Multisensor integration using neuron computing for land-vehicle navigation Kai-Wei Chiang Æ Aboelmagd Noureldin Æ Naser El-Sheimy

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1 Multisensor integration using neuron computing for land-vehicle navigation Kai-Wei Chiang Æ Aboelmagd Noureldin Æ Naser El-Sheimy Abstract Most of the present navigation sensor integration techniques are based on Kalman-filtering estimation procedures. Although Kalman filtering represents one of the best solutions for multisensor integration, it still has some drawbacks in terms of stability, computation load, immunity to noise effects and observability. Furthermore, Kalman filters perform adequately only under certain predefined dynamic models. Neuron computing, a technology of artificial neural network (ANN), is a powerful tool for solving nonlinear problems that involve mapping input data to output data without having any prior knowledge about the mathematical process involved. This article suggests a multisensor integration approach for fusing data from an inertial navigation system (INS) and differential global positioning system (DGPS) hardware utilizing multilayer feedforward neural networks with a back propagation learning algorithm. In addition, it addresses the impact of neural network (NN) parameters and random noise on positioning accuracy. Introduction Today, most vehicle navigation systems mainly rely on global positioning system (GPS) receivers as the primary source of information to provide the position of the vehicle (Shin and El-Sheimy 2002). GPS is a satellite-based all-weather radio navigation system, developed by the United States Department of Defense (DoD), which became fully operational in The system can provide precise positioning information to an unlimited number of Received: 17 May 2002 / Accepted: 27 July 2002 Published online: 5 November 2002 ª Springer-Verlag 2002 K.-W. Chiang (&) Æ A. Noureldin Æ N. El-Sheimy Department of Geomatics Engineering, The University of Calgary, 2500 University Dr. NW, Calgary, Alberta T2N 1N4, Canada kwchiang@ucalgary.ca Tel.: or users anywhere on the planet. Since its advent, the number of applications using GPS has increased dramatically, including tracking people, a fleets of trucks, trains, ships or planes and how fast they are moving; directing emergency vehicles to the scene of an accident; mapping where a city s assets are located; and providing precise timing for endeavors that require large-scale coordination. However, GPS can provide this type of information only when there is direct line of sight to four or more satellites. In other words, the system does not work well in urban areas due to signal blockage and attenuation, which may deteriorate the positioning accuracy. For the moment, any sophisticated urban application, which essentially demands continuous position determination, cannot depend on GPS as a standalone system. More recently, and accepting that these techniques must inevitably cost more than GPS as a standalone system, the concept of combining complimentary navigation systems, such as a dead reckoning (DR), inertial navigation system (INS), or a navigation aid, such as digital map database, have been integrated in commercial applications. Certainly it has always been a maxim in safety-related applications that it is imprudent to depend on a single navigation technique. The complimentary navigation systems should have error mechanisms that are disjoint. The resultant system design is then driven by a trade-off between cost and performance (El-Sheimy and Naser 2000). This article focuses on the implementation of a multisensor integration based on utilizing multilayer feed-forward neural networks with a back propagation learning algorithm. The basis of multisensor integration is to fuse all available data from various sensors in order to obtain an optimal navigation solution (Ashkenazi et al. 1995). Traditionally, a Kalman filter is used to combine data from various sensors, which may contain different sources of errors. Figure 1 shows a simplified scheme of the Kalman filter process. Before the estimation process starts, values for the initial error state ^x þ 0 and the corresponding error covariance P þ 0 are assumed. Consequently, the filter projects the state and error covariance ahead to estimate ^x k andp k, this is called the prediction mode. If new measurements at time epoch k are available, the filter starts the updating mode by computing the Kalman gaink k and updating the error state and error covariance to estimate ^x þ k and Pþ k. The Kalman filter incorporates all of this information together to provide an optimal estimate of the error states at time k (Brown and Hwang 1992). DOI /s GPS Solutions (2003) 6:

