The block is discrete with a sample time of 0.1 seconds. The Extended Kalman Filter itself has been implemented using an The range noise has a variance of 50 while the bearing noise The Extended Kalman Filter may be found inįor the tracking problem under consideration the measured data is the object'sĪctual range and bearing corrupted with zero-mean Gaussian noise and sampled atĠ.1s intervals. The Extended Kalman Filter uses a predictor-corrector algorithm to estimate This corresponds to the settings given in the In this example the object is assumed to start in the north-west and be (The gain in the first order filterĭetermines the rate at which the velocity is allowed to change.) This corresponds to an object that is manoeuvering with a A simpler model could use either aĬonstant velocity (subject to random perturbations) or a constant acceleration The accelerations are generated by the acceleration model Which are generated by integrating velocities, which in turn are generated by These are calculated from the x and y displacements, Ultimately the properties being measuredĪre the range and bearing. The blocks that are coloured black are used to model the actual trajectory of an Used to estimate the trajectory of the object from measured data. Trajectory of the object being tracked and secondly the Extended Kalman Filter There are two main parts to this model: firstly the blocks that model the actual The object's trajectory is shown in Figure 2.įigure 2: Simulink Model for Tracking a Flying Object using an ExtendedĪ zip file containing the model of Figure 2 may be Problem discussed above and which uses an Extended Kalman Filter to estimate Vector to avoid cluttering the equations.) Hence the Jacobian for theĪ Simulink model that implements the basic tracking (Note that the sample time subscript k has been dropped from the state To the x and y displacements by the equations, The measurement update equation is slightly more complex – relying on theĭifferentiation of a trigonometric identity. Velocity remains constant (in both the x and y directions). Δ t times the velocity (in both the x and y directions) and that the The above equation says that over a small period of time the position changes by Over a small period of time the displacement can be considered to changeĪccording to the first order approximation, Matrices for the state and measurement equations. The Extended Kalman Filter algorithm requires the calculation of Jacobian This is an ideal problem to solve using an Extended Kalman Filter. Given that theĭisplacements and velocities are non-linearly related to the range and bearing Given only noisy measurements of range and bearing. The object but also its x and y velocities. The tracking problem involves estimating not only the x and y displacements of (This tutorial does not consider the altitude of the object.) distances from the observer) in both the x and yĭirections. The range and bearing are generated fromĭisplacements (i.e. Often the observer is considered the location of a radarĭish tracking the object. The basic problemįigure 1: Relationship between displacements and range-bearing.Īt each point in time the object being tracked has a given range and bearingįrom the observer. One of the earliest applications of the Extended Kalmanįilter was to solve the problem of tracking flying objects. If you are unfamiliar with the mathematics behind the Kalman Generic Simulink tutorials discussing how to build and execute simple models. If you are unfamiliar with Simulink then look This tutorial presents an example of how to implement an Extended Kalman filter Using an Extended Kalman Filter for Object Tracking in Simulink
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