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Master Thesis 30 hp: State estimation for extended targets with improper sensor characterization

Göteborg, Sweden
Closing date: 26 November 2022


Evaluating the posterior distribution for target states, where targets are described by models of different types, given a set of noisy measurements, is central in being able to meaningfully interpret the target scene observed by sensor systems. Boats, airplanes, missiles and UAVs are examples of target types that are of interest to observe with long-range surveillance radars, such as those in the Saab product portfolio.

Depending on the size of a target compared to the sensor resolution, a target may be considered as either a point target or an extended target. Boats are an example of targets of the latter type, and for such targets, it is of importance to include the target extension in the target model.

At longer ranges, state estimation for boats is associated with a number of interesting challenges:

  • The target is of comparable size as the sensor resolution, giving rise to few detections in each scan. Hence, each scan only provides a highly uncertain estimate of the extension state.

  • Targets may contain several scattering objects; a combination of a scattering volume with some intensity and a number of point scattering objects.

  • Incorrect knowledge of the measurement uncertainties obscures the estimated target extent and its dynamics, unless the measurement uncertainties are estimated alongside with the target state.

  • An occasionally complicated signal environment that may result in sequences of measurements exhibiting soft outlier behavior.

  • As the target passes by islands and other objects its extension may be partially masked.

Evaluating the posterior distribution of an extended target, using models incorporating these complexities presents a great challenge. Although there is a wide range of filters relying on varying degree of approximation, it would be of value to assess the posterior distribution for more complicated models with a small amount of approximation. Consequently, we wish to explore the application of Markov Chain Monte Carlo methods for the extended target estimation problem in the presence of imprecise knowledge of the measurement model.

By doing this, we wish to achieve:

  • Increased capabilities of inferring properties of extended targets based on real sensor data in complicated environments characterized by ambiguity between center of mass motion, extension dynamics and details of the measurement model.

  • To create a benchmark that can be used to evaluate filter performance for filters with more restrictive approximations that are needed for online use.

  • Possibility to infer properties about the background, which may aid target tracking by appropriately assigning priors for outlier statistics, e.g. dependent of geography.

Project description

In this project, we wish to apply Markov Chain Monte Carlo methods to sample the posterior distribution for extended targets using models involving a variety of the above-described challenges.

The estimation problem is high dimensional and somewhat sparse, with a prior exhibiting a mix of continuous and discrete parts. We are in particular interested in exploring the prospects of Sticky Piece-wise Deterministic Markov Processes (J. Bierkens et al, 2022) for this problem.

The project  involves addressing how Sticky Piece-wise Deterministic Markov Processes can be adapted and applied in a computationally efficient way to this problem, followed by exploration of models for extended targets (involving an uncertain measurement model), as well as bench-marking with respect to filters for extended targets that exist in literature.

Your profile:

We are looking for one or two students at the end of master studies in either mathematics or physics. In order to successfully complete the project, you will need a strong background in mathematics and preferably knowledge of Bayesian statistics.

This position requires that you pass a security vetting based on the current regulations around/of security protection. For positions requiring security clearance additional obligations on citizenship may apply.

What you will be a part of

Saab is a leading defence and security company with an enduring mission, to help nations keep their people and society safe.

Empowered by its 18,000 talented people, Saab constantly pushes the boundaries of technology to create a safer, more sustainable and more equitable world.

Business area Surveillance offers world-leading sensor technology in monitoring and decision support to protect against threats. The portfolio covers airborne, ground-based and naval radar, electronic warfare, C4I solutions, aviation systems and cyber security.

Affärsenheten Radar Solutions ansvarar för radarsystem för flyg, mark och sjö. Du kommer att tillhöra vår utvecklingsorganisation Engineering i Göteborg under avdelningen Signal and Data Processing Application som ansvarar för mjukvaruutveckling. Sektionen består av ca 150 personer.

Saab is a company with a strong people-orientation. We offer a friendly work environment where we support and help each other to be at our best. Continuous learning, career & talent development and employee well-being are examples of areas where we always put the strongest effort to offer great opportunities.