Dynamic Association of Semantics and Parameter Estimates by Filtering

TL;DR

The paper addresses linking semantic classifications to multiple vehicle-parameter estimates in a time-varying setting. It develops a probabilistic framework using a Dirichlet-normal-gamma prior and Bayesian Moment Matching to fuse multivariate measurements from categorical and Gaussian-mixture likelihoods. By introducing dynamics in the map parameters, it achieves exponential forgetting and robust tracking of time-varying semantic-parameter associations, with compute that scales linearly in the measurement dimension. Numerical experiments in a driving context show improved handling of time-varying friction properties compared to static approaches, and the method is positioned for integration with model predictive control and real-data validation.

Abstract

We propose a probabilistic semantic filtering framework in which parameters of a dynamical system are inferred and associated with a closed set of semantic classes in a map. We extend existing methods to a multi-parameter setting using a posterior that tightly couples semantics with the parameter likelihoods, and propose a filter to compute this posterior sequentially, subject to dynamics in the map's state. Using Bayesian moment matching, we show that the computational complexity of measurement updates scales linearly in the dimension of the parameter space. Finally, we demonstrate limitations of applying existing methods to a problem from the driving domain, and show that the proposed framework better captures time-varying parameter-to-semantic associations.

Figures (5)

• Figure 1: Semantic map in a driving application. $K=3$ semantic classes (red, green, and blue) are inferred from images passed through a segmentation model, and the map is updated using a categorical likelihood \ref{['eq:interpolatedcategorical']}. The semantics are associated with properties through the Gaussian mixture model \ref{['eq:extendedgmm']}, here visualized along one of $J$ dimensions at two locations.
• Figure 2: Average compute time over $10^6$ problems for a single Bayes update using the BMM scheme as a function of the measurement dimension $J$.
• Figure 3: Convergence towards a true distribution (black) as a function of the number of samples $k$, from blue to red with $(J,K)=(5,5)$. Error bars indicate variance in class probabilities through the categorical likelihood, and only the first two dimensions of the property likelihood are shown.
• Figure 4: True and estimated likelihoods with the static BMM (center) and the dynamic BMM (right). The likelihoods are shown at two points in time, 10% ($k = 0.1N$) and 100% ($k = N$) into the simulation, respectively.
• Figure 5: Trajectories of the latent parameters in the static case (blue) and dynamic case (red) versus the true map parameters (black) when the underlying parameters are time-varying $(\gamma = k/N)$.

Theorems & Definitions (18)

• Lemma 1: Dirichlet, sufficient moments, jaini2016online
• Lemma 2: Normal-gamma, sufficient moments
• proof
• Example 1: Driving
• Lemma 3: Posterior after categorical update
• proof
• Lemma 4: Posterior after Gaussian mixture update
• proof
• Lemma 5: Moment-matched posterior
• proof