# Straight Line Trajectory Straight Line Scenario Computer Science Essay

**Published:** **Last Edited:**

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

This document presents the outcomes of tests carried out to investigate the usability of inertial navigation sensors available in todays smartphones to enhance a navigation solution computed with the EGNOS SDK.

The following -lists the executed test scenarios

Straight line trajectory simulations

Straight line trajectory reference scenario …… done

Straight line trajectory (with noise in Accelerometer's measurements) …… done

Straight line trajectory (with noise in Gyroscope's measurements)

Straight line trajectory (with real test data collected using INS from smartphone)

Straight line trajectory (With GPS outage for 5 seconds) …… done

Circle trajectory simulations

Circle trajectory reference scenario

Circle trajectory (with noise in Accelerometer's measurements)

Circle trajectory (with noise in Gyroscope's measurements)

Circle trajectory (with GPS outage for 5 seconds)

## Straight Line trajectory

## Straight line Scenario

In this case, data from both GPS and INS are used to investigate the behavior for a straight line scenario. The 80 sample points are taken over the duration of 80 seconds. The result shows that for the first 10 epochs the standalone GPS provides more accurate positions, while for the remaining trajectory, the adaptive Kalman filter (AKF) provides better accuracy.

Figure 1.1 GPS and adaptive Kalman filter (GPS + INS) output

Difference between the positions computed through standalone GPS and AKF to the straight line trajectory, and the difference between the output from GPS and AKF is shown in figure 1.2. It is clear from this graph that only for the first 10 epochs, the standalone GPS provide more accurate position, from epoch 11-14 with similar accuracy, while for the rest of the path, position from AKF is more accurate. Adapting both measurement noise covariance matrix and dynamic model covariance matrix result in increased position accuracy reflected in figure 1.2 from epoch 45 - 80. Table 1.1 shows the statistical summary of the navigation errors (comprise position, velocity, and attitude). Figure 1.3 shows the DRMS of the covariance of position states derived from the estimated covariance matrix. It also illustrates the accuracy and precision of horizontal point position acquired from the GPS receiver and from the integrated GPS/INS system with a circular error probability of 68%. Statistics shows that adaptive Kalman filter provides 25% more accurate position than the stand alone GPS.

Figure 1.2 Errors between the output of stand-alone GPS and adaptive Kalman filter (integrated GPS/INS) to the trajectory, and the difference between the errors of GPS and AKF (m)

Figure 1.3 Accuracy graph of GPS and AKF with R68 for 80 seconds walk manifesting smaller confidence region for AKF compare to GPS

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.7482

0.7482

3.0794

3.07949

3.4

Adaptive Kalman Filter (GPS + INS)

0.7319

0.7318

2.309

2.30924

2.61398

Table .1 Comparisons of performance parameters of GPS and AKF

## Straight line trajectory (Noise in Accelerometer)

Performance of the GPS/INS integration is governed by the quality of INS data. The integrated solution enhances position accuracy if the INS data is accurate, but the same is true other way. The GPS/INS integrated solution become worse if the INS data is in-accurate/more noisy. Data collected from INS (sensed acceleration and attitude) available in smartphone is perturbed by noise. Error analysis from both of these parameters give an idea of how the error grows in the INS and on the basis of this error analysis, noise is acquainted with INS data to perform simulation in relevance to the real world situation. In this section the results are produced with introducing noise to the accelerometer. The output of the AKF depends on the performance of accelerometer and if the output from the accelerometer contains noise, then the overall performance of the AKF (integrated GPS/INS solution) is degraded, as shown in the following graphs. Statistics shows that overall position accuracy of AKF algorithm in comparison to GPS is decreased by 114%.

Figure 1.4 Output of GPS and AKF (Noise in Accelerometer)

The following error graph illustrates the position error between the outputs from a stand-alone GPS and an integrated GPS/INS system. Accelerometer render change in velocity information to observation vector is precipitated by scale factor (1mg/digit), initial bias, and noise density (218ug/sqrt (Hz)). The result shows that with-in the time period of 40 seconds, the position drifted by tens of meter (un-acceptable error level). Miss alignment of IMU with the body of moving person is among the leading source of position degradation. Mean GPS error and AKF error are shown in figure 1.6. Low cost and un-calibrated INS nourishes the high value of RMS demonstrated in figure 1.6. An average position error of 6.6 is noticed in the East direction. The output from accelerometer is integrated twice to compute Δs, which also integrate measurement noise along with the useful acceleration information synthesize the output further noisy. Statistical summary of the errors including position and velocity is presented in table 1.2.

