Gps-free Terrain-based Vehicle Tracking Performance as a Function of Inertial Sensor Characteristics

Prior experiments have confirmed that specific terrainbased localization algorithms, designed to work in GPS-free or degraded-GPS environments, achieve vehicle tracking with tactical-grade inertial sensors. However, the vehicle tracking performance of these algorithms using low-cost inertial sensors with inferior specifications has not been verified. The included work identifies, through simulations, the effect of inertial sensor characteristics on vehicle tracking accuracy when using a specific terrain-based tracking algorithm based on Unscented Kalman Filters. Results indicate that vehicle tracking is achievable even when low-cost inertial sensors with inferior specifications are used. However, the precision of vehicle tracking decreases approximately linearly as bias instability and angle random walk coefficients increase. The results also indicate that as sensor cost increases, the variance in vehicle tracking error asymptotically tends to zero. Put simply, as desired precision increases, increasingly larger and quantifiable investment is required to attain an improvement in vehicle tracking precision. INTRODUCTION Several safety-critical and mission-critical applications [1], such as path planning, navigation and collision avoidance, require the ability to accurately and inexpensively localize and track the position of a vehicle. While the Global Positioning System (GPS) has placed itself as a viable contender for being the default system used to perform localization and tracking, it has many shortcomings that cannot be ignored, especially in safety-critical and mission-critical scenarios. Specifically, poor GPS signal reception, the ability to jam GPS signals and the requirement to maintain redundancy in vehicle automation and driver assist systems necessitates the development of other localization and tracking techniques [2]. These factors, along with the miniaturization and cost reduction of inertial sensors, have resulted in the growth of inertial navigation technology. This paper considers one of the promising alternatives to GPS, hereafter called terrain-based localization, which utilizes only terrain information such as attitude (pitch, roll and yaw) or features generated thereof, to localize and track vehicles [3] [4]. Put simply, terrain-based localization works by comparing the current attitude measurement against a database of previously recorded terrain attitude maps. The algorithm then utilizes a filtering scheme, such as particle filtering or Kalman filtering, to localize and track the vehicle through continuous correlation of incoming sensor measurements to the terrain database. Today, a wide range of options exist for the system engineer trying to identify the appropriate sensor for a desired application. With regards to terrain attitude measurements in ground vehicles, several sensing techniques exist, which utilize LIDAR [5] [6], cameras [7] [8] or inertial sensors [9]. Typically, though, inertial sensors are used for attitude measurements in ground vehicles due to their ease of use, robustness and ruggedness. Within the category of inertial sensors too, there exist various options, separated by several orders of magnitude in terms of cost and precision [10]. With the development of micro electro-mechanical systems (MEMS) devices, inertial sensors have found applications in fields ranging from automotive safety and navigation to virtual reality and motion-based video games [11]. MEMS inertial sensors are typically low-cost, small-sized, designed for large volume production and lie at the lower end of the accuracy scale [10]. On the other hand, the development of optics-based inertial sensors, such as ring laser gyros and interferometric fiber optic gyroscopes (IFOG), has led to remarkable improvement in the quality of inertial measurements. However, optics-based inertial sensors are typically expensive and lie at the higher end of the accuracy scale. The choice and accuracy of inertial sensors plays a major role in the ability of the terrain-based localization algorithm to provide an accurate estimate of the vehicle‟s position. The accuracy of a sensor is usually characterized by quantifying the various individual noise sources that contribute to sensor measurement error, such as white noise, bias etc. [12] [13]. For example, for inertial sensors, manufacturers usually specify angle random walk, in-run bias instability, overtemperature bias instability, resolution, bandwidth etc. to characterize the constituent gyroscopes and accelerometers. Prior research indicates that fusing low-cost inertial sensors with GPS can provide accurate estimates of vehicle states [14] [15]. However, in the present context where only terrain information is available, such a correction is not possible. Thus, for the applications discussed above, it becomes necessary to identify how inertial sensor characteristics affect the localization accuracy of the algorithm. Further, the adoption of terrain-based localization methods requires that the system engineer know how to translate the application requirements, such as desired vehicle tracking accuracy, into the correct sensor specifications, in order to select the appropriate inertial sensor for the application. In this paper, the effects of inertial sensor characteristics on vehicle localization accuracy, given a specific algorithm and environment, will be discussed. The given algorithm is a terrain-based localization algorithm that utilizes an Unscented Kalman Filter for performing vehicle tracking [16], and the given environment is the test track facility at the Larson Transportation Institute at the Pennsylvania State University. Thus, the paper attempts to elucidate a relationship between sensor characteristics and localization accuracy and in the process show that low-cost MEMS inertial sensors are indeed a viable option for terrain-based vehicle tracking. The remainder of this paper is organized as follows. Section 2 discusses the sensor modeling, characterization and simulation procedures. Section 3 includes a simulation-based analysis of the effects of sensor characteristics on vehicle tracking accuracy. Section 4 compares existing inertial sensors available on the market in terms of their ability to track a vehicle using the terrain-based localization algorithm. Section 5 concludes the paper with an overview of important results. SENSOR MODELING, CHARACTERIZATION AND SIMULATION This section discusses the various noise sources in inertial sensor measurements. It also details the procedure for identifying inertial sensor characteristics through Allan variance analysis and simulating a signal emanating from an inertial sensor with known characteristics. It is assumed that the measurements obtained from a sensor are corrupted by a variety of noise sources inherent to the sensor. For example, random flickering in the sensor‟s electronic components can cause bias drift or bias instability in inertial sensors [16]. The measurement error caused by these noise sources can be approximated by developing noise models for each source. Noise modeling is the process of specifying a functional form and a set of parameter values that represent a noise source. For example, bias instability is modeled as a first-order GaussMarkov process [12]. On the other hand, sensor characterization is the process of identifying and quantifying the model parameter values of the noise sources that contribute to sensor measurement error, using actual measurements collected from a sensor. In the included work, sensor characterization is performed using Allan variance and autocorrelation analyses due to the ease of error source identification they offer [13]. Sensor simulation is the process of using the known noise models to corrupt true values of the sensed variable in order to simulate „noisy‟ sensor measurements. In the following subsections, aspects of sensor modeling, characterization and simulation will be discussed. Noise Sources and Modeling The primary noise sources that contribute to measurement error in inertial sensors are angle random walk (η) and bias instability (b) [14]. The noisy sensor measurements are calculated by adding the errors due to various noise sources to the true value, as shown in Eq. (1) : ω = ωTRUE + η + b (1) Angle random walk is modeled as a white noise applied to the angular rate measured by the gyroscope. Integration of the corrupted angular rate yields a random walk error in the angle (attitude) measurements, giving the noise source its name. The parameter used to specify angle random walk is the angle random walk coefficient (N) which is the square root of the noise power [17],