  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.
