In providing acceptable navigational solutions, LocationBased Services (LBS) in land navigation rely mostly on integration of Global Positioning System (GPS) and Inertial Navigation System (INS) measurements for accuracy and robustness. The GPS/INS integrated system can provide better landnavigation solutions than the ones any standalone system can provide. Lowcost Inertial Measurement Units (IMUs), based on Microelectromechanical Systems (MEMS) technology, revolutionized the landnavigation system by virtue of their lowcost miniaturization and widespread availability. However, their accuracy is strongly affected by their inherent systematic and stochastic errors, which depend mainly on environmental conditions. The environmental noise and nonlinearities prevent obtaining optimal localization estimates in Land Vehicular Navigation (LVN) while using traditional Kalman Filters (KF). The main goal of this paper is to effectively eliminate stochastic errors of MEMSbased IMUs. The proposed solution is divided into two main components: (1) improving noise cancellation, using advanced stochastic error models in MEMSbased IMUs based on combined Autoregressive Processes (ARP) and firstorder GaussMarkov Process (1GMP), and (2) modeling the lowcost GPS/INS integration, using a hybrid Fuzzy Inference System (FIS) and SecondOrder Extended Kalman Filter (SOEKF). The results obtained show that the proposed methods perform better than the traditional techniques do in different stochastic and dynamic situations.
Steadily increasing economical and environmental constraints as well as stringent safety requirements have triggered the development and widespread use of lowcost Land Vehicular Navigation (LVN) systems over the last decade. LVNs have many applications: nonsafety applications, such as fleet management and traffic optimization, or active safety applications, such as Collision Mitigation Braking Systems (CMBS) and lane keeping systems. LVNs can also be used for protecting vehicles from theft in vehicle tracking systems or for reducing the greenhouse gas emissions in environmental monitoring systems. Besides, they can also be used in autonomous car navigation systems and emergency assistance services. Furthermore, the need for recognizing driver’s behavior in many applications requires lowcost and reliable estimation of vehicular position and attitude. Clearly, universal use of LVN in road transportation demands lower cost, widespread availability, and ever improving performance [
Advanced commercial LocationBased Services (LBS) must be able to solve difficult positioning problems, especially those in indoorparking, urban canyons, or dense foliage situations, by providing acceptable customer support, whenever the GPS signal is lost. One issue that is recently investigated in positioningbased systems relies on multiGlobal Navigation Satellite Systems (GNSS) environment which is realized due to the effective usage of the global constellation of GLONASS, satellites of Galileo, and Chinese BeiDou Navigation Satellite System (BDS). MultiGNSS environment offers several advantages over a standalone GPS. Indeed, multiGNSS environment may increase the availability of navigation satellites where the received GPS signals are less than 4 satellites in urban canyons. Moreover, it can improve the accuracy of positioning, especially when the navigation system considers the horizontal positioning accuracy [
However, multiGNSSbased techniques may increase the intersystem interference, particularly when multiGNSS environments broadcast navigation signals in overlapped frequency bands. Moreover, these techniques impose higher levels of complexity, because the analogpart of the receiver should deal with multiplesystem, multiple frequencies and considerable bandwidths [
MEMSbased IMUs are classified based on their mass position recognition, their operation mode, and their fabrication procedure. Piezoresistive, Capacitive, Piezoelectric, and Resonant element sensors are different types of MEMS sensors which are placed in the classification of mass position recognition [
The first part of the proposed methodology consists of augmenting the navigation solution with 1storder GaussMarkov Process (1GMP) for dynamically estimating and compensating the stochastic errors of MEMSbased lowcost IMUs. Two different identification methods were exploited in this study to identify the 1GMP parameters. The first one is a traditional method based on the analysis of Autocorrelation Function (ACF) and the second one is based on analysis of 1storder Autoregressive Process (ARP) model. ACF does not fully match the random error characteristics of lowcost MEMSbased IMUs. What mainly causes this mismatch is the high nonlinearity of the lowcost inertial sensor errors leading to higher order GMPs (i.e., 2nd or 3rdorder GMPs) distributions instead of 1GMP [