2 Fig. 1 Outline of Kalman filter Fig. 2 Basic model of neuron Although the Kalman filter represents one of the best solutions for multisensor integration, it still has some drawbacks. The Kalman filter only works well under certain pre-defined models. If the filter is exposed to input data that does not fit the model, it will not result in reliable estimates (Forrest et al. 2000). Another problem related to the Kalman filter is the observability of the different states. The system is considered to be non-observable if there are one or more state variables that are hidden from the view of observer (i.e., the measurements). Consequently, if the unobserved process is not stable, the corresponding estimation errors will be similarly unstable (Brown and Hwang 1992; Ibrahim et al. 2000). For example, if the error state equation of an INS is examined, one can determine an azimuth error state that is weakly coupled with the velocity error states (Salychev 1998). Therefore, optimal estimates of the velocity errors provided by the Kalman filter due to GPS position or velocity updates will not benefit the azimuth accuracy. Therefore, the azimuth error state is a weakly observable component (Noureldin 2002). The objectives of this paper are to (1) suggest a new multisensor integration method utilizing multilayer feedforward neural networks with a back propagation learning algorithm, (2) evaluate the proposed architecture utilizing field test data, and (3) investigate the impact of the neural network parameters and the random noise on position errors. Artificial neural network-based method for multisensor integration Artificial neural networks (ANNs) are designed to mimic the human brain and duplicate its intelligence. Based on their highly parallel architecture, ANNs are powerful tools for solving nonlinear problems that involve mapping input data to output data (Abhijit and Robert 1996). It has been shown that an ANN can approximate any continuous and differentiable function to any degree of accuracy and it can model complex problems without any prior knowledge of the mathematical processes involved (Chansarkar 1999). An ANN will internally adjust the processing structure according to the discrepancy between the network s output value(s) and the desired target output value(s) in the training session. The adaptability, the nonlinear processing and the parallel processing are characteristics that make the ANNs 210 GPS Solutions (2003) 6:

3 Fig. 3 Sigmoid (logsig) activation function Fig. 4 Proposed multilayer neural network topology important in wide variety of applications (Dumville and Tsakiri 1994). Adaptability is a powerful learning algorithm utilized by ANNs in order to adapt to a continually changing environment. Nonlinear processing is the ability of ANN to perform tasks involving nonlinear input/output mapping relationships (Ham and Kostanic 2001). The parallel processing property allows the ANN to have architectures with a large number of neurons enhanced by extensive interconnectivity. This provides concurrent processing as well as parallel-distributed information storage. In general, ANNs could be divided into two classes. The first class is the supervised NN, which is trained by exposing the network to a series of training samples. These training samples contain an input data set as well as the desired output data set (i.e., multilayer feed-forward network trained by a back propagation algorithm). The second class is the unsupervised NN, which groups similar input vectors together without the use of desired output data to specify what a typical member of each group looks like or to which group each vector belongs (i.e., selforganizing map; Haykin 1999). Basic model of neurons ANNs are constructed from small processing units (neurons) that are interconnected within the network using weighted links. Figure 2 shows the basic model of the neuron, which contains three major components: (1) weight links w kj ; (2) an adder for summing the input signals that are weighted by respective synapses of the neuron (m k ) and external bias (b k ); and (3) an activation function uðþ for limiting the amplitude of the neuron output and the final output y k. A nonlinear activation function is utilized so that the non-linearities can serve to enhance the network s classification, approximation capabilities, and reduce the impact of noise (Reed and Marks 1999). Figure 3 shows the sigmoid (logsig) activation function, which is defined as follow: uðvþ ¼ 1 1 þ expð avþ where (a) is the slope parameter. ð1þ ANN design criterion The proposed architecture uses a three layer feed-forward NN with a back propagation learning algorithm to integrate the data from INS and differential global positioning system (DGPS) and mimic the dynamical model of the Fig. 5 Proposed multilayer neural network training GPS Solutions (2003) 6:

