# Applied Estimation

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Welcome to EL2320/EL3320 Applied Estimation. Course info

This course mainly focuses on estimation using Kalman filter and particle filter.  A broader course is DD2420 which can be a natural followup to this course but can also be taken on it's own.  So in this course you will go into depth and get very familiar with two methods that in the other course you will learn are specific examples of  wider classes of methods.

Estimation is a an integral part of many systems. It is used for signal processing and controllers but also as a component for information gathering of autonomous systems, artificial intelligence and machine learning. The problem is to understand data from one of more noisy sensors. In this course 'understand' means develop a probabilistic model of the 'real world' based on this sensor data.

Estimation is concerned with the value of some variable(s) that may for example correspond to the position of a mobile robot, the target in a target tracking system, the position of your car on a road map, the frequency shift of a signal, the object location on a conveyer belt viewed by a camera, the rotation angle of a motor etc. In cases where these values can be measured directly for example using a GPS in the case of the position of the robot this may seem simple, but GPS is not consistently accurate or available. How does one estimate the position given a number of measurements of varying quality with imperfectly known robot motion between them. What if you only can make measurements that perform indirect information about what you want to determine. For example, what if you only can make noisy measurements of the angle to some landmarks. How do you make the best estimate of the values in question given the imperfect information you have?

Many have heard of the Kalman Filter which gives the optimal solution for a linear system. However, what if the system is not linear? Also the Kalman filter assumes that we can represent the uncertainty about the state we try to estimate using a Gaussian distribution. This does not work well in cases where we have a multi modal distribution, that is when the probability distribution has several peaks. In those cases we may need several hypotheses for the state near each peak. In the case of a mobile robot this happens frequently if the landmarks that the robot can use to find its position are not unique. How to deal with this?

The particle filter is a popular method for dealing with this. It is simple to implement and it works very well in cases when the state we try to estimate is not high dimensional. What about trying to estimate something very high dimensional and non-linear?

We will use the domain of robotics to draw the examples to illustrate the problems in the course.

### Prerequisites

Multivariable Calculus, Probability Theory, Linear Algebra, and basic Matlab programming.

### Literature

The course book is "Probabilistic robotics" by Thrun, Burgard, and Fox, The MIT Press, ISBN 0-262-20162-3 covers most of the material in the course from a robotics points of view. The book will be augmented with selected papers. One must read the assignments for each lecture before coming to class. Some of the material in the course will be published research articles.

For lectures there will be pointers to required reading that covers this material. This in combination with what is said during the lectures and contained in the labs will be the main source of information. The interested student will look for other sources of information in the course.