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Fig. 2. Bayesian network representation of the FastSLAM algorithm. Grey nodes are observed variables, white nodes are latent. Given the robot path there is no other path between landmarks; i.e. given the path the landmark locations are independent. This independence enables us to estimate each landmark separately.

Figure 2 Bayesian network representation of the FastSLAM algorithm. Grey nodes are observed variables, white nodes are latent. Given the robot path there is no other path between landmarks; i.e. given the path the landmark locations are independent. This independence enables us to estimate each landmark separately.

Related Figures (14)

Fig. 1. In a building (1) a set of devices (grey dots) is installed (2) with a user (red dot) that walks around (dashed line). Based on measured RSSI values and motion data from the user we locate devices in the building (3).
Fig. 1. In a building (1) a set of devices (grey dots) is installed (2) with a user (red dot) that walks around (dashed line). Based on measured RSSI values and motion data from the user we locate devices in the building (3).
Fig. 3. The received signal strength (RSSI) of a device is influenced by distance, but the amount of noise is substantial. For this figure, a Bluetooth device was set up as a beacon to continuously broadcast its unique identifier. Another device was placed at various distances and acted as a recording device. With a 1 Hz sample rate RSSI values were sampled. For the ‘room’ case, the transmitter was placed in an adjacent room to show the effect of walls.
Fig. 3. The received signal strength (RSSI) of a device is influenced by distance, but the amount of noise is substantial. For this figure, a Bluetooth device was set up as a beacon to continuously broadcast its unique identifier. Another device was placed at various distances and acted as a recording device. With a 1 Hz sample rate RSSI values were sampled. For the ‘room’ case, the transmitter was placed in an adjacent room to show the effect of walls.
Fig. 4. The effect of a Kalman filter on raw RSSI data sampled from a static device (i.e. no movement on both the receiver or transmitter end). The Kalman filter removes a large part of the noise from the signal.
Fig. 4. The effect of a Kalman filter on raw RSSI data sampled from a static device (i.e. no movement on both the receiver or transmitter end). The Kalman filter removes a large part of the noise from the signal.
Fig. 5. Visualisation of a single step of the SLAC algorithm. The diagram shows the update step of a single device based on a single observations. In reality, multiple observations and devices can be updated between the sample and resample step.
Fig. 5. Visualisation of a single step of the SLAC algorithm. The diagram shows the update step of a single device based on a single observations. In reality, multiple observations and devices can be updated between the sample and resample step.
Based on the Jacobian we calculate the Kalman gain. Note that, due to our static motion model for the landmarks, the covariance matrix estimate is not updated (i.e. sl a] = 5 Ply, Updating the previous state and computing the weight com- pletes processing the measurement. This process is performed for each landmark and for each particle. D. Resampling After the observation is processed all particles have been updated and contain new importance weights. We can now perform resampling. We utilise Sequential Importance Re- sampling (SIR) to prevent resampling on each step and only perform resampling when there is enough information in the particles. The importance weights are computed and nor- malised, which are used to calculate the effective number of particles (Nesp). If the effective number of particles drops below a given threshold we resample.
Based on the Jacobian we calculate the Kalman gain. Note that, due to our static motion model for the landmarks, the covariance matrix estimate is not updated (i.e. sl a] = 5 Ply, Updating the previous state and computing the weight com- pletes processing the measurement. This process is performed for each landmark and for each particle. D. Resampling After the observation is processed all particles have been updated and contain new importance weights. We can now perform resampling. We utilise Sequential Importance Re- sampling (SIR) to prevent resampling on each step and only perform resampling when there is enough information in the particles. The importance weights are computed and nor- malised, which are used to calculate the effective number of particles (Nesp). If the effective number of particles drops below a given threshold we resample.
Fig. 7. SLAC application running on both an iOS tablet and an Android phone.
Fig. 7. SLAC application running on both an iOS tablet and an Android phone.
Fig. 9. Examples of a SLAC simulation at various stages. Blue lines shows the ground truth of the user. Each grey line represents a particle’s estimate o’ the user’s path. The green line is the current best estimate. Black squares show the ground truth of landmark locations, red squares represent the current bes estimate. Coloured small squares at screen one and two represent individual initialisation filters.
Fig. 9. Examples of a SLAC simulation at various stages. Blue lines shows the ground truth of the user. Each grey line represents a particle’s estimate o’ the user’s path. The green line is the current best estimate. Black squares show the ground truth of landmark locations, red squares represent the current bes estimate. Coloured small squares at screen one and two represent individual initialisation filters.
Fig. 10. Showing the average localisation error of the four live test runs (first four) in comparison to the simulations (last two).
Fig. 10. Showing the average localisation error of the four live test runs (first four) in comparison to the simulations (last two).
REPEATED-MEASURE-ANOVAS USING LANDMARK POSITION AS THE WITHIN-SUBJECT FACTOR.
REPEATED-MEASURE-ANOVAS USING LANDMARK POSITION AS THE WITHIN-SUBJECT FACTOR.
TEST RESULTS. THE ‘COMPLETE’ COLUMN OF THE TABLE DESCRIBES THE PERCENTAGE OF RUNS THAT FOUND AN ESTIMATE FOR ALL DEVICES.
TEST RESULTS. THE ‘COMPLETE’ COLUMN OF THE TABLE DESCRIBES THE PERCENTAGE OF RUNS THAT FOUND AN ESTIMATE FOR ALL DEVICES.
Fig. 12. Pictures of our live testbed. Seven landmarks were placed in wall sockets around the room. None of the furniture or objects were removed before lesting. The room’s dimensions are around 10 x 10m.
Fig. 12. Pictures of our live testbed. Seven landmarks were placed in wall sockets around the room. None of the furniture or objects were removed before lesting. The room’s dimensions are around 10 x 10m.
Fig. 13. Overview of the idea of map fusing. Three different users (top, red dots) walk around (dashed lines) inside the same building but their individual runs only result in partial estimates of the environment (devices are depicted as grey dots, walls are black lines). By fusing these estimates together a more complete map of the environment can be created (bottom).
Fig. 13. Overview of the idea of map fusing. Three different users (top, red dots) walk around (dashed lines) inside the same building but their individual runs only result in partial estimates of the environment (devices are depicted as grey dots, walls are black lines). By fusing these estimates together a more complete map of the environment can be created (bottom).
Related topics:
Computer ScienceReal Time ComputingSimultaneous Localization and MappingCognitive Artificial Intelligence
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