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Posterior Cramér-Rao bounds for target tracking

Posterior Cramér-Rao bounds for target tracking

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In this chapter, we present a review of recent developments in the calculation of estimation error performance bounds for target tracking. We concentrate on the posterior Cramér-Rao bound (PCRB), which is computationally the simplest of a general class of lower bounds. We present full details of an efficient recursive formula for the PCRB for the general non-linear filtering problem, and of PCRB methodologies in cluttered environments (i.e. in which there can be missed detections and spurious false measurements). In such environments, the measurement origin uncertainty is shown to manifest itself as an information reduction factor that degrades tracking performance according to the severity of the clutter. A tutorial of the key PCRB methodologies in cluttered environments is provided, and via simulations, PCRBs are calculated for a scenario in which a single target is tracked using measurements generated by a stationary radar. The PCRBs are compared to the performance of an extended Kalman filter, and the results demonstrate the efficacy of the PCRB as an efficient theoretical predictor of the capability of the tracker. We also present a discussion of applications that would benefit greatly from the development of a PCRB methodology. These applications include sensor scheduling in passive coherent location networks; and performance assessment of algorithms designed for image fusion, data assimilation for meteorology/oceanography, simultaneous localization and mapping and quantum estimation.

Chapter Contents:

  • Abstract
  • 9.1 Introduction
  • 9.2 Literature review
  • 9.3 Bayesian performance bounds
  • 9.3.1 Discrete time estimation
  • 9.3.2 General class of lower bounds
  • 9.4 Posterior Cramér-Rao bound for non-linear filtering
  • 9.4.1 General recursion
  • 9.4.2 Calculating the constituent matrices
  • 9.4.2.1 Case 1: Exploiting target ground-truth data
  • 9.4.2.2 Case 2: The case of hidden states - exploiting historical sensor data
  • 9.4.3 Simplifications - Linear models and Gaussian noise
  • 9.5 Posterior Cramér-Rao bounds for non-linear filtering in cluttered environments
  • 9.5.1 Target generated measurements and false alarms
  • 9.5.2 Information reduction factor bound
  • 9.5.2.1 General approach
  • 9.5.2.2 Calculation of the information reduction factors
  • 9.5.2.3 Extension to multi-sensor systems
  • 9.5.3 Measurement sequence conditioning bound
  • 9.5.3.1 General approach
  • 9.5.3.2 Extension to multi-sensor systems
  • 9.5.4 Measurement existence sequence conditioning bound
  • 9.5.5 Relationships between the performance bounds
  • 9.6 Simulations
  • 9.6.1 Scenario specification
  • 9.6.2 Tracking methodology
  • 9.6.3 Quantifying the performance of the tracker
  • 9.6.4 Calculating the posterior Cramér-Rao bounds
  • 9.6.4.1 Information reduction factor bound
  • 9.6.4.2 Measurement sequence conditioned bound
  • 9.6.5 Simulation results
  • 9.7 Further development of posterior Cramér-Rao bounds
  • 9.7.1 Improvements in computational efficiency
  • 9.7.2 Passive coherent location networks
  • 9.7.2.1 General scenario
  • 9.7.2.2 Complicating factor - state-dependent measurement errors
  • 9.7.3 Image fusion
  • 9.7.4 Data assimilation for meteorology/oceanography
  • 9.7.5 Simultaneous localization and mapping
  • 9.7.6 Quantum estimation
  • 9.8 Summary
  • Acknowledgement
  • References

Inspec keywords: target tracking; telecommunication scheduling; recursive estimation; data assimilation; nonlinear filters; Kalman filters; radar clutter; image fusion; radar tracking

Other keywords: simultaneous localization; estimation error performance bounds; image fusion; extended Kalman filter; recursive formula; stationary radar; mapping; oceanography; cluttered environments; posterior Cramέr-Rao bounds; sensor scheduling; meteorology; data assimilation; nonlinear filtering problem; passive coherent location networks; information reduction factor; spurious false measurements; target tracking; PCRB; quantum estimation

Subjects: Radar equipment, systems and applications; Filtering methods in signal processing; Radar theory; Other topics in statistics

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