1 / 9

Kalman Filter: State Estimation for Dynamic Systems

Understand the Kalman Filter algorithm for state estimation in dynamic systems and its applications in radar tracking, stock market analysis, and more. Explore Kalman Filter vs. Particle Filter algorithms for time series data.

lorenzak
Télécharger la présentation

Kalman Filter: State Estimation for Dynamic Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Kalman Filter Notes Prateek Tandon

  2. Generic Problem • Imagine watching a small bird flying through a dense jungle. • You glimpse intermittent flashes of motion. • You want to guess where the bird is and where it may be in the next time step. • Bird’s state might be 6-dimensional: [x,y,z,x’,y’,z’] – three variables for position and three for velocity.

  3. Kalman Filter Xk = Fk xk-1 + Bk uk + wk (state update) Zk = Hkxk + vk (measurement update) Xk – current state Xk-1 – last state Uk – control input Wk ~ N(0,Qk), represents process noise distributed via multivariate zero-mean normal distribution with covariance Qk Vk ~ N(0,Rk), represents observation nose distributed via multivariate zero-mean normal distribution with covariance Rk Fk – state transition model Bk – control input model Hk – observation model

  4. Kalman Filter Algorithm PREDICT: Predicted State Predicted Covariance UPDATE: Innovation and Measurement Residual Innovation on CovarianceOptimal Kalman GainUpdated State EstimateUpdated Covariance Estimate

  5. Applications • Radar tracking of planes/missles/navigation • Smoothing time series data • Stock market • People tracking / hand tracking / etc • Sensor Data • GPS Location Data smoothing application

  6. Particle Filter Algorithm Function PARTICLE-FILTERING(e,N,dbn) returns a set of samples for the next time step Inputs: e, the new incoming evidence N, the number of samples to be maintained Dbn, a DBN with prior P(X0), transition model P(X1|X0), sensor model P(E1|X1) Persistent: S, a vector of samples of size N, initially generated from P(X0) Local variables: W, a vector of weights of size N For i=1 to N do S[i]  sample from P(X1 | X0 = S[i]) W[i}  P(E | X1 = S[i]) S  WEIGHTED-SAMPLE-WITH-REPLACEMENT(N,S,W) Return S

  7. Particle Filter Example Rain0 Rain1 Umbrella1

  8. Particle Filter Example Raint+1 Raint+1 Raint+1 Raint (a) Propagate (b) Weight, [Not Umbrella observed.] (c) Resample

  9. References • "Kalman Filter." . WIKIPEDIA, 13 APRIL 2013. Web. 13 Apr 2013. <http://en.wikipedia.org/wiki/Kalman_filter>. • Russell, Stuart, and Peter Norvig. Artificial Intelligence: A Modern Approach. 3rd. New Jersey: Pearson Education Inc., 2010. Print.

More Related