Autonomous Tracking and State Estimation With Generalized Group Lasso.

Area of Science:

• Signal Processing
• Control Systems
• Optimization

Background:

• Classical Bayesian filters and smoothers have limitations in accuracy for dynamic signal tracking.
• Autonomous systems require robust state estimation for navigation and control.

Purpose of the Study:

• To enhance tracking and state estimation accuracy for dynamic signals using a structured sparsity assumption.
• To develop novel algorithms that outperform traditional Bayesian methods.

Main Methods:

• Formulated the estimation problem as a dynamic generalized group Lasso problem.
• Developed smoothing-and-splitting methods, specifically Levenberg-Marquardt iterated extended Kalman smoother-based multiblock alternating direction method of multipliers (LM-IEKS-mADMMs).
• Applied augmented recursive smoothers to solve minimization subproblems within the ADMM framework.

Main Results:

• Demonstrated ability to handle large-scale problems without dimensionality reduction.
• Successfully solved nonsmooth, nonconvex optimization problems.
• Proved convergence to a stationary point under mild conditions.
• Validated practical effectiveness through simulations and real-world data (marine vessel tracking, autonomous vehicles, audio signal restoration).

Conclusions:

• The proposed LM-IEKS-mADMMs offer a significant improvement in autonomous tracking and state estimation accuracy.
• The methods are scalable and robust, applicable to diverse real-world dynamic systems.
• This work advances the field of state estimation for autonomous and dynamic signal processing.