Figure 1.5 Difference of error of GPS and AKF

Figure 1.6 Accuracy graph of GPS and AKF

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.7482

0.7482

3.0794

3.07949

3.43

Adaptive Kalman Filter (GPS + INS)

1.25427

3.0339

0.7757

6.59499

8.3659

Table 1.2 Comparison of performance parameters of GPS and AKF

## Straight line trajectory (Noise in Gyroscope)

In this section, simulation is performed with introducing noise to the output from gyroscope. Attitude information to the observation vector is contributed by the gyroscope. As mentioned earlier, adaptive Kalman filter is sensitive to the gyroscope measurements. Noisy measurements/less accurate observation provided by gyroscope lead the filter to diverge. The overall position accuracy of the adaptive Kalman filter algorithm (integrated GPS/INS) is decreased by 94% as compare to GPS.

Figure 1.7 Output of GPS and AKF (Noise in the output of gyroscope)

For more closure observation, the following error graph is produced. It shows the horizontal position error between the ideal trajectory positions and the positions computed by GPS and the adaptive Kalman filter. The integration of angular velocity ω sensed by gyroscope gives change in position, but it also integrates noise from the measurement. The Non-linearity of 0.2%, bias error, and a scale factor of 0.07deg/s/digit contribute to the noise. The reason for less position drifts in the beginning from epoch 3-21 and higher at the end from epoch 60-80 is the integration of attitude error with time. Misalignment of ISA with the moving body is one of the error sources. Figure 1.9 shows the standard error in horizontal positions from the known positions in the direction of the coordinate axis. Higher DRMS, mean error, and bigger confidence region reflects the inaccuracy of positions computed by AKF algorithm due to inaccurate attitude information obtained from gyroscope. Statistical summary of positions and attitude errors are given in table 1.3.

Figure 1.8 Difference of errors of GPS and AKF (Noise in the output of gyroscope)

Figure 1.9 Accuracy graph of output from GPS and AKF (Noise in the output of gyroscope)

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.74822

0.7482

3.0794

3.07949

3.4

Adaptive Kalman Filter (GPS + INS)

2.03351

2.1503

5.81157

5.9828

7.388

Table 1.3 Comparison of performance parameters of GPS and AKF

## Straight line trajectory (using real test data from INS of smartphone)

In this section, real test data for walking in a straight line trajectory is collected from INS of the Samsung Galaxy S-II smart phone. The effect of noise at the output of accelerometer and gyroscope can be analyzed from this figure. In the first subplot, raw data from accelerometer is plotted which shows the change of acceleration (speed up, speed down) between 4 - 8m, and ±5m at the end, which is not realistic for a normal pedestrian walk. It became even worse after integrating twice to compute ΔS. The other two subplots represent the raw measurements from gyroscope. The graph shows delta angle with a variation of ± 17 degree for a straight line trajectory, which is not reasonable. Low cost of MEMS INS available in the smartphone is the major reason behind less accurate data as cost is directly proportionally to quality.

Figure 1.10 Real test data collected using INS from Samsung Galaxy S-II smartphone

## Straight line trajectory (With GPS outage)

Handling GPS signal outage is very crucial where high speed and accurate navigation information is required and is therefore deeply focused during this dissertation. The AKF algorithm can be termed as 1+1 algorithm, since it provides navigation information even if there is an outage of GPS signal for specific interval of time. In this section, the simulation is performed with GPS signal outage for 5 seconds i.e. from epoch 31 to 36, as shown in figure 1.11. The black arrow highlighted the time period of the simulated GPS signal outage. In this case the prediction of next epoch is achieved by using the state vector of the previous epoch (the last point where the GPS signal was available) plus the current observation about change in velocity and attitude obtained from INS. The outage of GPS signal degrade the position accuracy but still the overall position accuracy of AKF is 23.4 % better than the standalone GPS.

Figure 1.11 Output of stand-alone GPS and adaptive Kalman filter algorithm (integrated GPS/INS) with a GPS signal outage for 5 seconds

Fig. 1.12 is the error plot of the navigation results with the simulated GPS signal outage. There is position and velocity drift (North and East) during the GPS outage, while the attitude does not have a clear drift as it principally depend on the MEMS INS. The dispersion of each point is picked, measured the magnitude of varying quantities (position and velocity) and then the average drift is summarized to get the standard deviation, average error and dRMS as given in table 1.4. After dropping the GPS signal (GPS updates) for 5 seconds, the position drifted for 0.52 - 1.03 meter (from the position obtained in section 1.1), which meant that the INS navigation result is reliable and bridge the GPS gap precisely. Mean error of stand-alone GPS and the integrated GPS/INS from the reference point are shown in figure 1.13. 68% of the navigation result comes under the corresponding circle for each system. Higher the dRMS values, the less accurate the position. UP to some extent, the RMS value also reflects both the mean and the drift error in horizontal position during the GPS outage.

