Tracking Unknown Number of 1D signals, 'multisignal_demo'
In this demonstration we track unknown and time-varying number of one dimensional Gaussian signals from noisy measurements, which are corrupted by noise and clutter.
The dynamics of the signals are modeled with one dimensional discretized Wiener velocity model. The signal conditioned measurements are modeled as signal values plus some white Gaussian noise. Every measurement has an equal chance of originating form each of the visible signals and 1% change of being due to clutter. Figure 1 shows the true values of visible signals and the generated measurements on each time step.
Figure 2 shows the filtered (left) and smoothed (right) estimates produced by the RBMCDA algorithm using the death model parameters α = 2 and β = 1 with N = 10 particles. There is noticable delays in the signal disappearances as the death model is slightly too slow. This can also be seen in figure 3, which shows the estimated number of signal on each time step.
By changing the β parameter of the death models Gamma distribution we can alter the speed of the target disappearances. Figure 4 shows the filtered (left) and smoothed (right) estimates produced by the RBMCDA algorithm using the parameters α = 2 and β = 0.1 with N = 10 particles. The targets disappear almost ten times faster now, so the delays in the signal disappearances have been removed. On the other hand the too fast death model causes the signals to disappear and reappear on time instances, when there are random gaps in the signals due to uneven measurement times. This can also be seen in figure 5, where the estimated number of signals is plotted on each time step.
The above observations would suggest that the value of β should lie somewhere between the two tested values. Figure 6 shows the filtered and smoothed estimates using the parameters α = 2 and β = 0.4 with N = 100 particles. The smoothed estimates are now very close to real signal values.
Files used in this example:
Tracking multiple 1D Gaussian signals demo
Same as above with the death processing in the prediction step
Plots filtered and smoothed signals