4 Fig. 6 a Smooth curve trajectory. b Harsh curve trajectory. c Training plot example for smooth curve (512 neurons). d Training plot example for harsh curve (512 neurons) vehicle. After training the NN, it can be used to predict the vehicle s position during GPS signal blockage. As shown in Fig. 4, the network inputs are the INS velocity V(t 1), and the INS heading wðt 1Þ. The network outputs the difference in coordinates between two different epochs, i.e., N(t) and N(t 1) for the north component and E(t) and E(t 1) for the east component. The proposed architecture contains an input layer, a hidden layer, and an output layer. The input layer consists of neurons that receive input from the external environment. The output layer consists of neurons that communicate the output of the system to the user or external environment. There are usually a number of hidden layers between these two layers, yet the proposed architecture consists of only one hidden layer. A hidden layer, together with a nonlinear activation function, enables the ANN to solve a nonlinear input/output relationship. When the input layer receives the input, its neurons produce an output. The output is then input to the other layers of the system. The process continues until a certain condition is satisfied or until the output layer is invoked and fires their output to the external environment. In general, the optimal architecture is empirically chosen. Hence, there is no guideline for specifying how many hidden layers and neurons should be used. Yet it might be appropriate to use more hidden layers and neurons for complex problems. Insufficient neurons might result in the divergence of the network while too many neurons could result in over-constraining the model (Lippman 1987). The INS navigation parameters are continuously computed and applied to the NN. Position differences between the current and the previous DGPS solutions, DN(t) and DE(t), are set at the output side of the NN as the desired target. It was decided to use the position differences instead of the position itself during the training procedure 212 GPS Solutions (2003) 6:

5 Fig. 7 Impact of number of neurons on position errors to simplify the learning process. In fact, the differences helped to reduce the complexity of the input/output function relationship as they provide a more efficient NN training and reduce the required training time. Real-time learning process The learning process is performed in real-time to determine the NN parameters (the weights and the biases). The INS velocity and heading information are used as inputs and the NN outputs are compared with the DGPS position differences. As long as the DGPS signal is available, the learning process is continuously improving the estimation error in order to obtain optimal values of the NN parameters. During and beyond a GPS outage, the NN parameters are used in prediction mode to provide estimates for the position components along the east and the north directions. Back propagation algorithm ANNs do not need any prior knowledge of the mathematical model of the problem. They learn by training samples, which include the input data and the desired output data. As shown in Fig. 5, the signals are propagated through the network. The final network outputs y k (t), [DN(t), DE(t)] are compared with the desired outputs D k (t) [GDN (t), GDE (t)] and the network error E k (n) is computed. E k ðtþ ¼D k ðtþ Y k ðtþ ð2þ Standard back propagation is a gradient descent algorithm and the term back propagation refers to the manner in which the gradient is computed for nonlinear multilayer networks. The back propagation algorithm runs backwards from the output layer through all the hidden layers to the Table 1 Factors in different simulated cases Cases Velocity errors Heading errors A B C D a b c Standard deviation 1 (m/s) 10 (m/s) 50 (m/s) 100 (m/s) GPS Solutions (2003) 6:

6 Fig. 9 Effect of heading errors on position errors Fig. 8 Effect of velocity errors on position errors input layer. The network error is used to adjust the weights associated with the connection and neurons by applying a generalized Delta rule (Haykin 1999). This rule states that the learning process is proportional to the difference between the NN output and desired output. The whole procedure starts with initializing the NN parameters (the weights and the biases) and the learning-rate parameter (ç). The learning parameter is a small positive constant that controls the step size of the iterative changes during the learning process (0<ç<1). The training samples are then utilized and the forward computation of the error signal E k (t) is performed. Consequently, backward computation of the local gradient (d) is determined. This local gradient is defined as follows: d ð Þ j ðtþ ¼ 8 >< >: duðv ð Þ j dt ðtþþ E j ðtþ duðvl j Þ dt for neurons j in output layer L P d ð 1Þ k ðtþw 1 kj ðtþ for neurons j in hidden layer k ð3þ The weights are adjusted according the generalized delta rule as follows: DW ji ðnþ ¼gd ð Þ j ðnþy ð 1Þ ðnþþadw i jiðn 1Þ ð4aþ W ð Þ ji ðn þ 1Þ ¼W ð Þ ji ðnþþdw ð Þ ji ðnþ ð4bþ where (a) is the momentum constant. The forward and backward computations are iteratively repeated by injecting new epochs of the training data to the network until the performance criteria are met. Once the performance metric is met, the training process is stopped. Alternatively, the training procedure may be stopped and the NN is switched to the operating mode if the DGPS signal is lost. Results and discussion The experiment is divided into two parts. The first part presents simulation results, which is created with two different trajectories. Each trajectory contains simulated velocity and heading information from INS measurements and simulated DGPS position information. The network 214 GPS Solutions (2003) 6:

