Internship | Analysing reachability and safety of Kalman filters for radar systems

Verifying safe operation of radar systems is key for humans to trust adding autonomous and adaptive techniques into these safety-critical systems. Safety and/or reachability of the Kalman filter for object tracking is analysed using formal methods.


Den Haag

Education type

university (wo)


Internship and graduation project

Hours a week

Fulltime – 40


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What will be your role?

Future generation radar systems should operate with a high degree of autonomy. More specifically, these systems should be able to adapt and react on unknown or unforeseen conditions with limited human intervention. Moving towards adaptive and autonomous systems raises the following important challenge on how engineers can offer guarantees regarding system performance or system correctness.

This project is a mathematically heavy and exploratory MSc internship and/or MSc thesis to bring formal verification into the domain of signal processing of radar systems. In this project, the focus will be on verifying reachability and safety of a Kalman filter by state-of-the-art techniques. Kalman filters are applied for object tracking over time. The main difficulty will be on creating meaningful (discrete-time Markov Chain) abstractions or approximations of the time-varying Kalman filter in order to infer safety and/or reachability. Using the abstractions, safety and/or reachability properties defined by probabilistic temporal logic can explored using, e.g., dynamic programming.

You will perform this assignment in the Department of Radar Technology. We are a passionate and creative group of professionals (60 people) dedicated to the specification, development and evaluation of innovative, high-performance MMICs, miniaturised and integrated RF subsystems, antennas and front-ends, and signal processing algorithms. The department is at the heart of novel, game-changing radar system and signal processing concepts for the military, space and civil domains.

How do you want to contribute to tomorrow's world? How big can your impact be? Come and work at TNO and envision it.

What we expect from you

You are in the final stages of your MSc degree in artificial intelligence, computer science, systems and control engineering, physics, mathematics, electrical engineering, or a similar master topic and have some track record in hybrid system modelling, Lyapunov theory, and dynamic programming. You have experience in programming in Matlab, Python and/or related language, you are quick in understanding new software, and you are pragmatic and focused on making things work. Next to technical expertise, we value communication skills and a results-driven attitude.

What you’ll get in return

You want to work on the precursor of your career; a work placement gives you an opportunity to take a good look at your prospective future employer. TNO goes a step further. It’s not just looking that interests us; you and your knowledge are essential to our innovation. That’s why we attach a great deal of value to your personal and professional development. You will, of course, be properly supervised during your work placement and be given the scope for you to get the best out of yourself. Naturally, we provide suitable work placement compensation.

TNO as an employer

At TNO, we innovate for a healthier, safer and more sustainable life. And for a strong economy. Since 1932, we have been making knowledge and technology available for the common good. We find each other in wonder and ingenuity. We are driven to push boundaries. There is all the space and support for your talent and ambition. You work with people who will challenge you: who inspire you and want to learn from you. Our state-of-the-art facilities are there to realize your vision. What you do at TNO matters: impact makes the difference. Because with every innovation you contribute to tomorrow’s world. Read more about TNO as an employer.

The selection process

After the first CV selection, the application process will be conducted by the concerning department. TNO will provide a suitable internship agreement. If you have any questions about this vacancy, you can contact the contact person mentioned below.

For this internship vacancy it is required that the AIVD issues a security clearance (VGB) after conducting a security screening. Take into account that this process may take about 8 weeks. If you have been abroad for more than 6 consecutive months, or if you do not have the Dutch nationality, it may take longer. Please visit for more information the AIVD website.

Due to Covid-19 and the consequent uncertainties and restrictions, students who are not residing in the Netherlands may currently not be able to start an internship or graduation project at TNO.

Has this job opening sparked your interest?

Then we’d like to hear from you! Please contact us for more information about the job or the selection process. To apply, please upload your CV and covering letter using the ‘apply now’ button.

Contact: Pepijn Cox
Phone number: +31(0)88-86 60975

Note that applications via email and third party applications are not taken into consideration.


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