# Generalized Kalman Smoothing: Modeling and Algorithms

arXiv: https://arxiv.org/abs/1609.06369 · HTML: https://mlsanity.com/paper/1609.06369/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2016.

## Built on by (most cited first, 10 of 10)

- [Deepfakes Generation and Detection: State-of-the-art, open challenges, countermeasures, and way forward](https://mlsanity.com/paper/2103.00484/) (2021)
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- [Outlier-Insensitive Kalman Filtering Using NUV Priors](https://mlsanity.com/paper/2210.06083/) (2022)
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- [Training Structured Mechanical Models by Minimizing Discrete Euler-Lagrange Residual](https://mlsanity.com/paper/2105.01811/) (2021)
- [Multi-kernel Correntropy-based Orientation Estimation of IMUs: Gradient Descent Methods](https://mlsanity.com/paper/2304.06548/) (2023)
- [Outlier-Insensitive Kalman Filtering: Theory and Applications](https://mlsanity.com/paper/2309.09505/) (2023)
- [Maximum likelihood inference for high-dimensional problems with multiaffine variable relations](https://mlsanity.com/paper/2409.03495/) (2024)
- [A joint optimization approach to identifying sparse dynamics using least squares kernel collocation](https://mlsanity.com/paper/2511.18555/) (2025)
- [Hierarchical Variational Kalman Filtering](https://mlsanity.com/paper/2607.00877/) (2026)

## Abstract (arXiv)

State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a convex quadratic objective function with structure induced by the dynamic model. These classical formulations fall short in many important circumstances. For instance, smoothers obtained using quadratic penalties can fail when outliers are present in the data, and cannot track impulsive inputs and abrupt state changes. Motivated by these shortcomings, generalized Kalman smoothing formulations have been proposed in the last few years, replacing quadratic models with more suitable, often nonsmooth, convex functions. In contrast to classical models, these general estimators require use of iterated algorithms, and these have received increased attention from control, signal processing, machine learning, and optimization communities. In this survey we show that the optimization viewpoint provides the control and signal processing community great freedom in the development of novel modeling and inference frameworks for dynamical systems. We discuss general statistical models for dynamic systems, making full use of nonsmooth convex penalties and constraints, and providing links to important models in signal processing and machine learning. We also survey optimization techniques for these formulations, paying close attention to dynamic problem structure. Modeling concepts and algorithms are illustrated with numerical examples.