Maximum correntropy Kalman filter

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

Maximum Correntropy Kalman Filter

In this paper, the application of Artificial Neural Networks to perform the thermal calibration of bias for Micro Electro-Mechanical gyros that are installed in Inertial Measurement Units is discussed. In recent years, the interest in using these systems to perform integrated inertial navigation has increased. Several new applications, related to the use of autonomous systems and personal navigation systems in GPS-challenging environments, have been developed. Thermal calibration of bias is a key issue to be assessed to achieve the best performance of a Micro Electro-Mechanical gyro. It can reduce sensor bias to one order of magnitude lower than non-calibrated conditions. Usually, thermal calibration is performed by exploiting polynomial fitting, i.e. finding the least-square polynomial that fits experimental data collected during laboratory tests in a climatic chamber. Polynomials have some drawbacks when they are applied to Micro Electro-Mechanical gyro calibration. They are not adequate to model abrupt change of bias trend in small temperature intervals and sensor hysteresis. For this reason, in the present paper, the use of Back Propagation Artificial Neural Networks is suggested as an improvement of polynomial fitting. Indeed, Neural Networks have intrinsic adaptive configurations and standard training and testing techniques, so that they can be adequately adopted for mapping thermal bias variations. In this paper, the polynomial fitting and Neural Network compensation algorithms are compared on selected testing points where the two techniques have the largest difference. Results highlight that the proposed method has better performance on these points. Therefore, the time in which the flight attitude accuracy meets the requirements imposed by the current regulations is improved by 20%.

MEMS gyros temperature calibration through artificial neural networks

Recent advances in acoustic navigation methods are enabling extended autonomous underwater vehicles’ (AUVs) mission time while maintaining their XY position error within appropriate limits. Furthermore, while advances in inertial sensor technology are drastically lowering the size, power consumption, and cost of these sensors, these sensors remain noisy and accrue error over time. This paper builds on the research and recent developments in single beacon one-way-travel-time acoustic navigation and investigates the degree of bounding position error for small AUVs with a minimal navigation strapdown sensor suite, relying on a consumer grade microelectromechanical system inertial measurement unit (IMU) and a vehicle's dynamic model velocity. An implementation of an extended Kalman filter that includes IMU bias estimation and coupled with a range filter is obtained in the field on two types of AUVs. Results from these field trials in controlled environments and ocean show that the reported navigation solution possesses an accuracy comparable to existing methods.

A Navigation Solution Using a MEMS IMU, Model-Based Dead-Reckoning, and One-Way-Travel-Time Acoustic Range Measurements for Autonomous Underwater Vehicles

A Comprehensive Overview of Inertial Sensor Calibration Techniques

Inertial Measurement Units, the main component of a navigation system, are used in several systems today. IMU's main components, gyroscopes and accelerometers, can be produced at a lower cost and higher quantity. Together with the decrease in the production cost of sensors it is observed that the performances of these sensors are getting worse. In order to improve the performance of an IMU, the error compensation algorithms came into question and several algorithms have been designed. Inertial sensors contain two main types of errors which are deterministic errors like scale factor, bias, misalignment and stochastic errors such as bias instability and scale factor instability. Deterministic errors are the main part of error compensation algorithms. This study explains the methodology of how the deterministic errors are defined by 27 state static and 60 state dynamic rate table calibration test data and how those errors are used in the error compensation model. In addition, the stochastic error parameters, gyroscope and bias instability, are also modeled with Gauss Markov Model and instant sensor bias instability values are estimated by Kalman Filter algorithm. Therefore, accelerometer and gyroscope bias instability can be compensated in real time. In conclusion, this article explores how the IMU performance is improved by compensating the deterministic end stochastic errors. The simulation results are supported by real IMU test data.

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Estimation of deterministic and stochastic IMU error parameters

MEMS based Inertial Measurement Units, which include MEMS accelerometers and gyroscopes, have a wide range of applications due to their low cost, small size and low power consumption. IMU error should be reduced to the lowest level so as to minimize errors of navigation systems which use MEMS IMU. MEMS sensors have bias, scale factor as well as temperature change of these errors. In the error compensation algorithm, polynomials are used to compensate temperature dependent change of errors. The degree of polynomials, which are determined according to sensor characteristics, affect IMU performance. Therefore, optimum degree must be determined by various methods and studies. In this paper, temperature dependent errors of MEMS inertial sensors will be defined and how to determine degree of polynomial will be explained so as to compensate errors by the optimum way. Several simulation studies are supported with real sensor data.

