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**Temperature Compensation of MEMS Inertial Sensors based on Neural Network**

*Golrokh Araghi, René Jr Landry, Department of electrical engineering, LASSENA, École de Technologie Supérieure, Canada*

**Location:** Big Sur

Micro-electromechanical Systems (MEMS) inertial sensors have the advantage of small size, light weight, low cost, low power consumption and high reliability. However, relative to macro-scale inertial sensors, MEMS inertial sensors are more prone to error sources and noise. Moreover the effect of the temperature variation on the MEMS inertial sensors outputs are more prominent relative to their conventional counterparts. In fact, the main substance of MEMs inertial sensors is silicon whose physical characteristics change with the temperature. Sensor’s packaging and electronics are also highly sensitive to the temperature variation. When using for navigation, due to integration process performed in inertial measurement system (INS) mechanism, these errors accumulate rapidly in time and make the navigation completely inaccurate. Normally, inertial navigation system and global positioning system (GPS) are integrated into a hybrid system, in which GPS is responsible for continuous update for the INS, while on the other hand the INS is used to provide navigation information in the environments where the GPS signals are unavailable. Therefore it is essential to develop a temperature dependent model for MEMS inertial sensors, in order to enhance the overall system accuracy such that it can work properly in the stand-alone in GPS-denied environments in land vehicle navigation applications.

The objective of this paper is to develop a temperature dependent model for calibration of low-cost MEMS inertial sensors and to compensate the temperature-induced errors. Traditional temperature calibration methods rely on a polynomial regression method, which fails to take into account the nonlinearities inherent in the sensor errors. In this paper a temperature compensation model based on radial basis function neural network is proposed. Based on this method the significant deterministic errors of accelerometer and gyroscope triads can be compensated in a full temperature range. A neural network based model has the ability to implicitly detect complex nonlinear relationship between dependent and independent variables.

At first stage, a temperature compensation model based on polynomial regression is addressed. To do so, first it is required to find the deterministic errors (bias, scale factor and misalignment) at various temperature points. For this purpose, the 6-position method is employed in which the inertial measurement unit (IMU) is oriented with each sensitive axis alternatively up and down relative to the local gravity. This results in six different orientations. For an accelerometer triad, error terms are determined by comparing the magnitude of measured specific force in three axes with the magnitude of local gravity vector. Since Earth’s rotation rate is a weak signal (15 °/h), it cannot be measured by low-cost MEMS gyroscope, therefore a single axis rate table is used as a reference value for gyroscope calibration. At the end, a series of error terms along with their corresponding temperature is obtained. Any correlation between the error terms and temperature variation then can then be defined through a polynomial function, typically of order 3. The coefficients of the polynomials will be stored in the IMU processor and will be used for online calibration of inertial sensors.

At the second stage, the proposed method based on neural network is addressed. In this method, temperature compensation of inertial sensors is regarded as a function approximation problem. A common challenge in statistic is approximating a function from some input-output example pairs without any a priori information about the function. In the neural network concept, this problem is the task of supervised learning and these input-output pairs are called training set. Similarly, the nonlinear mapping between the sensors measured value, the temperature and the error can be obtained by employing a radial basis function neural network (RBFNN) to be used as tool for function approximation. In this method, the error terms are not considered separately, instead they are all lumped together as a single error term which is considered to be the difference between measured and true value of the sensor.

The idea of RBFNN is to interpolate the target function to be approximated, by using a linear superposition of a number of radial basis functions. The training of RBFNN has two steps. At first the center and width of the hidden neurons are chosen and in the second step the weights of the hidden neurons are determined through a simple optimization problem.

The inertial measurement unit used in this paper, is a consumer grade IMU consisting of three MEMS accelerometers and three MEMS gyroscopes from. A single axis rate table with a velocity accuracy of ±0.01 % which is enclosed in a thermal chamber has been used to provide reference measurements for the gyroscope triad. Thermal tests are based on soak method in which the IMU is allowed to be stabilized in the desired temperature point before recording the data.

In order to verify the effectiveness of the proposed algorithm, various static and dynamic tests have been implemented. In static tests, the IMU is kept stationary while being heated with a heater gun or being cooled with a cooler, and drift in position and velocity obtained from accelerometers are compared between polynomial regression and the proposed method based on neural network. In another in-lab test, the IMU is moved in a pre-determined closed path and the drift in attitude and position are investigated. The algorithm performance is also analyzed in dynamic tests outside with a car in different scenarios.

Preliminary results in static position are as follows: the gyroscope error (the difference between true value and measured value by the sensor) can be reduced up to 84.5 % by applying third order polynomial while and up to 98.2 % with the proposed method based on neural network. For accelerometers, reduction in error is up to 77.1 % with the third order polynomial and up to 95% with the proposed method.

In addition, the position drift in stationary mode is also calculated. For example the position drift of one accelerometer in only 60 s is around 965 m. With polynomial regression method the drift in position is 470 m and with new proposed method the position drift is decreased to 41 m. Overall with polynomial regression method, there is 57% improvement in position drift in static mode, while with the neural network-based method, the improvement is above 95%.

Based on the preliminary analysis, it can be concluded that the new temperature compensation method based on neural network significantly outperforms the traditional polynomial regression method.

The significance of this work is the compensation of both accelerometer and gyroscope triads and implementing various real tests in order to show the effectiveness of the proposed method, which has been rarely addressed in the previous works.

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