Figure 1.12 Error plot of output from GPS and AKF showing GPS outage from epoch 31 - 36

Figure 1.13 Accuracy graph of GPS and AKF (GPS outage for 5 seconds)

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.7734

0.77348

3.0864

3.08644

3.4

Adaptive Kalman Filter (GPS + INS)

0.6524

0.6523

2.3636

2.3637

2.6061

Table 1.4 Comparison of performance parameters of GPS and AKF

## Circle trajectory

## Circle trajectory reference scenario

In this section, a system similar to the integrated GPS/INS used in the field test for circular trajectory is simulated. The stand-alone GPS and the integrated GPS/INS computes position for 80 data points. Figure 2.1 shows the positions computed by these two systems along a circular trajectory.

Figure 2.1 Output of GPS and AKF

The error graphs i.e. figure 2.2 shows the error in position computed by GPS and the integrated GPS/INS (AKF) to the reference positions. Until epoch 30, the position accuracy is almost equal (with a slight up-down) between GPS and AKF, but after epoch 30 till 80, the AKF algorithm provides more accurate positions than their counter part GPS. The Computation of Variance-covariance matrix using windowing function of size 15, used to adapt both measurement noise covariance matrix and dynamic model covariance matrix results in better position accuracy after epoch 30. DRMS of the position errors is shown in figure 2.3. Smaller value of DRMS (0.93) and smaller confidence region (with 68% circular error probability) reflect the higher position accuracy of AKF than stand-alone GPS. Summary of position, velocity and attitude errors are presented in table 2.1. Statistics shows that adaptive Kalman filter provides 32% more accurate positions than the stand-alone GPS.

Figure 2.2 Difference between the error of GPS and AKF

Figure 2.3 Accuracy graph of GPS and AKF

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.9362

0.3176

0.02784

1.1844

1.2136

Adaptive Kalman Filter (GPS + INS)

0.62439

0.3881

0.124612

0.7957

0.9287

Table 2.1 Comparison of performance parameters of GPS and AKF

## Circle trajectory (Noise in accelerometer)

In this case, simulation is performed with noisy measurements from accelerometer. Adaptive Kalman filter is sensitive to accelerometer's readings. In case of in-accurate observation from accelerometer, the output from AKF will diverge. Figure 2.4 shows accumulative graphs of reference trajectory, GPS, and AKF measurement for the estimated positions. The stand-alone GPS more closely follow the reference trajectory than the AKF (GPS + INS).

Figure 2.4 Output of GPS and AKF

The comparison between the position error computed for GPS and AKF are shown in figure 2.5. The error graph clearly shows the divergence of AKF output. MEMS accelerometer having a frequency of 10 Hz is affected by several noise parameters like scale factor error (±10%), bias error (±20mg), and bias change vs. temperature (±0.1mg/°C). Integrating the acceleration (sensed by the accelerometer) twice also escalate the noise. Misalignment of ISA with the body of the moving person is also among the error sources. From epoch 0 - 15, the error is small, but afterword the error grows rapidly because the noise is summing-up during the each iteration of Kalman cycle. Accuracy and precision achieved by the GPS receiver and the AKF algorithm are shown in figure 2.6. Higher value of Kalman mean error (3.303) represents the degree of closeness of estimated observation to their reference. Bigger confidence region of AKF in contrast of smaller GPS region shows that the estimated position computed by AKF is perturbed by the noisy observation from accelerometer. Error summary for GPS and AKF are given in table 2.2. Statistics shows that the position accuracy of AKF is decreased by 192% as compare to GPS.

Figure 2.5 Difference in the error GPS and AKF

Figure 2.6 Accuracy graph of GPS and AKF

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.93629

0.3176

0.02784

1.1844

1.213

Adaptive Kalman Filter (GPS + INS)

1.3069

1.498

-2.4635

3.464

4.356

Table2.2 Comparison of performance parameters of GPS and AKF

## Circle trajectory (Noise in gyroscope)

In this case the noise is added to the output of gyroscope. Gyroscope provides change in attitude of the moving body to the observation vector. In case of in-accurate attitude information, the estimated position accuracy greatly suffered. Figure 2.7 provides the plot for trajectory computed by GPS and AKF.

