Kalman Filter Tracker

Unofficial implementation of SORT, A simple online and realtime tracking algorithm for 2D multiple object tracking in video sequences.

SORT is based on the idea of a discrete Kalman Filter,representing each object to be tracked.

Kalman Filter estimates the state vector X of a discrete-time controlled process that is governed by the linear stochastic difference equation.

---

Using Kalman Tracker (SORT) with YOLOV4

Colab Example Enable GPU (Oxford TownCentre)

Prerequisites

• Numpy
• scipy.optimize.linear_sum_assignment

• removeTrackAfternFramesThres - Number of frames to try to match a missed object before you delete it
• uncertaintyCount - Number of frames to consider an object as a confirmed tracker (an object can be Confirmed ("C"), UnCertain ("U), Missed ("M"))

$ git clone https://github.com/marwankefah/Kalman-Tracking-Single-Camera

 from Kalman_Tracking_Single_Camera.src import tracking
 from Kalman_Tracking_Single_Camera.src import helpers as hp 
 tracker=tracking.KalmanTracking(IOUThreshold=0.3 ,removeTrackAfternFramesThres=40,uncertaintyCount=1)
 
LOOP 
 GET DETECTION FROM YOUR DETECTION MODEL [[xminNew, yminNew, xmaxNew, ymaxNew],....]
 ## Return trackers in the form [[id,[xminNew, yminNew, xmaxNew, ymaxNew]],...] that matches the confirmed state
 trackers=tracker.match(detections,state="C")
END LOOP    

Tracking with constant velocity (linear observation model)

Equation of Motion

• y^'' (t)= 0 (acceleration a) (constant Velocity model)

• y^'(t)=y^'(to) - a(t-to)

• y(t)= y(to) + y^'(to) (t-to) - a/2 (t-to)^2

State Representation

• X = A X_t-1 + B_t U_t + R_t

• Z = C_t X_t + Q_t

  • X (state of persons in the system)
  • z (measurements taken from Object Detection Model)
  • A (Matrix that maps previous state to current State)
  • B (Matrix that maps actions to states)
  • U (Actions Taken)
  • C (Matrix that maps mesurement to state)
  • R (Process Noise, noise comming from the motion model)
  • Q (Measurement Noise, noise comming from the object detection model)

Q and R covariance matrices are assumed to be independent and normally distributed. Q is chosen to be small as it correlate with how well your Object Detection Model Performs. R was assumed and adopted from the official Repository of SORT. However, someone can try to estimate such matrix from this paper.

• State X is (nx1), where n=8 (dimensions) =[X,Y,A,H,Vx,Vy,Va,Vh]

• Measurement Z vector is [X,Y,A,H] (Object Detection Model)

  • X (bounding box center position along the x axis)
  • Y (bounding box center position along the y axis)
  • A (Aspect Ratio of the bounding box calculaed by Width/Height)
  • H (Height of the bounding box)
  • V_x, V_y, V_a,V_h are the rate of change of the above variables (velocity) respectively.