## Archive for the ‘**Uncategorized**’ Category

## Resources on Kalman filters for tracking applications

For the last couple of months, I have been working with Kalman filter and its variations for aircraft tracking applications. I have found following resources helpful in the course of learning about Kalman filters.

Prof. Y. Bar-Shalom is well known in the area of tracking applications. This book by Bar-Shalom and co-authors is the standard text book for anyone interested in learning about applying Kalman filters. The authors aim to “*make things simple, but not too simple; clear but not too clear*“. The book not only presents theoretical derivation of filters, but also discusses implementation details. I have found the discussion on practical issues extremely helpful in the course of implementing the filters myself.

**Kalman and Bayesian Filters in Python**

This is a book by Roger Labbe. This book covers a wide range of topics related to Kalman filters and its applications with focus on practical applications. What I liked about this book is that the entire book is composed as a Jupyter notebook. As a result, Roger not only presents the mathematical background but also presents code implementation of the filters. FilterPy is the accompanying python package which provides implementation of all the filters discussed in the book. If you are interested, it is straight forward to change the sample code in the chapter notebooks and see changes for yourself. This book is a fine example of literate programming.

## Traceroute to Nepal

traceroute is a wonderful tool to analyse network structure. According to its man page,

traceroute tracks the route packets taken from an IP network on their way to a given host. It utilizes the IP protocol’s time to live (TTL) field and attempts to elicit an ICMP TIME_EXCEEDED response from each gateway along the path to the host.

From time to time, I like to run my traceroute to explore how I connect to different websites via my ISP’s network. It is specially interesting for me to to traceroute tests from US to servers hosted in Nepal, as I have some idea about how internet traffic flows in/out of Nepal. Today I’ll present results on traceroute test to Nepal Telecom’s (NT) website. Since NT had optical fiber links through to India and beyond, it will be interesting to see which links are utilized for a packet to reach from US to NT.

**Analysis:**

- Hops 1 – 9 , the packets are still in US
- The trace starts from my router and goes into Comcast network and to BOS (Boston) in hop 4 and comes down to NYC ( New York City ) in hop 7 via routers at Woburn and Needham MA in hos 5 and 6 respectively
- At NYC, the packet drops off from Comcast network to L3’s 10 Gigabit ethernet links. Since NYC is the main landing site for Trans-Atlantic optical fiber cables coming ashore east coast in US, it is expected that the packet going out to Nepal would also follow the same path.
- From NYC , the next hop(9) is to Airtel in India via L3’s 10Gigabit link
- Among several telecom operators in India, NT has bought the largest bandwidth with Airtel, so it makes sense that the route via Airtel’s network is most viable one.
- At hop 11, the packet reached India. This is evident from the jump in round trip delay to ~400ms which translates to ~ 11,000 km. The fiber landing site is most likely Mumbai, India.
- From there on, the packet enters Nepal at hop 12. The router IP 202.70.x.x belongs to NT. The router at hope 12 is a Border Gateway router, most probably at Bhairahawa where most of NT connection goes through to India.
- The the packet goes through Butwal to Pokhara (pkr.btw) in hope 13
- From Pokhara, the packet reaches NT’s Intn’l Exchange Bldg at Patan on hop 14. From there on the packet finally reaches the webserver at NT’s central office at Bhadrakali.

This was a traceroute analysis through Comcast network. Next I’ll do the same kind of analysis for trace through Verizon DSL network.

## RMTool for Polynomial Method : The Bottleneck?

I have been reading The Polynomial Method for Random Matrices by N. Raj. Rao and A. Eldeman as a part of literature review for my PhD research. In this paper, the authors present a method to determine the limiting eigen distribution of a particular subset of random matrices called* algebraic random matrices. * In the proposed method, the Stieltjes transform of the limiting eigen distribution is encoded as a root of a bivariate polynomial. A defined set of transformations ( deterministic and stochastic ) on the matrix is mapped to an *operation* on the bivariate polynomial. The limiting eigen distribution of the resulting matrix can be determined from the new bivariate polynomial.

This method heavily relies on the symbolic computation methodology. In parallel with the development of the mathematical framework for the polynomial method, the authors have developed a Matlab toolbox called the RMTool which leverages the symbolic computation capability of Matlab. However the RMTool uses the Maple Symbolic Toolbox for Matlab which Mathworks no longer supports (Above version 2009a). The original RMTool might even have been written in Maple itself and later forked to a Matlab toolbox. This has made RMTool extremely platform dependent tool preventing it from being used by other researchers. The method was proposed sometime in 2005 but I can hardly find an alternative reference on this topic or its application. It seems me that the rigidity of the RMTool may be limiting its potential as a powerful tool in random matrix analysis and application to engineering problems.

I have been looking at possibilities of porting the RMTool to the new Matlab Symbolic Toolbox which is based on MUPad. I am also planning on developing a new package ( from scratch :o) on a more robust and compatible platform ( Python with Sage ). But these ideas are still in early phase and need a thorough understanding of the polynomial. method.

## Fall 2011 at UMassD

The Fall 2011 semester officially commenced from 7th September. In the beginning of the summer I had already registered for a course on Discrete Mathematics ( MTH 550) and also planned to audit the CIS course on Algorithms and Data Structures.. I am also registered for Abstract Algebra (MTH 441) as suggested by my advisor. In addition to all that I am also attending the course on Random Signals and Systems being taught by my advisor.

## Welcome

I have started this blog as a place where I can put forward my ideas and thoughts on my research/studies. This blog was inspired by my friend Abhishek Dutta who also maintains a blog about his research.