轨迹数据挖掘-介绍讲解学习.ppt

Mean Filter Also called “moving average” and “box car filter” Apply to x and y measurements separately zx t Filtered version of this point is mean of points in solid box “Causal” filter because it doesn’t look into future Causes lag when values change sharply Help fix with decaying weights, e.g. Sensitive to outliers, i.e. one really bad point can cause mean to take on any value Simple and effective (I will not vote to reject your paper if you use this technique) Mean Filter 10 points in each mean Outlier has noticeable impact If only there were some convenient way to fix this … outlier Median Filter zx t Filtered version of this point is mean median of points in solid box Insensitive to value of, e.g., this point median (1, 3, 4, 7, 1 x 1010) = 4 mean (1, 3, 4, 7, 1 x 1010) ≈ 2 x 109 Median is way less sensitive to outliners than mean Median Filter 10 points in each median Outlier has noticeable less impact outlier Joke The one about the statisticians who go hunting Kalman Filter My favorite book on Kalman filtering Mean and median filters assume smoothness Kalman filter adds assumption about trajectory Assumed trajectory is parabolic data dynamics Weight data against assumptions about system’s dynamics Big difference #1: Kalman filter includes (helpful) assumptions about behavior of measured process Kalman Filter Big difference #2: Kalman filter can include state variables that are not measured directly Kalman filter separates measured variables from state variables Running example: measure (x,y) coordinates (noisy) Running example: estimate location and velocity (?!) Measure: Infer state: Kalman Filter Measurements Measurement vector is related to state vector by a matrix multiplication plus noise. Running example: In this case, measurements are just noisy copies of actual location Makes sensor noise explicit, e.g. GPS has σ of around 4 meters Kalman Filter Dynamics Insert a bias for how we think system will change through time location is standard