Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Kalman Filter: Linearized vs Extended

In course

ENV-548: Sensor orientation

Determination of spatial orientation (i.e. position, velocity, attitude) via integration of inertial sensors with satellite positioning. Prerequisite for applications related to remote sensing, environmental monitoring, mobile mapping, robotics, space expl ...

Description

This lecture explains the concept of a linearized Kalman filter and its limitations when dealing with strong nonlinear cases. The instructor introduces the extended Kalman filter as a method to address these limitations by continuously updating the estimated trajectory based on observations, moving away from the linearized approach.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Jan Skaloud

Official source

Related concepts (10)

Kalman filter

For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.

Nonlinear filter

In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage R(t) at any moment is the square of the input voltage r(t); or which is the input clipped to a fixed range [a,b], namely R(t) = max(a, min(b, r(t))).

Particle filter

Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system.

Ensemble Kalman filter

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting.

Filter (signal processing)

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist.

Related lectures (26)

Kalman Filter: Linearized vs Extended

Explores the linearized and extended Kalman Filters, illustrating their application in nonlinear systems and the estimation of unknown parameters.

Image Filtering: Basics and Techniques MOOC: Image Processing and Analysis for Life Scientists

Explores image filtering techniques, including linear and nonlinear filters, for artifact removal and feature enhancement.

Kalman Filter: Time Series

Covers structural modeling, state space models, and the Kalman filter in time series analysis.

Neural Signals and Signal Processing

Explores neural signal processing for brain-computer interfaces, including decoding techniques like Kalman filters and spike sorting.

Time-Varying Kalman Filter: Properties and Applications