 2-10) P(n+1|n) = A P(n|n) A T + B Q(n) B T (2-11)