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Recently, the newest methods based on Artificial Intelligence (AI) are used in order to provide reliable positioning information for various navigation applications for ground vehicles with the help of (GNSS) technology, with integrated inertial navigation system (INS).
All existing methods based on Artificial Intelligence (AI) rest upon the INS system error regarding the correct INS operation, at certain times, and do not take into account the error relation for the past INS values. This study presented, therefore, suggests the use of entry-Delayed Networks Neural (IDNN) to model both the INS position and velocity errors based on past samples of the current INS position and speed of travel respectively.
This aspect leads to a more reliable positioning solution during interruption longer GNSS signals. The proposed method is evaluated using different data paths for both roads and INS navigation test are mounted inside the ground vehicles and integrated with GNSS receivers. IDNN performance - on which the model is based is also compared with both conventional (mainly based on Kalman filtering) and recent techniques based on Artificial Intelligence (AI). The results showed a significant improvement in positioning accuracy in particular cases using INS and long interruptions of receiving GNSS signals.
Keywords:GNSS, Artificial Intelligence, Artificial Intelligence (AI), Inertial Navigation System (INS), Delayed Networks Neural (IDNN), GNSS signals, Kalman filter
Most of the ground vehicles of today have an inbuilt (GPS) in order to give the correct position and faster information. Nevertheless, there are more situations in which the GPS cannot sustain certain difficult situations, such as:
Total system interruption (cycle slips)
Precision damage (due to multipath effects and clock errors).
Thus, the GPS is usually combined with an initial navigation system (INS), which is normally an autonomous system, which incorporates three octagonal accelerometers and three octagonal gyroscopes. They monitor the linear accelerations of the vehicle and the rotation rate. A set of mathematical transformations regarding integration according to time are applied to these prime measurements, so as to determine position, speed and altitude. Nevertheless, INS precision deteriorates over time due to errors incidental to a possible sensor (white noise, random correlated noise, imbalance inequality, and random angular deviation) which presents a considerable long-term increase.
As a result, GPS integration with INS offers a navigation system with a higher performance compared to a GPS or INS used separately as a system.
For example, GPS position components have approximately white noise characteristics with restricted errors, and so it can be used to update INS and to improve its long term precision. On the other hand, INS offers GPS positioning information during GPS signal failures and regains the signal after interruption and diminishes the necessary search area for detecting and adjusting the GPS cycle slips. Also, INS is capable of providing position and data altitude information at higher speeds than the GPS.
The Kalman filter (KF) was applied during a number of years so as to offer an optimum GPS / INS integrated by the module. More recently, further techniques based on Artificial Intelligence (AI) were nominated to replace KF, in order to eliminate some of its slips.
Major failures related to using the Kalman Filter (KF) for GPS/ INS integration represent the need to have a pre-defined exact random model for each of the sensor's errors. Furthermore, previous information regarding value co-variation for two INS and GPS data, as well as statistic characteristics (e.g. time variation and correlation) for each sensor system must be known precisely.
The main idea behind all of these models is to imitate the most recent movements in the vehicle's dynamics by the AI formation module during the GPS signal readiness. An empirical model of the INS output processes (position or speed) offers a correct INS positioning and the speed error which can be established during the updating (training) procedure. In the case of GPS intermissions, this model works in a prediction module in order to fix the INS output inadequacies.
All existing AI - based on internal models refer to the INS error at one point and a certain period of time for the INS position or the speed at that time. The major inconvenience with these types of models is their inability to imitate the INS error tendency, either for the INS position or velocity during the update procedure. As a result, during relatively long GPS intermissions, any of the existing models, based on AI, might not be capable to offer a reliable and exact positioning solution, especially for tactical and low-cost systems. Furthermore, some of the recently published results have shown that some of the AI techniques based on the first few seconds of GPS intermissions could be performed with an efficient KF . This fact is due to the inexact linear dynamic error model used by the KF and INS. This linear model works properly only during short GPS intermissions. In the case of long GPS intermissions, the nonlinear and movement ignore elements increase to high values and make worse the general INS positioning accuracy.
The negative impact of the random inadequate models of inertial sensors also appears in the case of long GPS intermissions.