As these static errors have both high frequency (HF) term and low frequency (LF) term, decreasing both of them is needed in order to develop the accuracy of the lowcost inertial sensors. Wavelet Denoising Techniques (WDTs) have been utilized in similar research studies, due to their significant role in removing the HF noises [
Traditionally, GPS/INS integration is carried out by using Kalman Filter (KF) techniques. This approach has been validated in many studies, where highend IMUs were used [
The conventional 1storder EKF is used extensively for integration of highend INS and GPS data, which can achieve a suboptimal estimation of Minimum Mean Square Error (MMSE) of the vehicle state vector [
Several research groups investigated the possibility of using sampling techniques to cope with highly nonGaussian multimodal error distributions in GPS/INS integration and thus avoiding linearization of the dynamic models [
The second part of the proposed approach is to combine both linearized navigation filters and AI techniques into an intelligent cognitive navigator. SOEKF as the linearized navigation filter helps in reducing the linearization error during the filtering process and FISbased approach as an AI technique, predicting the error states of the SOEKF based on a Covariance Matching Estimation Technique (COMET). In fact, the dynamic characteristics of vehicle motion in body frame and the navigation frame form based on the SOEKF process. The FIS can be exploited to increase the accuracy and the robustness of the SOEKF and to prevent its divergence in the tuning phase of SOEKF. The performances of the proposed methods were evaluated by a road test, using Matlab. The results show that the proposed method is effective in reducing the root mean square error (RMSE) of position by 45% compared with the SOEKF.
The remainder of the paper is organized as follows: Section
This section presents details on background of techniques and ideas used in this study. More specifically, two main topics will be studied in this section: SecondOrder Extended Kalman Filter (SOEKF) as a datafusion technique for automotive navigation and stochastic error modeling technique in Inertial Navigation Systems.
Linear state estimators have been widely used in the early literature for guidance, navigation, and control of various types of vehicles, including aircraft, space shuttles, ships, submarines, and automotive land vehicles [
In this study, SOEKF was addressed for proposed datafusion of lowcost INS and GPS aided with FIS. Thus, a summary of SOEKF performance is presented in this section. The SOEKF is an estimator method, which can solve the problem of estimating the state of a controlled process. The model of SOEKF is
Techniques developed for the correction of inertial sensor errors can generally be divided into two categories that are (1) deterministic error calibration procedures and (2) stochastic error estimation models. Only the stochastic error estimation models are considered in this work.
In general, stochastic errors can be separated into two categories, that is, white noise and colored (or correlated) noise. White noise is a random process characterized by an Autocorrelation Function (ACF) of the form of a Dirac. On the other hand, colored noise may exhibit different ACFs depending on the nature of the noise (pink, red, grey, etc.).
White noise can generally be mitigated using adequate lowpass filter or Wavelet Denoising Technique (WDT) while colored noise must be precisely modeled in order to be estimated and compensated. Traditionally, colored noise of IMUs is modeled as a firstorder GaussMarkov Process (1GMP) with an exponentially decaying ACF. This section presents details on stochastic processes to model the colored noise as well as Wavelet Denoising Technique (WDT) to eliminate the white noise in IMUs.
The most important errors to consider are stochastic errors since these errors, if not dealt with, will have a significant negative impact on the accuracy of vehicular tracking output [
Although there are several stochastic processes, this section addresses only those that were considered for this study, namely, firstorder GaussMarkov Process (1GMP) and Autoregressive Processes (ARP). The relation between these two stochastic processes and proposed stochastic error modeling will be detailed in Section
Classically, 1GMP’s parameters can be estimated by Autocorrelation Function (ACF). Several studies investigated the use of ACF in analyzing the stochastic error of the inertial sensors and also to acquire 1GMP’s parameters. It can be modeled with an exponentially decaying ACF, as shown in Figure
Autocorrelation Function (ACF) for 1GMP.
Wavelet Denoising Technique (WDT) is based on the wavelet filtering method, which can eliminate the stochastic error in the measurements of the inertial sensors at High Frequencies (HFs) without altering important information contained in the signal [
Application of Wavelet Denoising Technique (WDT) with different Levels of Decomposition (LODs).
