Multi-Object Tracking using Unscented Kalman Filters

This project implements an Unscented Kalman Filter to estimate the state of multiple cars on a highway using noisy LiDAR and Radar measurements.

Building the project

The main program can be built and ran by doing the following from the project top directory.

1. mkdir build
2. cd build
3. cmake ..
4. make
5. ./ukf_highway

Structure

main.cpp is using highway.h to create a straight 3 lane highway environment with 3 traffic cars and the main ego car at the center. The viewer scene is centered around the ego car and the coordinate system is relative to the ego car as well. The ego car is green while the other traffic cars are blue. The traffic cars will be accelerating and altering their steering to change lanes. Each of the traffic cars has its own UKF object generated for it, and will update each indidual one during every time step.

The red spheres above cars represent the (x,y) lidar detection and the purple lines show the radar measurements with the velocity magnitude along the detected angle. The Z axis is not taken into account for tracking, so we are only tracking along the X/Y axis.

Other Important Dependencies

• cmake >= 3.5
  • All OSes: click here for installation instructions
• make >= 4.1 (Linux, Mac), 3.81 (Windows)
  • Linux: make is installed by default on most Linux distros
• gcc/g++ >= 5.4
  • Linux: gcc / g++ is installed by default on most Linux distros
• PCL 1.10

Normalized Innovation Squared (χ² test)

In order to determine how well the uncertainty of the system was captured, the Normalized Innovation Squared (NIS) scores for each measurement were taken and evaluated.

From the following table we find that a system of 2 degrees of freedom (DOF) like the LiDAR sensor, a 95% value of 5.991 (χ².050) is to be expected - i.e. 95% of all NIS values for a system of 2 DOF are less than 5.991 - whereas a system of three DOF like the Radar has an according 95% value of 7.815:

Initially,

• an acceleration standard deviation of 2 m/s², and
• a yaw acceleration standard devation of 45°/s²

were assumed. At this configuration, the following NIS scores were observed for the LiDAR.

Here, we can observe that approximately 93% of all values are below threshold, i.e. we overestimated the system's uncertainty.

For the Radar we find that about 90% of all values are below threshold, reinforcing the point.

After this, the uncertainty was tuned to have less uncertainty in angular acceleration:

• acceleration standard deviation: 2 m/s²
• yaw acceleration standard devation: 22.5°/s²

Interestingly, this affected the LiDAR measurements, which now closely resemble the wanted distribution:

The Radar measurments, however, did not change significantly:

Increasing the acceleration uncertainty such that

• acceleration standard deviation: 12 m/s²
• yaw acceleration standard devation: 22.5°/s²

gave good feedback for both the LiDAR measurements:

... as well as the Radar measurements:

By observation, the RMSE values obtained in the simulator appeared to be lower with a slightly reduced acceleration autocovariance of 8 m/s².

The result of this process is shown at the beginning of this README.