This study wishes to suggest the development of an integration module based on GPS AI / INS, while remembering the error tendency of the INS and thus offering a better positioning precision during both short and long GPS failures.
Such a technique combines the advantages of some of the existing models with the advantages of neural dynamic networks in displaying the sequential data input process (INS position or speed).
This way, it should be possible for the suggested module, both the INS position and velocity errors based on current and past tests of the INS position and velocity.
2. DYNAMIC NEURAL NETWORKS USED BY THE INS AND IDNN
2.1. Method description
The error of the dynamic INS model used by the KF is a linear equation of 1 degree.
What is more, the random error model for the sensor errors is also linear, as differential equations of 1 degree.
Such a static space model is needed for the KF operation.
The nonlinear and non-stationary elements of the INS errors are not modeled for the KF, and so the positioning precision is damaged, especially on a long-term.
This leads to severe positioning errors in the case of relatively long GPS intermissions. Nonlinear complex AI - capabilities based on modeling. So, it has been suggested in this request study.
In fact, there are more considerable disadvantages in using vehicles in KF navigation. These include:
The need for exact stochastic modeling, which cannot occur in the case of tactical sensors;
The requirement for previous information of the measuring system and co-variation matrices for each new sensor, which might represent a challenge for precise determination;
Relatively poor precision during GPS signal intermissions;
The need to adjust the parameters of the stochastic model and the previous information for each new sensor system.
The benefit of using AI methods as opposed to the conventional (KF) method is that the above stated short-comings of the KF method could be discovered while using the AI method.
In addition, the advantage of using the suggested IDNN as being better than other methods, because the AI-IDNN method performs a time processing which gives complete information about the time relation model for the input model, which is the main challenge in studying the INS error which incorporates major time dimensions.
The dynamic networks are generally stronger than static networks (although they can be harder to use) . Because the dynamic networks have a memory, they can be thought to learn sequential or time-variable models. In fact, in order to predict temporal models, an ANN requires two distinct components: a memory and an associate. The memory preserves the relevant past information and the associate uses memory in order to predict future events. In this case, the associate is simply a static MLPNN network, and the memory is generated by a time-delay unit (or movement registry) which represents the exploit delay line .
In fact, the MLPNN model does not perform the time processing, because the output vector coding space does not offer the model any information regarding the time relation of the input.
The traditional MLPNN is a memory-less static network and is efficient when making nonlinear static cartography complex. In fact, INS velocity or the error prediction position is a procedure for the case in which the previous steps of the INS velocity and the position errors must be seriously taken into account. Apparently, the INS modeling error involves a major time dimension and in the RNA context there are efficient methods to represent the process for such models .
A common method is to take into consideration a slide (or movement) of the input sequence window. This approach was widely used with a MLPNN standard. In this case, a fixed number of past information elements are selected and introduced into the entry layer of the network. Thus, the network is provided with a static memory, which has specific expert-dependant knowledge.
A major limitation of the MLPNN with a gliding window entry sequence is the increase of computer complexity, because the entry layer must have a neural number equal to the number of past tests. For example, if the model based on entry error in the past and present needs two tests, the MLPNN entry layer should have three entry neurons. As a result, both the complexity of the network and the training time will increase dramatically .
2.2. IDNN - ENTRY-DELAY IN NEURAL NETWORKS
Another way to work with time models is to use an internal time delay operator inside the MLPNN network. This leads to the neural delay network, mentioned from now as neural Input-Delay Network (IDNN). In this case, the static MLPNN is transformed into a dynamic network by replacing each static synaptic weight with an answer finite-impulse filter. So, the incorporated delay number offers a network with a short-term memory. The neural number associated with the entry level is equal to the number of entry variables, thus, IDNN integrates implicit time model information and acknowledges them as being time models which have random time intervals or random effect length over time.
Therefore, IDNN is suited for situations in which the time models should be considered. This has a positive effect on prediction exactness, which represents the major purpose of this study. In addition, IDNN can also be trained with the standard back-range algorithm .
Figure 1 shows the general architecture of an input-delayed network neural, in addition to the zoom over the internal structure of a single neuron.