Polynomial degree determination for temperature dependent error compensation of inertial sensors

MEMS inertial sensors (gyroscope and accelerometer) are widely used in many areas from automotive to space applications. Inertial sensors are critical components in navigation applications as they provide valuable measurements such as acceleration and rotation. The structure and material used in MEMS inertial sensors are affected from some environmental factors such as vibration, mechanical shock, humidity, electromagnetism, and temperature. The most restrictive environmental factor for MEMS inertial sensors is temperature. The characteristics of noise and deterministic errors change under different temperature conditions. Therefore, these drawbacks of temperature have to be degraded before using inertial sensors in navigation applications. Generally, calibration tests are performed under different temperature conditions to identify the behavior of deterministic errors in the operating temperature range. This process is time-consuming; hence, many IMU producers try to determine the minimum sufficient number of temperature conditions, which are used in the calibration tests. In this study, deterministic error parameters are estimated for two different temperature conditions in separate calibration processes. One of the calibration processes is performed at eleven different temperature points to determine temperature dependent behavior of the deterministic errors in the operating temperature range. Then, second calibration process is carried out at five different temperature points in the operating temperature. Moreover, calibration verification tests have been performed under three different temperature conditions to examine how deterministic error parameters are affected by decreasing temperature points from 11 to 5 points. 8 uncalibrated IMUs from same batch are taken into consideration and their deterministic error characteristics are investigated.

Determining efficient temperature test points for IMU calibration

Modeling and simulation studies are used to measure the desired performance prior to the hardware implementation of inertial navigation systems. Inertial measurement units are the main components of the inertial navigation systems. Therefore, IMUs should be modeled within the scope of modeling and simulation studies of inertial navigation systems. Several time and frequency domain analysis are implemented in these simulation studies. In addition to deterministic and stochastic error parameters, frequency and delay characteristics of the sensors required for inertial sensor identification. Hence, transfer functions of accelerometer and gyroscope channels are required. Generally, transfer functions of COTS IMUs, accelerometers and gyroscopes are not provided to end-users. Therefore, identification of sensor transfer functions becomes a problem. In order to identify sensor transfer function several methods have been examined. This study explains the how the transfer functions of inertial sensors are defined by using system identification with Kalman Filter. System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system. System identification consists of data record, generating of model set and determining of the best model steps and lots of several methods can be used in these steps. In the scope of this study Kalman Filter is used to generate candidate transfer function set in the generating of model set step of the system identification. Transfer function identification process will be completed by selecting the best model from the model set. Thereby, effects of frequency and delay characteristics on the system performance can be observed. An IMU can be modeled in frequency domain with transfer function by using the methodology which is explained in this study.

Implementation of identification system for IMUs based on Kalman Filtering

Nowadays, changes of bias and scale factor errors with temperature is compensated by error compensation algorithms of MEMS-based IMUs. Changing these errors with temperature is calculated by different degrees of polynomials which are used in error compensation algorithm. Sometimes, these polynomials use large amount of resources of processor or FPGA in which algorithm runs. This problem is encountered as a result of the increase in the degree of polynomials. In order to overcome this problem, the use of Look up table is come into question. The use of Look Up Table vanishes the calculation of higher degree polynomial in each step of algorithm. Besides, lower degree polynomials are used due to the capacity of FPGA or processor and this prevents to increase the reliability of error calibration. Look up Table increases the sensitivity of error calibration because it can be formed by higher degree polynomials. This study presents the comparison between temperature-variated error compensation of different degrees of polynomials and Look up Table. The amount of use of the resources in FPGA and processors are evaluated for each method. Simulation studies are supported with real sensor datum.

Derya Unsal

Papers

Estimation of deterministic and stochastic IMU error parameters

Polynomial degree determination for temperature dependent error compensation of inertial sensors

Determining efficient temperature test points for IMU calibration

Implementation of identification system for IMUs based on Kalman Filtering

Look up table implementation for IMU error compensation algorithm