7 Fig. 10 Effect of velocity errors and heading errors on position errors has first been trained offline to increase the training speed. The second part is based on field observations where the architecture was tested using the NovAtel BDS GPS/inertial measurement unit (IMU) system (the IMU is a Honeywell HG1700). Simulation results To investigate the impact of both the neurons and the random noise on position errors, two simulated trajectories were used. The first, shown in Fig. 6a, represents a smooth trajectory, and the second, shown in Fig. 6b, represents a harsh trajectory. Figure 6c, d shows the learning curves corresponding to the two trajectories shown on Fig. 6a, b, respectively (Haykin 1999). The training goals were set as and the training samples were 360 s for both cases. Samples contain simulated INS velocity measurements, simulated INS heading measurements, and simulated DGPS measurements. As shown on Fig. 6c, d, with 512 neurons NN architecture, the smooth trajectory and the harsh trajectory have converged in 605 and 548 s, respectively. Impact of neurons on position errors To investigate the impact of the number of neurons on the achieved positional accuracy, the number of neurons was altered in the hidden layer from 16 to 1,024 for the two trajectories. Although increasing the number of neurons increases the NN complexity, it can be seen in Fig. 7a, b that the network can achieve accurate predictions of the output. This is mainly because increasing the number of neurons results in an improvement of position errors. Two important aspects of the NN design should be further discussed. First, insufficient neurons may result in divergence during the training process (e.g., the case of 16 and 32 neurons in the hidden layer) because the neurons and the corresponding weights do not express the nonlinear input/output relationship accurately. Second, the higher number of neurons in the hidden layer does not necessarily ensure a significant improvement if the number of neurons exceed a certain limit. This limit is set by the minimum number of neurons that are required to maintain the desired accuracy while minimizing the convergence time. In this study, 512 neurons in the hidden layer provided acceptable accuracy given the training time. In some situations, the overflow neurons architecture results in an over-constrained problem, which may lead to an unreliable output even though the network converges in the training stage (Haykin 1999). Effect of random noise on position errors during NN prediction mode To investigate the impact of noise, random noises with different standard deviations were added to the simulated GPS Solutions (2003) 6:

8 highest position errors correspond to the combined cases of (Ac), (Bc), (Cc), and (Dc), while (c) corresponds to the largest heading error factor (see Table 1). Thus, during the blockage of the GPS signal, the heading errors have a larger impact on the position errors than the velocity errors. In addition, these figures imply that the NN is not very sensitive to noise. This may be due to the NN s nonlinear characteristic. Fig. 11 a Reference trajectory and NN-generated trajectory. b NN-generated trajectory Field test results To examine the performance of the proposed architecture, field tests were conducted in a land vehicle using the NovAtel BDS GPS/IMU system (IMU Honeywell HG1700). The duration of the test was about 2,000 s. During the first 1,800 s, both the IMU and the DGPS measurements were available and the NN was in training mode. For the last 200 s, the GPS data was intentionally removed and only the IMU measurements were processed, thus leaving NN to run in the prediction mode. Figure 11a shows the reference trajectory. Figure 11b shows the NN update (first 1,800 s) and the NN prediction mode trajectories. Double-differenced GPS measurements were chosen as the reference trajectory (accuracy of less than 10 cm) for the rest of the figures in this paper. It can be depicted from Fig. 12a, b that the behaviors of the position error are similar during prediction along both the east and the north channels. Large position errors occur when the coordinates/directions dramatically change. This may happen in sharp vehicle turns. Figure 13 shows the RMS of the position errors along the trajectory. The proposed architecture operates with acceptable positioning accuracy (errors less than 3 m) when the NN runs in prediction mode. The experimental results demonstrated the capabilities of the new approach in terms of its performance, where the 3-m position errors are below the expected performance from the IMU used in the NovAtel BDS GPS/IMU system over 200 s of stand alone INS operation. velocity and heading measurements to study which measurement error source dominates the position errors. It was first decided to isolate each error source and study its impact individually. Afterwards, the two noise sources were lumped together to investigate their combined impact. Table 1 lists the cases used in this simulation. Figures 8a, b and 9a, b show the effect of the noise on the position errors. Comparing the position errors of the four different cases, as shown in Fig. 8a, b, the NN seems to be less sensitive to the level of noise added to the velocity measurements. In particular, although the velocity noise level in case D is doubled compared with case C, Fig. 8a shows that almost the same position error is obtained. A similar performance was observed for the effect of heading noise on the position error (see Fig. 9a, b). In addition, comparing Fig. 8a, b with Fig. 9a, b, it can be concluded that the effect of heading noise on the position error is larger than the velocity noise. Figure 10a, b shows the effect of the combined random noises on the positioning accuracy. It is obvious that the Conclusions It was shown that the three layers feed-forward NN with back propagation was capable of efficiently integrating measurements from an IMU and DGPS. The paper also demonstrates that optimal NN parameters, such as the number of hidden layers and neurons, are based on experimental results. The NN runs in updating mode when DGPS signals (desired output) are available. Otherwise, it runs in predicting mode based on the latest updated weights. The major error source, which dominates the position accuracy of the proposed architecture, is the IMU heading errors. The proposed architecture was tested in a land vehicle using the NovAtel BDS GPS/IMU system (Honeywell HG1700). The experimental results demonstrated the advantages of the new approach in terms of performance and computational efficiency. The field tests 216 GPS Solutions (2003) 6:

