Kalman filtering and it's applications
- 1. KALMAN FILTERING & ITS APPLICATIONS PREPARED BY: Y.MADHAVASAI 17A51A04B8
- 2. Rudolf Kalman was born in Hungary on 19 May 1930. He completed his Master's degree in Electrical Engineering from Madras institute of technology in 1953-54 respectively. He left M.I.T. and continued his studies at Columbia University where he received his ScD. in 1957 under the direction of Professor J. R. Ragazzini. Based on recursive Bayesian he developed a filter in two years time period i.e., from 1960-61. Rudolf e kalman
- 3. In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), It is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies It produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán , one of the primary developers of its theory.
- 4. Kalman filter-Basic block diagram:
- 5. • A kalman filter is a more sophisticated smoothing algorithm that will actually change in real time as the performance of various sensors change and become more or less reliable. • What you want to do is filter out noise in our measurements and in our sensors and kalman filter is one way to do that reliability
- 6. Kalman filters are used to estimate states based on linear dynamical systems in state space format. The process model defines the evolution of the state from time k−1 to time k as: xk=Fxk−1+Buk−1+wk−1 Where, F -state transition matrix B -control-input matrix Wk−1 - noise vector assumed to be zero mean gaussin .
- 7. The process model is paired with the measurement model that describes the relationship between the state and the measurement at the current time step k as: zk=Hxk+νk where zk is the measurement vector, H is the measurement matrix, and νk is the measurement noise vector that is assumed to be zero NOTE : sometimes the term “measurement” is called “observation” in different literature
- 12. Estimation in kalman filter:
- 14. APPLICATIONS Image processing Terrain-referenced navigation Gps tracking devices Computer vision
- 18. TERRAIN-REFERENCED NAVIGATION 1)Terrain-referenced navigation (TRN), also known as terrain-aided navigation (TAN) 2)it provides positioning data by comparing terrain measurements with a digital elevation model (DEM) stored on an on-board computer of an aircraft. 3)It also known as terrain-aided navigation (TAN),