The maximum amount of information about the original signal
This paper proposes combining two independent and complementary solutions into a global integrated navigation system to provide stable lowcost ubiquitous automotive navigation in severe urban environments. The first proposed solution consists of augmenting the navigation solution with combined 1GMPARP for dynamically estimating and compensating the static errors of lowcost inertial. The second proposed solution is to combine both linearized navigation filters and AI techniques into an intelligent cognitive navigator. SOEKF as the linearized navigation filter helps in reducing the linearization error during the filtering process; and FISbased approach as an AI technique helps in predicting the error states of the SOEKF. This section presents details on these two proposed solutions.
Autocorrelation Function (ACF), which is presented in Section
Furthermore, Wavelet Denoising Technique (WDT) can be combined with the ACF (as the experimental method to estimate the classical 1GMP parameters) or with proposed combined 1GMPARP (as an alternative method to estimate the parameters of 1GMP) to investigate the stochastic error of inertial sensors. After applying the technique, the coefficients of 1GMP obtained by ARP, or ACF, were determined from the enduring noises. These combinations are augmented in GPS/INS integration system to improve the navigational solution and their results are presented in Section
Two different approaches of adaptive Kalman filtering, namely, Innovation Adaptive Estimation (IAE) and Multiple Model Adaptive Estimation (MMAE), are considered by several research groups [
The dynamic characteristics of vehicle motion in body frame and the navigation frame form the basis for the SOEKF process. The FIS can be exploited to increase the accuracy and the robustness of the SOEKF and to prevent its divergence in the tuning phase of SOEKF. Hence, FIS was used as a structure for identifying the dynamic variations and for implementing the realtime tuning of the nonlinear error model. It can provide a good estimation in maintaining the accuracy and the trackingcapability of the system. Figure
Proposed hybrid FISSOEKF model in navigation system.
Fuzzy Inference System (FIS) is a rulebased expert method that can mimic human thinking and understand linguistic concepts, rather than the typical logic systems [
FIS architecture performs three types of operations: fuzzification, fuzzy inference, and defuzzification. Fuzzification converts the crisp input values into fuzzy values; fuzzy inference maps the given inputs into an output, and defuzzification converts the fuzzy operation into the new crisp values. The FIS can convert the inaccurate data to normalized fuzzy crisps, which are represented by the ranges of possible values, Membership Functions (MFs), and the confidencerate of the inputs. In addition, the FIS are capable of choosing an optimal MF under certain specific criteria, applicable to a specific application. The deterministic output of FIS and its performance depend on the effective fuzzy rules, the considered defuzzification process, and the reliability of the MF values.
The proposed FIS model is based on the innovation process of the covariance matrix as the input of the FIS as well as the difference between the actual covariance matrix and the theoretical covariance matrix. Figure
Proposed FIS part for hybrid FISSOEKF in navigation system.
In fact,
If
If
If
If
If
Membership Functions (MFs) for (a)
The static raw data for analysis of the stochastic error was obtained from the wireless Microintelligent Black Box (MicroiBB), which was designed and assembled by the VTADS team of the LASSENA Lab in the ETS. MicroiBB consists of a triad of accelerometers, gyroscopes, magnetometers, and a temperature sensor. The serial numbers of the accelerometer, the gyroscope, and the demonstration board are LSM303DLHC, L3GD20, and STEVALMKI119V1, respectively. The selected aiding devices in MicroiBB consist of a GNSS receiver (ublox 7). Table
Technical specification of the angular rate and the acceleration sensors in microiBB.
Accelerometer  Gyroscope  

Data rate  200 Hz  Data rate  200 Hz 
Temperature range  −40~+85°C  Temperature range  −40~+85°C 
Input range  ±2 g  Input range  ±250°/sec 
Linear sensitivity  2 mg/LSB  Sensitivity  m°/sec/digit 
Acceleration noise density  220 
Rate noise density  0.03°/sec/√Hz 
Nonlinearity  0.2%°/sec 
Wireless Microintelligent Black Box (MicroiBB).
This section analyzes the stochastic error to determine the effect of random errors on gyroscopes and accelerometers of the MicroiBB. First, the ACFs were considered after recording the raw data. WDT was applied before data processing to weaken high frequency noises and remove preliminary biases in the sensors. By using WDT, uncorrelated and colored noises in the signal could be reduced. Figure
WDT with different LODs for (a)
ACF of 1GMP for (a) accelerometers and (b) gyroscopes, in MicroiBB after employing WDT with 6 LODs.
