Introduction to Kalman Filter (Part 2)

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Introduction to Kalman Filter (Part 2)

By: Mad Helmi Bin Ab. Majid (PhD Student)

 

In this article we will discuss basic concept of Kalman Filter as continuation from the previous discussion. It is necessary for us to have prior knowledge of state and initial measurement data before the process begin. There are five major steps in implementing the Kalman filter as listed below:

 

1. Next stage prediction

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2. Project the error covariance ahead

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3. Computing the Kalman gain

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4. Update the estimate with measurements from sensors

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5. Update the error covariance

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In the next part, we will discuss how to implement these steps for the problem we discussed in the Part 1 of the article i.e. determine GPS position.

EKF-SLAM Algorithm

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EKF-SLAM Algorithm

By: Herdawatie Abdul Kadir (PhD Student)

 

 

Non-linear SLAM is mostly implemented using the extended Kalman filter (EKF). The Extended Kalman Filter formulation of simultaneous localisation and mapping (EKF-SLAM) were represent as below.

The environment data of set elements { S, A, F1…….,Fn} were represented by a map 5a aug15 where 5b aug15 is the state vector of the vehicle with estimated mean 5c aug15

5d aug15

and estimated eror covariance 5e aug15

5f aug15

 

where vector 5c aug15 described the estimated location of vehicle A and the environment features F1…….,Fn , all with respect to the base reference, s.

In the case of the vehicle, the location vector 5g aug15 describes the transformation from s to A.

 

5j aug15

 

 

 

In case of an environment features j, the parameters that compose its location vector 5h aug15 for point features. The diagonal elements of matrix represent the estimated error covariance of the difference features of the state vector and the vehicle location where the off-diagonal elements represents the cross-covariance matrices between the estimated location of the corresponding features.

Let assume there are point feature observed in the map and the position estimate is given by mean estimates 5i aug15 and covariance matrix 5k aug15.


Reference(s):

  1. Castellanos. Jose A. Jose Neira, and Juan D. Tardos. "Map building and SLAM algorithms. "Autonomous Mobile Robots: Sensing, Control, Decision Making and Applications (2006).


 

Image Segmentation

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Image Segmentation

By: Mohd Faid Bin Yahya (PhD Student)

 

Image segmentation is defined as the process of separating an image into regions based from the differences in pixel values. The process is as shown in Figure 1. Basically, the aim is to locate an object of interest in the image. This is important in order to understand the object in a scene and while the concept is clearly straightforward it is still a very challenging task. For the most important part, the segmentation algorithm needs to be robust and still can perform within the confined boundaries to assumptions made.

 

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Figure 1: Examples of pixel classification [1]

 

In general, image segmentation process consists of three important steps as shown in Figure 2. The first step basically deals with classification or assigning pixels to either object or not object. The pixel in the image is displayed as white or black pixel after the image had been preprocessed earlier. Then, in the second step, adjacent pixels of the same class are connected to form a spatial set.The set can be represented by assigning a set label to each pixel or by a list of pixel coordinates that defines the boundary of the connected set. In the third and final step, the sets are identified in terms of scalar or vector-valued features such as its size, position, and shape.

 

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Figure 2: Image Segmentation Process

 

 

Reference(s):

  1. R. Corke (2011). Robotics, vision, and control.1st Edition, Springer.

 

 

Compass Module Test

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Compass Module Test

By: Song Yoong Siang (PhD Student)

 

The reliability of compass module HMC 6352 is tested in order to know whether it gives correct information. Before the test, the direction of North is confirmed using smart phone. After that, the direction of North is marked using compass paper as shown in Figure 1(a). Compass paper is used to measure the heading value of vehicle instead of magneto compass. This is to avoid the reading of compass module affected by magneto compass. Next, the compass module is placed on the top of the compass paper as shown in Figure 1(b). The output of compass module is recorded using Arduino Mega. The testing is repeated 7 times by increasing the heading 45°clockwise.

 

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Figure 1: (a) Confirm about the direction of North using compass from a smart phone (b) Put the frame containing compass module on top of the compass paper

 

Table 1 below shows the result of reliability test. The compass module recognizes the direction of North as 0°. This value is increased when the direction is turning counterclockwise. The maximum heading value given by compass module is 359.9°. The heading value read by compass module is taken 20 times in order to observe its consistency. From Table 4.1, all the three readings for difference heading are near. The biggest range of the three reading is 0.4°, which is considered small and acceptable. Therefore, a conclusion has been made that the reading of compass module is consistent.

 

Table 1: Reliability test result of compass module

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The result of reliability test is analyzed using graphical methods. Figure 2 shows the individual chart of error of compass module versus heading value. From the graph, the control limit range of error is from -5.78° to 14.51°. The average error of compass module is 4.36°. The error occurs because the compass module is placed near the aluminum frame. The aluminum frame is affecting the reading of compass module. However, the error of compass module is considered acceptable.

 

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Figure 2: Individual chart of error of compass module versus heading value

 

 

Reference(s):

  1. (n.d.).Compass Module – HMC6352 – SEN-07915 – Sparkfun electronics. Retrieved from: https://www.sparkfun.com/products/retired/7915 [Date accessed: 12 September 2014]

 

 

Group Decisions Making (GDM): Human Inspired

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Group Decisions Making (GDM): Human Inspired

By: Herdawatie Abdul Kadir (PhD Student)

 

The GDM problems is a generally occurred in most companies and organizations where a decision process do not guranteed the decision is agreed by all the members. There are several method of GDM which involved broad concepts of : (1) Conflict(2) Majority Rule and Competition (3) Consensus and Cooperation (4) Proposals

In order to introduce mutual agreements among group members , the consensus were introduce to the GDM problems. Here, the decision made were agreed and sat isfied all of the members[1]. The experts members were requires to modified their solution towards a satisfory options for the group benefits.

Defination of Consensus:

“Consensus process, on the other hand, creates a cooperative dynamic. Only one proposal is considered at a time. Everyone works together to make it the best possible decision for the group. Any concerns are raised and resolved, sometimes one by one, until all voices are heard. Since proposals are no longer the property of the presenter, a solution can be created more cooperatively”                                                                        

(Butler and Rothstein,2006)

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Fig. 1 Example of general consensus progress scheme[1]

 

 

A general scheme of the phases of the consensus progress are briefly described below.

(1) Gather preferences:

Each expert member provides facilitator a solution with their own opinion based on the alternatives.

(2) Determine degree of consensus:

The facilitator values the level of agreement

(3) Consensus control: The consensus degree were compared with a threshold level and when the degree is enough go to the next page. Otherwise more discussion is needed

(4) Generate feedback information: The facilitator identifies furthest preferences from consensus and consults the members to achived the desired output and the process keep on repeating after the best solution is satified by all members.

 

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Fig. 2   Example of formal consensus progress scheme[2]

 

Reference(s):

  1. Palomares, I.; Martinez, L.; Herrera, F., "A Consensus Model to Detect and Manage Noncooperative Behaviors in Large-Scale Group Decision Making," Fuzzy Systems, IEEE Transactions on , vol.22, no.3, pp.516,530, June 2014.
  2. C. Butler and A. Rothstein, On Conflict and Consensus: A Handbook on Formal Consensus Decision Making.   Takoma Park, MD, USA , 2006.