[Paper Review] Backprop KF: Learning Discriminative Deterministic State Estimators

Tuomas Haarnoja, Anurag Ajay+2 more|arXiv (Cornell University)|May 23, 2016

Human Pose and Action Recognition23 references101 citations

TL;DR

The paper presents Backprop KF (BKF), a discriminative, deterministic state estimator that unrolls a Kalman filter into a differentiable computation graph and trains it end-to-end with backpropagation, enabling input from high-dimensional observations like images.

ABSTRACT

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory observations, such as camera images, since they must model the entire distribution over sensor readings. Discriminative models do not suffer from this limitation, but are typically more complex to train as latent variable models for state estimation. We present an alternative approach where the parameters of the latent state distribution are directly optimized as a deterministic computation graph, resulting in a simple and effective gradient descent algorithm for training discriminative state estimators. We show that this procedure can be used to train state estimators that use complex input, such as raw camera images, which must be processed using expressive nonlinear function approximators such as convolutional neural networks. Our model can be viewed as a type of recurrent neural network, and the connection to probabilistic filtering allows us to design a network architecture that is particularly well suited for state estimation. We evaluate our approach on synthetic tracking task with raw image inputs and on the visual odometry task in the KITTI dataset. The results show significant improvement over both standard generative approaches and regular recurrent neural networks.

Motivation & Objective

• Motivate discriminative state estimation that handles high-dimensional observations without modeling full observation distributions.
• Propose a deterministic computation-graph formulation of state estimators that enables end-to-end training.
• Incorporate domain knowledge via a Kalman filter core while allowing expressive observation models (e.g., CNNs).
• Demonstrate improved performance on vision-based tracking and KITTI visual odometry over standard generative methods and vanilla RNNs.

Proposed method

• Construct a deterministic computation graph by unrolling a Kalman filter with a discriminatively trained observation model g_theta(o_t).
• Train end-to-end with backpropagation through time (BPTT) by differentiating through κ(s_{t-1}, z_t), q(s_t), and l(φ_{y_t}).
• Output z_t and R_t from a CNN that processes raw observations o_t, enabling the filter to weigh observation uncertainty.
• Use an extended Kalman filter (or KF variant) for the state update while optimizing both the observation network and the filter parameters.
• Ground the architecture in probabilistic filtering while treating the overall model as a deterministic RNN-like computation graph.

Experimental results

Research questions

• RQ1 Can a discriminative, deterministic state estimator matched to the structure of probabilistic filters outperform traditional generative filters when handling high-dimensional observations such as images?
• RQ2 Does end-to-end training of the observation model and the filter improve state estimation accuracy on vision-based tasks (tracking with occlusions and KITTI visual odometry) compared to piecewise training and generic RNNs?
• RQ3 How does incorporating observation-dependent uncertainty (R_t) influence estimation performance under occlusion and noise?

Key findings

• BKF outperforms standard generative KF-based estimators and vanilla LSTMs on a synthetic visual tracking task with occlusions.
• BKF achieves lower RMS tracking error (0.0537) than the feedforward (0.2322), piecewise KF (0.1160), and LSTM variants (0.1407–0.1423).
• In KITTI visual odometry, BKF yields superior translational and rotational accuracy across various training set sizes compared to piecewise KF and LSTM baselines.
• End-to-end training with a CNN-based observation model enables the filter to adapt observation uncertainty (R_t) to maximize final state estimation performance.
• BKF maintains data efficiency advantages by leveraging domain knowledge (KF structure) while benefiting from expressive discriminative observation processing.