Figure
The parameters needed to model 1GMP with different methods for ARP after 6 LODs of WTD.
Models  ACFbased  YWARPbased  MCOVARPbased  BURG’sARPbased  








 
Acc 

1/2600  
1/380  
1/740  
1/1100 
Acc 

1/2300  
1/740  
1/1100  
1/1500 
Acc 

1/1100  
1/320  
1/630  
1/900 
Gyr 

1/1700  
1/60  
1/520  
1/1600 
Gyr 

1/800  
1/150  
1/330  
1/500 
Gyr 

1/1500  
1/90  
1/570  
1/1200 
To evaluate the performance of the proposed models of GPS/INS integration, their results are compared with those of the conventional methods of GPS/INS integration. For demonstration, the loosely coupled GPS/INS integration was utilized in a threedimensional navigation system. In the loosely coupled GPS/INS integration, position and velocity observed by GPS are the auxiliary measurements. So, in the SOEKF measurement model can be as follows:
The proposed landnavigation solution was implemented with an experimental setup for a road test. The tests were performed by MicroiBB, whose specifications are detailed under Section
The raw data of the routetest was gathered from different sensors of MicroiBB. The selected trajectories satisfy the overall quality and reliability requirements of the proposed models of this study in real environments of various conditions. The first trajectory was figured out in an urban freeway which allowed the authors to drive at high speed. The second trajectory was in downtown area that contains numerous prominent skyscrapers. The test along this trajectory was performed at slow speed with frequent stops because of high traffic and crowded road intersections.
The goal is to investigate the efficiency of the proposed hybrid FISSOEKF using different LODs of WDT and using various algorithms to estimate ARP’s coefficients for 1GMP. The WDTs considered for this purpose are 2 LODs, 6 LODs, and 8 LODs and the algorithms are MCOV, YW, and Burg’s algorithm. The proposed combinations are compared with traditional SOEKF and two hybrid FISSOEKFs, which used ACF to estimate the 1GMP coefficient with different LODs of WDT. All the hybrid FISSOEKF solutions followed the idea of updating stochastic error states to the gyroscope and accelerometers measurements. RMSEs were estimated in all navigational solutions with Novatel SPAN as the reference solution.
The first routetest trajectory selected for this study starts from freeway #5 near Viger East Avenue (45.509023, −73.557511) and ends at freeway #71 near Lebeau Avenue (45.524299, −73.652472) in Montreal, QC, Canada, by boulevard VilleMarie/highway #720 West and highway #15 North (see Figure
The freeway trajectory showing the five outages: (a) on google map and (b) on Matlab.
Figure
Available satellites in each outage for freeway trajectory: (a) outage #1, (b) outage #2, (c) outage #3, (d) outage #4, and (e) outage #5.
Figure
(a) Root mean square error and (b) maximum errors, in horizontal positioning during five GPS outages in the first scenario (freeway).
From the foregoing data, it can be seen that the proposed hybrid FISSOEKF, which used ACFbased 1GMP after 6LOD denoising, performed significantly better than did the traditional SOEKF without updating stochastic error states. This is because the proposed hybrid FISSOEKF can deal with the nonlinearity of systems and models; however, SOEKF exploits secondorder linearized models to estimate the state of systems. The results also show that “BURG’sARP” outperformed “SOEKF” and also the proposed hybrid FISSOEKF that used ACFbased 1GMP after denoising.
Furthermore, in terms of the ARPbased 1GMP after 6LOD denoising, “BURG’sARP6” shows a major improvement in positioning accuracy as compared with the performance of “YWARP6” and “MCOVARP6.” This is because Burg’s algorithm provides the highest accuracy when applied to lowcost MEMSbased INS as compared to the other algorithms that determine the ARP’s coefficients ideally. During the second outage of 180 sec duration, it can be seen that the performance of all solutions degraded considerably, because at least four satellites are needed in loosely coupled GPS/INS integration. Against this requirement, the number of satellites available was less than four for more than half of the outage duration, besides the duration itself being quite long. In addition, using the lowcost MEMSbased INS worsened this situation. So, the second outage gave the worst result, with the maximum horizontal error being 630 m and mean horizontal error 187 m; these cannot be shown in the figure as the values are high.
