Spatial Angular Velocity vs Body Frame Angular Velocity

A while ago I had written about IMU pre-integration (blog-link). Particularly, I had played around with the inertial measurements data (IMU data) and tried to dig a bit deeper on what exactly does the IMU measurements mean. So the conclusion was that the IMU measure the body frame angular velocity and body-frame angular velocity (and … Continue reading Spatial Angular Velocity vs Body Frame Angular Velocity →

IMU Preintegration Theory

A while ago, I had explored the theory of IMU preintegration in the context of sensor fusion using a factor graph. The basic concept is that to use imu measurement as between factors for optimization we need to know the previous state. This is not convenient, however, a mathematical trick helps us make the between … Continue reading IMU Preintegration Theory →

Generating randoms from a specified CDF

This post deals with generating random numbers given a CDF (Cumulative distribution function). CDF may be specified as an analytical function or as a table of values. We also assume that we have a source of pseudo-random uniformly distributed numbers. Probability Integral Transform At the core of this issue is the 'Probability Integral Transform'. It states that, … Continue reading Generating randoms from a specified CDF →

Soft Indicator Function

Very often we come across indicator functions denoting class membership. These functions in their native form are neither continuous nor differentiable. I will describe a trick to convert such indicator functions to an approximate continuous and differentiable function. This blog is organized as follows: Describe a computation case with indicator function Trick to convert More remarks … Continue reading Soft Indicator Function →

Computing Padé Approximation with Maxima

Computationally intensive software programs can have a sharp performance profile. What I mean with sharp profile is that, there might be a couple of functions which are most time consuming. Very often such expensive functions are trigonometric functions. A way to increase performance is by use of approximations for trigonometric function. There is a trade … Continue reading Computing Padé Approximation with Maxima →