Figure 1 - Input-Delayed Neural Network architecture and single neuron calculations
IDNN based on suggested GPS / INS integration module establishes models both for the speed and position along the East, North INS errors and along vertical directions, in order to describe in a reliable manner the INS error tendencies, and to compensate their impact during GPS intermissions. The models will be insured by applying the early-stop criteria during the update (training) of the procedure based on IDNN module while the GPS signals are available. Moreover, in real-time, the performance shall be based on the use of an overlap in non-window movement, when the GPS / INS move the real-time data window, with steps equal to the window size.
This window system presents more advantages compared to conventional steps, this method only once using a sliding window .
3.1. CONFIGURING THE MODEL USED IN ROMANIA
While the GPS signal is available, the IDNN module operates in update mode. In order to train the network, the INS velocity error provisioned at the exit of this IDNN module must be compared to a certain objective or a wanted answer. In this case, the target (or real) INS velocity error dVINS | GPS represents the difference between the original INS velocity and the corresponding GPS velocity:
The difference between the IDNN (dVINS) output mode and the real velocity error dVINS | GPS is the calculation error (D(DV)) of the IDNN module.
The training procedure continues and repeats for all GPS / INS data windows until an intermission of the GPS is detected. When the satellite signal is blocked (during the GPS intermissions), the system is switched to prediction mode when the IDNN module is being used for the INS Vins entry velocity process and predicts corresponding velocity error (dVINS) using the latest IDNN parameters obtained before losing the satellite signal. The INS models and the speed of the GPS components obtained in the data window are used to train the IDNN module in order to mimic the most recent movements in the vehicle's dynamics and the INS error tendency. They are also used to determine the optimum value of the IDNN parameters and to offer a calculation of (dVINS).
3.2. THE INS ERRORS AND THE DELAY OF THE ENTRY PROCESS
If the INS position and error velocity are examined, one can observe that they are accumulative, and, as usual, they increase over time and follow a certain trend. It cannot be possible to precisely and with the appropriate model imitate this trend with a model based on Ai which refers to the corresponding INS error output (either in position or speed), for a certain amount of time.
In this study we have taken into account one, two and three time - step sequences. For a second delay effect one will take into account the IDNN model for experiment, in the entry layer, previous to a single sample step in addition to the current INS situation or velocity test. Moreover, the higher degree error can be considered as having two and three time entry-delay steps.
4. ROAD TEST EXPERIMENT
The road test was made in Romania in July 2010.
Because the GPS position was available during the entire course of the experiment, the performance for IDNN of the suggested module is evaluated by comparison with the GPS output, which was taken as reference. Nevertheless, because of the application time and the real-time processing limitation, the IDNN updating procedure for each window was cancelled after a few formation trials, besides the RMSE made. In order to examine the value of the IDNN based on suggested module for GPS / INS integration, it is crucial to compare the positioning precision of the IDNN with conventional techniques, mainly based on the Kalman Filter and on the AI based module. For both road trials the results of the model are compared to the Kalman Filter results, which are considered to be an exact base-line level for positioning the vehicle.
5. RESULTS AND DISCUSSIONS
The suggested IDNN - GPS / INS module are examined and analyzed during the updating (training) and prediction modes for operations using the INS testing navigation data. The fast-stop benefits and the impact of the number of entry-delay elements are also exploited. The validation performance along another trajectory while other types of navigation systems are being used is made with INS data.
While the IDNN based on the module which was suggested have shown a slight improvement of accuracy when three entry elements are used instead of one in delay, the added delay elements greatly complicated the updating procedure (as a result, it requires a long training period), which is not wanted for real-time applications. In fact, we have observed that when the IDNN engaged three entry-delayed elements instead of one or two, the processing time during the test and the stopping on the first stages were almost triple. Such high performance on this technique comes as a result of using the IDNN module which offers higher precision compared to the Kalman Filter.
This research introduced a new technique for GPS / INS integration based on IDNN which mimics the INS error tendency and offers reliable calculations for the INS position and velocity errors.
Compared to conventional methods and recent AI - GPS / INS integration techniques, the IDNN mode has shown a higher performance during short and long GPS signal intermissions.