Figure
Different navigation solutions for the freeway trajectory: (a) outage #2 and (b) outage #4.
The second routetest trajectory selected starts from McGill Street near La Commune Ouest Avenue (45.498718, −73.552831) and ends up at Pins Ouest Avenue (45.501466, −73.584548) in Montreal, QC, Canada, by Boulevard StLaurent/Shebrooke Ouest Street and Peel Street (see Figure
Second (downtown) trajectory showing the five outages: (a) on google map and (b) on Matlab.
Figure
Available number of satellites during each outage for downtown trajectory: (a) outage #1, (b) outage #2, (c) outage #3, (d) outage #4, and (e) outage #5.
Horizontal positioning errors during the five GPS outages in the downtown scenario: (a) root mean square error and (b) maximum errors.
Figure
Different navigation solutions for downtown trajectory: (a) outage #2 and (b) outage #4.
From the data presented, it can be seen that the proposed hybrid FISSOEKF, which used ACFbased 1GMP after 2LOD and 6LOD denoising, “FS(ACF2)” and “FS(ACF6),” performed significantly better than did the traditional SOEKF without updating stochastic error states. The results also show that “FS(BURG’sARP),” among all the “SF (ARP)” navigation solutions, outperformed “SOEKF,” “FS(ACF2),” and “FS(ACF6).” Furthermore, in terms of the ARPbased 1GMP after 6LOD denoising, “FS(BURG’sARP6)” shows a major improvement in positioning accuracy in the downtown scenario, as compared with the accuracy obtained by “FS(YWARP6)” and “FS(MCOVARP6).” This is because Burg’s algorithm provides the highest accuracy when applied to lowcost MEMSbased INS, as compared to the other algorithms that determine the ARP’s coefficients perfectly.
As regards the number of satellites and the duration of each GPS outage, it can be seen that there are less than 4 satellites for twothirds of the duration and less than 5 satellites during the remaining part of the duration for outages #2 and #4. However, RMSE in outage #4 is much more than that in outage #2, because the duration of outage #4 (180 sec) is longer than that of outage #2 (110 sec). The results also show that outage #5 presents, in spite of its longest duration (310 sec), lesser RMSE than that of outages #3 and #4. This is because 6–8 satellites existed for less than half of the duration of outage #4 and less than 4 satellites for threequarters of the duration. Outage #2 shows the lowest error (2 m) because of its short outage duration.
In this paper, two novel auxiliary methods are proposed to improve the performance of ultralowcost MEMSbased IMU in a vehicular navigation system. The proposed methods can cover two areas: modeling stochastic errors and performing GPS/INS integration. The proposed 1GMPARP consists of a complete stochastic error modeling of the noise components in MEMS lowcost inertial sensors. This paper shows a big cooperation between 1GMP, ARP, and WDT to characterize the noise components. Different levels of decomposition in denosing technique as well as various methods to identify the ARP’ parameters were considered to clarify the best one for stochastic error modeling in MEMS lowcost inertial sensors. Result presents that Burg’s method, after applying the six levels of decomposition in denosing technique, performs much better than modifiedcovariance and YuleWalker methods with different levels of decomposition. The second proposed method consists of an integration of SOEKFFIS to enhance the performance of lowcost GPS/INS integration for navigation data fusion. The FIS part is exploited for dynamic adjustment of the process noise covariance, by observing the innovation process, which is utilized in SOEKFpart to maintain further enhancement in the estimation of the accuracy. The results confirm that the proposed hybrid FISSOEKF can provide further improvement in the overall performance compared to SOEKF in harsh environment.
Future research work related to this study will focus on more complicated GPS/INS integration structures such as tightly and ultratightly coupled and noise modeling with higher order stochastic error to reduce the errors in the positing of the navigation system. In addition, GPS/INS integration will expand to GNSS/BDS/lowcostINS integration to utilize the advantages of the multiGNSS environment.
The authors declare that they have no competing interests.
This research is part of the project entitled VTADS: Vehicle Tracking and Accident Diagnostic System. It is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and École de Technologie Supérieure (LASSENA Lab), in collaboration with two industrial partners, namely, iMetrik Global Inc. and Future Electronics.