[Paper Review] Kalman Filter Tuning with Bayesian Optimization

Zhaozhong Chen, Nisar Ahmed+2 more|arXiv (Cornell University)|Dec 17, 2019

Gaussian Processes and Bayesian Inference21 references10 citations

TL;DR

This paper proposes a Bayesian optimization (BO) framework for tuning Kalman filter noise parameters, using normalized innovation squared (NIS) as a ground-truth-free performance metric. By employing Student-t process regression for robust surrogate modeling, BO efficiently navigates the nonlinear, stochastic tuning landscape, achieving reliable and computationally efficient parameter estimation without requiring ground-truth states—demonstrated successfully on the Mars Science Laboratory Skycrane longitudinal state estimation problem.

ABSTRACT

Many state estimation algorithms must be tuned given the state space process and observation models, the process and observation noise parameters must be chosen. Conventional tuning approaches rely on heuristic hand-tuning or gradient-based optimization techniques to minimize a performance cost function. However, the relationship between tuned noise values and estimator performance is highly nonlinear and stochastic. Therefore, the tuning solutions can easily get trapped in local minima, which can lead to poor choices of noise parameters and suboptimal estimator performance. This paper describes how Bayesian Optimization (BO) can overcome these issues. BO poses optimization as a Bayesian search problem for a stochastic ``black box'' cost function, where the goal is to search the solution space to maximize the probability of improving the current best solution. As such, BO offers a principled approach to optimization-based estimator tuning in the presence of local minima and performance stochasticity. While extended Kalman filters (EKFs) are the main focus of this work, BO can be similarly used to tune other related state space filters. The method presented here uses performance metrics derived from normalized innovation squared (NIS) filter residuals obtained via sensor data, which renders knowledge of ground-truth states unnecessary. The robustness, accuracy, and reliability of BO-based tuning is illustrated on practical nonlinear state estimation problems,losed-loop aero-robotic control.

Motivation & Objective

• To address the limitations of heuristic and gradient-based Kalman filter tuning, which often fail due to nonlinearity and stochasticity in performance landscapes.
• To develop a tuning framework that does not require ground-truth state data, enabling practical deployment in real-world systems where such data is unavailable.
• To improve robustness and convergence in filter parameter tuning by leveraging Bayesian optimization with nonparametric Student-t process surrogate models.
• To validate the method on a challenging nonlinear aerospace application: longitudinal state estimation for the Mars Science Laboratory Skycrane.

Proposed method

• The method formulates Kalman filter tuning as a Bayesian optimization problem, treating the performance cost function as a stochastic black-box.
• It employs a nonparametric surrogate model based on Student-t processes to better handle uncertainty and outliers compared to standard Gaussian processes.
• The performance metric used is Normalized Innovation Squared (NIS), computed directly from sensor measurements and filter predictions, eliminating the need for ground-truth state data.
• The optimization framework sequentially selects new noise parameter configurations to maximize the probability of improving the current best solution, balancing exploration and exploitation.
• The approach is applied to extended Kalman filters (EKFs) and is generalizable to other state-space filtering algorithms.
• The method includes probabilistic inference over the entire parameter space, providing uncertainty estimates alongside optimal parameter values.

Experimental results

Research questions

• RQ1 Can Bayesian optimization with Student-t process surrogate models outperform traditional tuning methods in terms of convergence and robustness for Kalman filter noise parameter tuning?
• RQ2 Can NIS-based performance metrics enable effective filter tuning without access to ground-truth state data in real-world applications?
• RQ3 How does the proposed BO framework handle the nonlinearity and stochasticity inherent in the relationship between noise parameters and estimator performance?
• RQ4 To what extent can the method provide reliable and computationally efficient parameter estimates in a complex, nonlinear aerospace system like the Mars Skycrane?
• RQ5 Can the framework deliver not only optimal parameters but also probabilistic uncertainty estimates across the parameter space, as opposed to point estimates?

Key findings

• The BO-based tuning framework successfully identified optimal process and observation noise parameters for the Mars Skycrane longitudinal state estimation problem without requiring ground-truth state data.
• The use of NIS as a performance metric enabled effective tuning in real-world scenarios where ground truth is unavailable, validating its practicality.
• The Student-t process surrogate model demonstrated superior robustness to outliers and uncertainty compared to Gaussian processes, improving optimization stability.
• The method achieved reliable convergence to high-performing parameter configurations, avoiding local minima that commonly trap gradient-based approaches.
• The framework provided probabilistic uncertainty estimates across the parameter space, offering insights beyond point estimates—something not available in state-of-the-art auto-tuning methods.
• Simulation results confirmed the method's computational efficiency and reliability in a challenging nonlinear estimation task, demonstrating its potential for real-world deployment.