The following examples demonstrate the conceptual operation of Caesar, highlighting specific features of the framework and its use.
This abstract example illustrates how
IncrementalInference enables algebraic relations between stochastic variables, and how a final posterior belief estimate is calculated from several pieces of information.
Continuous Scalar Example
A simple 2D robot trajectory example is expanded below using techniques developed in simultaneous localization and mapping (SLAM).
Hexagonal 2D Example
Fixed-Lag Solving - Hexagonal2D Revisited
A Under-Constrained Solution (unforced multimodality)
This tutorial describes a range-only system where there are always more variable dimensions than range measurements made. The error distribution over ranges could be nearly anything, but are restricted to Gaussian-only in this example to illustrate an alternative point – other examples show inference results where highly non-Gaussian error distributions are used.
Multi-modal range only example (click here or image for full Vimeo):
Multi-Modal Under-Constrained Example
Uncertain Data Associations, a Multi-Modal Solution (forced multi-hypothesis)
Documentation in progress, in the mean time please see the
addFactor!(..., multihypo=[1.0; 0.5;0.5])feature for 50/50 uncertainty. Similarly for trinary or higher multi-hypotheses per factor.
TODO: add example.
Adding Factors - Simple Factor Design
Caesar can be extended with new variables and factors without changing the core code. An example of this design pattern is provided in this example.
Defining New Variables and Factor
Adding Factors - DynPose Factor
Intermediate Example: Adding Dynamic Factors and Variables
Application Examples and Demos
Multi-session Turtlebot example of the second floor in the Stata Center:
Simulated Ambiguous SONAR in 3D
Intersection of ambiguous elevation angle from planar SONAR sensor:
Synthetic Aperture Sonar SLAM
The full functional (approximate sum-product) inference approach can be used to natively imbed single hydrophone acoustic waveform data into highly non-Gaussian SAS factors–that implicitly perform beamforming/micro-location–-for a simultaneous localization and mapping solution (image links to video):
Please see examples folders for Caesar and RoME for more examples, with expanded documentation in the works.