Göm meny

Course content

The general problem is to estimate a state or parameter x from a multitude of sensor observations y distributed over time, space and modality (=type of sensor). The course and book are structured as follows.

The static case (x is constant)

  • General fusion theory.
    • Estimation theory in the linear case (y=Hx+e). Extensions to the non-linear case (y=H(x)+e, or H(y,x,e)=0).
    • Bayesian fusion perspective, the sensor fusion formula.
    • Computational estimation issues: Centralized versus decentralized fusion (information propagation and double-counting, covariance intersection techniques). Batch computations versus sensor iterations.
    • Detection theory T(x)>h: likelihood ratio concepts, Neyman-Pearson, GLRT and other tests.
    • Computational detection issues: Centralized and distributed detection. Censoring sensors.
    • Diagnosis H(i): x=x(i): The vector model. Error approximations.
  • Localization of a target based on one snap-shot from available sensors.
    • Sensor networks: Range and range-difference measurements. Triangulation from bearings. Information limitations and censoring sensors.
    • Measurement to target association, and extended target models (the fusion before detection principle).

The dynamic case (x is time-varying)

  • Filter theory.
    • General non-linear filter theory for dx/dt=f(x,u,v), y=h(x,u,e): Numeric evaluation using the point mass filter. Two special cases (KF and HMM) and fundamental limitations (CRLB). Structured models and marginalization.
    • Kalman filtering: Basic theory, implementation aspects, practical issues, information filter, smoothing).
    • Approximative algorithms for non-linear models (Extended KF and HMM, UKF and sigma-point filters, KF banks).
    • The particle filter: theory, implementation, proposal methods, sampling principles, smoothing, practical aspects.
    • Time synchronization and coordinate system calibration in filtering.
  • Dynamic state dimension problems.
    • Multi-target tracking: association, track handling
    • Simultaneous localization and tracking (SLAM).


  • Sensors, sensor models H(y,x,e)=0 and sensor-near signal processing.
    • Wheel speed sensors and odometry.
    • IMU and dead-reckoning.
    • GPS.
    • Camera
    • Radar, laser, sonar
    • Networked sensors: radio measurements, microphones, seismometers, magnetic field sensors
  • Motion models dx/dt=f(x,u,v)
    • Multi-purpose motion models
    • Standard models for different platforms (wheeled vehicles, surface and underwater vessels, aircraft,...).
    • Extended target models (track before detect, grid based methods for fusion)

Informationsansvarig: Gustaf Hendeby
Senast uppdaterad: 2022-06-02