9 Fig. 12 North and east channel position errors (prediction mode) Fig. 13 RMS position errors along the trajectory GPS Solutions (2003) 6:

10 clearly show that once the proposed architecture is trained for about 1,800 s and becomes stable, position errors of less than 3 m can be achieved even beyond a GPS signal blockage of 200 s (i.e., IMU stand-alone mode). These results are well beyond the performance characteristics expected from the IMU used in the NovAtel BDS GPS/IMU system. Appendix List of symbols ^x þ 0 Initial error state p þ 0 Initial error state covariance ^x k Prediction error state p k Prediction error state covariance K k Kalman gain ^x þ k Updated error state p þ k Prediction error state covariance w kj Weight links m k Summing function of the neuron b k External bias uðþ Activation function Vðt 1Þ INS velocity at epoch t 1 wðt 1Þ INS heading N(t), N(t 1) North position at two consecutive time epochs E(t), E(t 1) East position at two consecutive time epochs DN(t), DE(t) North and east position difference between two consecutive time epochs Y k (t) Network output D k (t) Desired output E k (n) Network error g Learning rate parameter d Local gradient a Momentum constant References Abhijit SP, Robert BM (1996) Pattern recognition with neural networks in C++. ISBN: , IEEE Press Ashkenazi A, Moore T, Dumville M, Lowe D, Tsakiri M (1995) An artificial intelligent highway system. Proceedings of the 8th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS-95), September, Palm Springs, CA Brown RG, Hwang PYC (1992) Introduction to random signals. Wiley, New York Chansarkar M (1999) GPS navigation using neural networks. Proceedings of the ION GPS-99, September, Nashville, TN Dumville M, Tsakiri M (1994) An adaptive filter for land navigation using neural computing. Proceedings of the 7th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS-94), September, Salt Lake City, UT El-Sheimy N (2000) An expert knowledge GPS/INS system for mobile mapping and GIS applications. Proceeding of the 2000 National Technical Meeting of the Satellite Division of the Institute of Navigation, January, CA Forrest M, Spracklen T, Ryan N (2000) An inertial navigation data fusion system employing an artificial neural network as the data integrator. Proceedings of the ION NTM 2000, January, Anaheim, CA Ham FM, Kostanic I (2001) Principles of neurocomputing for science and engineering. McGraw Hill, New York Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall, Englewood Cliffs Ibrahim F, Al-Holou Pilutii T, Tascillo A (2000) DPGS/INS integration using linear neurons. Proceedings of the ION GPS 2000, September, Salt lake city, UT Lippman RP (1987) An introduction to computing with neural networks. IEEE Acoustic, Speech Signal Process Mag 4(2):4 22 Noureldin A (2002) New measurement-while-drilling surveying technique utilizing sets of fiber optic rotation sensors. PhD Thesis, Department of Electrical and Computer Engineering, University of Calgary Reed DR, Marks JR (1999) Neural smithing artificial neural networks. MIT Press, Cambridge Salychev O (1998) Inertial systems in navigation and geophysics. Bauman MSTU Press, Moscow Shin E-H, El-Sheimy N (2002) Accuracy improvement of low cost INS/GPS for land applications. The US Institute of Navigation 2002 National Technical Meeting, January, San Diego 218 GPS Solutions (2003) 6: