This chapter is devoted to a special state representation for target tracking. The considered coordinates possess, in comparison with classical Cartesian ones, distinct advantages in particular in applications where angles are the only measurements available like, e.g. for jammed radar. In those applications, measurements are not Cartesian-complete and the range of a moving object under track is not observable unless the sensor platform performs manoeuvres. This chapter presents basic relations and properties of log-spherical coordinates. In particular, it is shown how those coordinates decouple the remaining coordinates from the unobservable range in angular-only tracking. The chapter discusses recursive filter algorithms and corresponding performance bounds. As an application example, it uses data fusion in a collision avoidance system based on a suite of sensors. The final topic is the so-called kinematic ranging, i.e. the extraction of range information from angular-only measurements by suitably chosen manoeuvres of the sensor platform. Presentation in this chapter covers both mathematical derivations as well as numerical simulation results.

Chapter Contents:

• Abstract
• 10.1 Introduction
• 10.2 Log-spherical coordinates
• 10.3 Tracking with angular-only measurements
• 10.3.1 Filter principles
• 10.3.2 Filter update
• 10.3.3 Filter propagation/prediction
• 10.3.4 Filter initialization
• 10.3.4.1 One-point initialization with prior
• 10.3.4.2 Multiple-point initialization with batch estimate
• 10.3.5 Performance bounds and observability
• 10.3.5.1 Fisher information and Cramér-Rao lower bound
• 10.3.5.2 Pseudo-measurements of normalized range rate
• 10.3.5.3 Prior information
• 10.3.5.4 Sample scenario
• 10.4 Collision avoidance
• 10.4.1 Sensor tracking
• 10.4.1.1 Radar
• 10.4.1.2 Passive optical sensor
• 10.4.1.3 ACAS or IFF with omnidirectional antenna
• 10.4.2 Track fusion
• 10.4.3 Performance bounds
• 10.5 Kinematic ranging
• 10.5.1 Propagation/prediction
• 10.5.2 Sample scenario
• 10.5.3 Observer trajectory planning
• 10.6 Summary
• Glossary
• Acronyms
• References

Inspec keywords: object tracking; telecommunication congestion control; recursive filters; radar receivers; numerical analysis; sensor fusion; target tracking; radar tracking; kinematics

Other keywords: log-spherical coordinate; log-spherical state space tracking; log-spherical state space fusion; numerical simulation; data fusion; sensor platform; target tracking; angular-only measurement; special state representation; mathematical derivation; radar jamming; kinematic ranging; recursive filter algorithm; classical Cartesian one; angular-only tracking; collision avoidance system

Subjects: Filtering methods in signal processing; Other numerical methods; Other numerical methods; Control applications in radio and radar; Radar equipment, systems and applications