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## The Kalman Filter

The Kalman Filter uses consecutive data inputs and a set of equations to determine or estimate the velocity and true position of an object. It is an iterative mathematical process applied when the measured values are erroneous or contain uncertainties. These Filters are almost similar to Just like with Machine Learning models, these filters are fed with some input data, perform calculations, and provide an estimate. This process is iteratively repeated to reduce the final loss. Here are the steps performed by Kalman Filter:

1. Kalman Gain Calculation
2. Current estimate calculation
3. Estimation error calculation

## Rauch-Tung-Striebel Smoother

The Kalman filter parameter matrices can be computed and measured using the expectation-maximization algorithm. The Rauch-Tung-Striebel smoother is usually used to ensure smoother results for this estimation. There are times when either the plant noise matrices or the state transition require estimation. In such cases, a series of one-time-step smoother co-covariance matrices founded on the Rauch-Tung-Striebel formulation is used.

## Particle Filter

Particle filter is computationally more expensive than Kalman filters. It is usually used to solve non-Gaussian noise problems. Particle Filters use simulation methods rather than analytical equations to solve estimation tasks. Some of the renowned areas where Particle Filters are mostly used include:

• Direct global policy search of Robots Localization
• Stochastic Processes analysis in Financial Marketing
• Reinforcement learning