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matrix in solving the four-tuple differential equation, the computational complexity is impractical for the high-dimensional problem, and the other is to consider the use of nonlinear filtering algorithms, such as the non-trace Kalman filter [5], particle filter, etc., but they are extremely complex and cumbersome com
model (State Transfer Matrix) used in the previous state. B [k] is used to control the input model (input and output matrix) on the control vector u [K ), U [k] is used to allow external control to be applied to the system W [k] is a process noise. If the mean value is 0 and the covariance is Q [K], W [k] ~ N (0, Q [k]) Assume that the real
the control value for the system at K moment. A and B are system parameters. For multi-model systems, they are matrices. Y (k) is the measured value at K time, and H is the parameter of the measurement system. H is the matrix of multiple measurement systems. Q (K) and R (k) represent process and measurement noise respectively. They are assumed to be white Gaussian noise and Their covariance is Q and R (Her
the previous two formulas, x (k) is the system state at K moment, and U (k) is the control value for the system at K moment. A and B are system parameters. For multi-model systems, they are matrices. Z (k) is the measured value at K time, and H is the parameter of the measurement system. H is the matrix of multiple measurement systems. W (K) and V (k) represent the process and measurement noise respectively. They are assumed to be white Gaussian nois
description involves some basic conceptual knowledge, including the probability (probability), the variable (random Variable), the Gaussian or normal distribution (Gaussian distribution), and the State-space model. However, the detailed proof of the Kalman filter can not be described here.First, we need to introduce a system of discrete control processes first. The system can be described by a linear stoch
......... (2) In formula (2), P (k | k-1) is the covariance of X (k | k-1), P (K-1 | k-1) is the covariance of X (K-1 | k-1, a' indicates the transpose matrix of A, and Q is the covariance of the system process. Formula 1 and 2 are the first two of the five formulas of Kalman
Kalman filter is an algorithm which uses the state equation of linear system to estimate the state of the system by the input and output data. The optimal estimation can also be regarded as the filtering process because of the influence of the noise and interference of the system.The core content of the Kalman filter i
perspective of the sense of view, welcome to discuss.Covariance represents what, covariance indicates the relationship or relationship between the two, the greater the relation, the greater the covariance. The smaller the error covariance, the less the relationship between process noise and measurement noise. The smaller the relationship, the less you can do, th
. We use P to represent covariance: P (k | k-1) = a p (K-1 | k-1) a' + q ......... (2) In formula (2), P (k | k-1) is the covariance of X (k | k-1), P (K-1 | k-1) is the covariance of X (K-1 | k-1, a' indicates the transpose matrix of A, and Q is the covariance of the system
These two days to learn some of the Kalman filtering algorithm related knowledge. Compared with other filtering algorithms, Kalman filter has a very low demand for computational capacity, and can achieve quite good filtering results.1. Algorithm principle See an article on the net http://www.bzarg.com/p/how-a-kalman-
-------This article as a waiver of ACM competition to the beginning of the Electronic Design Competition, ACM competition really need time, accurate say for me such a rookie is too waste of time, but then two years time from the real harvest a lot ofI do not understand the principle of Kalman filter, Ah, but with this library function to do a balanced car is absolutely no problem, so do not understand not t
Kalman filter is built onHidden Markov ModelIs a recursive estimation. That is to say,You only need to know the estimated value of the previous State and the observed value of the current State to calculate the optimal estimated value of the current state. You do not need earlier historical information. Two statuses of Kalman
First, we need to introduce a discrete control process system. The system can be described by a linear random differential equation (Linear Stochastic difference equation), coupled with the system's measured values: In the previous two statements, the system state at the moment is used to control the system at the moment. And are system parameters. For multi-model systems, they are matrices. It is the measured value of time and a parameter of the measurement system. For multiple measurement sys
I. Problems to be Solved by Kalman Filter First, let's talk about what kind of problems the Kalman filter should solve and how such systems should be modeled. Here we talk about the linear Kalman filter, which is a linear dynamic
A -A = Np.matrix ([[1.0, 0.0, DT, 0.0], the[0.0, 1.0, 0.0, DT], -[0.0, 0.0, 1.0, 0.0], -[0.0, 0.0, 0.0, 1.0]]) - + #Measurement Matrix - #We directly measure the velocity VX and VY +H = Np.matrix ([[0.0, 0.0, 1.0, 0.0], A[0.0, 0.0, 0.0, 1.0]]) at - #Measurement Noise Covariance -RA = 10.0**2 -R = Np.matrix ([[Ra, 0.0], -[0.0, RA]]) - in #Process Noise Covariance
The non-trace Kalman filter (unscented Kalman filter) needs no trace transformation. The unscented transform is described in Wikipedia as follows:The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear Transformation to a probability distribution, that's charact
deviation of the optimal value (24.56 degrees) of the K-moment. The algorithm is as follows: ((1-kg) *5^2) ^0.5=2.35. Here's 5 is the above K time you predict the 23 degrees of temperature deviation, the 2.35 is to enter the k+1 time after the K time estimate of the optimal temperature value deviation (corresponding to the above 3). In this way, the Kalman filter constantly recursive
Because Kalman filtering is used in the study, this is a very hard-to-understand control theory. It took me a long time to understand some basic concepts. Although opencv provides an example, however, this example is based on C, which is hard to understand and reuse. Later I sorted out a simple class, during the Forum, a handsome romantic french guy was studying the filter. Later I gave him the program and
It is difficult to understand the control theory. It takes me a long time to understand some basic concepts. Although opencv provides an example, this example is based on C, it was hard to understand and reuse. Later I sorted out a simple class. During the forum, a French guy with handsome Romantic was also studying this filter, later, I gave him the program and sent it to me after modification, so the code here also contains his part, which is a Sin
of the previous moment, and the current observed value y, you also need to establish the state equation and measurement equation.With this, you can use Kalman filter. Opencv comes with a routine to track the motion of a one-dimensional point. Although this point is moving in a two-dimensional plane, because it is moving on an arc, there is only one degree of freedom, angle, so it is still one-dimensional
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