Figure 2.7 Output of GPS and AKF (noise in Gyroscope)

The following error comparison graph shows the error in positions obtained from GPS and adaptive Kalman filter. The output of gyroscope is affected by various noise sources like scale factor change vs. temperature (±2%), noise density, non-linearity (0.2% FS), and misalignment of ISA with the surface of the moving body. Correct information of initial orientation is most important and inaccurate initial orientation escalates the position error. The error comparison graph shows that for the first 12 epochs, the AKF estimates more accurate positions than the GPS, but as the noise is integrating with time, the error grows exponentially to several meters. Figure 2.9 shows the scatter plot of the positions observed by the GPS and AKF. Mean Kalman error (dispersion from the true value) of 4.7m shows that the performance of AKF is severely compromised due to the in-accurate measurement of gyroscope. Table 2.3 list the errors obtained from the GPS and AKF measurements. Statistics shows that the position accuracy of adaptive Kalman filter is 308% less than the GPS.

Figure 2.8 Difference in error of GPS and AKF

Figure 2.9 Accuracy graph of GPS and AKF (Error in gyroscope)

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.9362

0.3176

0.0278

1.1844

1.2137

Adaptive Kalman Filter (GPS + INS)

2.5087

2.2724

-4.3215

4.8354

6.0308

Table 2.3 Comparison of performance parameters of GPS and AKF

## Circle trajectory (with GPS outage)

In this case the simulation is performed to consider a scenario when there is an outage of GPS signal for a certain period of time. In our case, the GPS signal is disappear for 5 seconds (from epoch 38 - 43). During this time, the adaptive Kalman filter provides accurate navigation information while mainly relaying on the readings from INS and the previous state information. The following figure shows the trajectory computed by GPS and the AKF. The outage of GPS signal is pointed with the arrow.

Figure 2.10 Output of GPS and AKF (GPS outage for 5 seconds)

Comparison between the reference trajectory and the error in position obtained from GPS and AKF is shown in figure 2.11. It also reveals the difference between the error in position computed by GPS and the AKF (the black line). GPS signal outage from epoch 38 - 43 is highlighted with GPS outage label. GPS outage handling is performed in the same way as explained above in section 1.4. During the GPS signal outage, the position is drifted by 0.5 - 1.5 m. Figure 2.12 shows the standard errors of estimated coordinates for each point. The smaller circular error probability (in which 68% of the points occur), and small dRMS for AKF in contrast of GPS, reveals that the position accuracy of AKF is still higher even the GPS signal is disappear for 5 seconds. Average error, standard deviation and dRMS are summarized in table 2.4. Statistics shows that the navigation accuracy of AKF is 21.3% higher than their counterpart GPS.

Figure 2.11 Difference in error of GPS and AKF (GPS outage for 5 seconds)

Figure 2.12 Accuracy graph of GPS and AKF (GPS outage for 5 seconds)

## Type

## Standard Deviation

## Average Error

## dRMS

North

East

North

East

GPS only

0.9296

0.3263

0.9594

1.19821

1.3

Adaptive Kalman Filter (GPS + INS)

0.66037

0.3278

0.0781

0.9431

1.0463

Table 2.4 Comparison of performance parameters of GPS and AKF

## Conclusion and future work

This thesis investigate the impact of integrating inertial navigation sensors available on smartphone with the EGNOS enhanced GNSS. Performance of INS and GPS were investigated during different field tests. Adaptive Kalman filter was designed and implemented using innovation based adaptive approach to integrate INS and GPS for better position estimation. The outage of GPS signal for 5s has been investigated, during this time the AKF algorithm relay on the INS and on the previous state vector. The results show that during the GPS outage, the positions are slightly drifted although maintained high navigation accuracy (effectively bridge the short GPS signal outage). Adapting measurement noise covariance matrix and dynamic model covariance matrix simultaneously using innovation based variance covariance method enhance position accuracy. It is observed from the simulation results that noise produced by the gyroscope measurements effect the output of AKF more than the accelerometer noise and diverge the filter. Therefore the raw data from INS can-not be used directly for integration with GPS. The results show that navigation accuracy provided by adaptive Kalman filter is better than the accuracy provided by GPS.

## Future work

This work can be extended by concentrating on the INS data. Output from the MEMS INS, available in the smartphone is unstable therefore it is important to perform some error correction/noise filtering technique to make the data reliable.

An algorithm should be developed to correct the misalignment of ISA with the moving body automatically.

The GPS/INS integration using adaptive Kalman filter will provide higher position accuracy than the stand-alone GPS if high accuracy INS is available.