Introduction:
"Visual Kalman Filter " is a visual math tool to simulate Kalman filter for linear or nonlinear system. Only three steps you need do,and you'll get the curve and the estimated results. Its price is only $49.95.
Advanced Features:
- The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes
the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown.
- 'Visual Kalman Filter' provides a visual method to estimate the state of a process. The users need not install matlab, and there are only three steps to operate it. Finally if you click the state you want to observe, the figure and the values of the estimated result will appear immediately.
- The main operation you need to do is to set initial matrice. User has two choices: 1. Open an existent matrice txt file edited beforehand. For example, user can open the txt files in the folder 'Demos' in the installed path. 2. Fill the matrice manually, and save them in a txt file at last.
About Rudolf Emil Kalman(Some From Wikipedia)
Rudolf Emil Kalman, born on May 19, 1930, in Budapest, Hungary, is a Hungarian-American electrical engineer, mathematical system theorist, and college professor, who was educated in the United States, and has done most of his work there. He is currently a retired professor from three different institutes of technology and universities. He is most noted for his co-invention and development of the Kalman filter, a complicated mathematical formulation that is widely used in control systems, avionics, and outer space manned and unmanned vehicles. The Kalman Filter is almost always implemented using electronic digital computers; thus, it is method that is associated with electronics engineering. For this work, Kalman was awarded by U.S. President Barack Obama with the National Medal of Sciences on 7 October 2009.
About Kalman Filter (Some From Wikipedia)
The Kalman filter is an efficient recursive filter that estimates the state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering applications from radar to computer vision, and is an important topic in control theory and control systems engineering. Together with the linear-quadratic regulator (LQR), the Kalman filter solves the linear-quadratic-Gaussian control problem (LQG). The Kalman filter, the linear-quadratic regulator and the linear-quadratic-Gaussian controller are solutions to what probably are the most fundamental problems in control theory.
Kalman filters are based on linear dynamical systems discretised in the time domain. They are modelled on a Markov chain built on linear operators perturbed by Gaussian noise. The state of the system is represented as a vector of real numbers. At each discrete time increment, a linear operator is applied to the state to generate the new state, with some noise mixed in, and optionally some information from the controls on the system if they are known. Then, another linear operator mixed with more noise generates the visible outputs from the hidden state. The Kalman filter may be regarded as analogous to the hidden Markov model, with the key difference that the hidden state variables take values in a continuous space (as opposed to a discrete state space as in the hidden Markov model). Additionally, the hidden Markov model can represent an arbitrary distribution for the next value of the state variables, in contrast to the Gaussian noise model that is used for the Kalman filter. There is a strong duality between the equations of the Kalman Filter and those of the hidden Markov model. A review of this and other models is given in Roweis and Ghahramani .
In order to use the Kalman filter to estimate the internal state of a process given only a sequence of noisy observations, one must model the process in accordance with the framework of the Kalman filter. This means specifying the matrices Ak, Hk, Qk, Rk, and sometimes Bk for each time-step k as described below.
The Kalman filter model assumes the true state at time k is evolved from the state at (k − 1) with a measurement z.
where
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Ak is the state transition model which is applied to the previous state xk−1;
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Bk is the control-input model which is applied to the control vector uk;
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wk is the process noise which is assumed to be drawn from a zero mean multivariate normal distribution with covariance Qk.
where Hk is the observation model which maps the true state space into the observed space and vk is the observation noise which is assumed to be zero mean Gaussian white noise with covariance Rk.
The initial state, and the noise vectors at each step {x0, w1, ..., wk, v1 ... vk} are all assumed to be mutually independent.
Many real dynamical systems do not exactly fit this model; however, because the Kalman filter is designed to operate in the presence of noise, an approximate fit is often good enough for the filter to be very useful. Variations on the Kalman filter described below allow richer and more sophisticated models.
The Kalman filter is a recursive estimator. This means that only the estimated state from the previous time step and the current measurement are needed to compute the estimate for the current state. In contrast to batch estimation techniques, no history of observations and/or estimates is required. In what follows, the notation X(m/n) represents the estimate of X at time n given observations up to, and including time m.
The state of the filter is represented by two variables:
- X(k/k), the estimate of the state at time k given observations up to and including time k;
- P(k/k), the error covariance matrix (a measure of the estimated accuracy of the state estimate).
The Kalman filter has two distinct phases: Predict and Update. The predict phase uses the state estimate from the previous timestep to produce an estimate of the state at the current timestep. In the update phase, measurement information at the current timestep is used to refine this prediction to arrive at a new, (hopefully) more accurate state estimate, again for the current timestep.
Predict
Predicted state |
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Predicted estimate covariance |
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Update
Optimal Kalman gain |
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| Updated state estimate |
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| Updated estimate covariance |
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The formula for the updated estimate covariance above is only valid for the optimal Kalman gain. Usage of other gain values require a more complex formula found in the derivations section.
Invariants
If the model is accurate, and the values for X(0/0) and P(0/0) accurately reflect the distribution of the initial state values, then the following invariants are preserved: all estimates have mean error zero
Frame
Visual Kalman Filter
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| $49.95 |
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| 971KB |
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