Hugo Hadfield
Cambridge University PhD student, Signal Processing and Communications Laboratory
Several high definition cameras
Automotive RADAR
Speed and steering sensors
LIDAR system
GPS and IMU/INS
Minimise \(C\) with respect to \(\Phi_i\) and \(Y_j\)
Minimise \(C\) with respect to \(\Phi_i\) and \(Y_j\)
This is a Convex Optimisation Problem
For derivatives we can simply construct the clifford algebra over the complex numbers or over the dual numbers!
We can calculate automatic derivatives through complex/dual number autodiff
See the work of Jeffrey Fike:
If we take our collection of cameras on a drive they can repeatedly do bundle adjustments and build up a 3D map of the world!
We could even use multiple frames from a single camera moving through space
Given a noisey sequence of measurements of the positions of a moving car how do you estimate its position at any point in time?
Describe each position with a rotor
Convex optimisation, minimising difference between position and measurment and function of the path
Describe the state of the car at a point in time with a vector
We include, combined position and rotation: \(\Phi\)
Combined linear and angular velocity: \(\Psi\)
Design a function that takes a given state and advances it one time step. Use this motion model to propogate uncertainty about the state of the car:
This is the basic setup required for an (extended/unscented) Kalman Filter
Set up a state like this:
Set up a process function (Cayley kinematic equation):
Set up a measurement function:
Given a depth image of the road, reject outliers and fit a plane
Monodepth machine learning models generate depth maps
force magnitude
force direction
3d point through which the line passes
By Hugo Hadfield
Cambridge University PhD student, Signal Processing and Communications Laboratory