978-1-4244-8551-2/10/$26.00 ©2010 IEEE ICIAfS10 Abstract— In this paper we first analyze the effects of least square based parameter estimation for a autoregressive stochastic model of inertial sensor errors. We then proceed to develop the recursive least squares (RLS) estimation of the autoregressive model parameters and also discuss a fast update method for recursive least square estimation to reduce the computation complexity. This reduction leads to an efficient online dynamic estimation of inertial sensor error model which can then augment a navigation system based on such sensors. Simulation results and actual inertial sensor data are analyzed and it is shown that the RLS estimate can achieve a 20% reduction in forward prediction error as compared to the non- recursive estimate. I. INTRODUCTION HE use of Micro-Electro-Mechanical Systems (MEMS) sensors in inertial navigation systems have gained much popularity in recent times due to their small size, low cost and low power requirements among variety of other reasons [1]. But as many have noted in the past [2],[3],[4] MEMS sensors despite their popularity, suffers from a host of errors which can severely affect the accuracy of navigations systems. Much work has been done in the past to analyze and model the errors in MEMS inertial sensors with the expectation of minimizing the impact of these errors on the overall navigation system performance [5],[6]. The availability of low cost Digital Signal Processing (DSP) units have fueled the development of many algorithms and filters which are capable of fusing erroneous inertial measurements with other inertial and non-inertial measurements in an optimal manner [3]. One common characteristic of almost all such filters is their dependence on apriori information of the stochastic properties of the errors present in the inertial measurements [3],[4],[5]. This dependence has led to thorough analysis of MEMS inertial sensors where the requirement is to develop and parameterize a stochastic model representing the non- deterministic sensor errors [7],[8]. Often an Auto-Regressive model of order 'p' ( AR(p) ) is used to model the errors in inertial sensors due to two main reasons[8],[9]. First, AR models can closely represent the auto-correlation function of many naturally occurring phenomena. Second, AR models have a simple structure which can be parameterized easily thus simplifying error model development process. Once the proper AR model is found for each inertial sensor, the resulting equations can easily be integrated to the navigation system to enhance the accuracy of such systems [8]. The development of an AR model to represent the non- deterministic errors of a given inertial sensor consists of two major steps [8]. First the parameters of the AR model are estimated and then the order of the AR model is determined, using experimental data obtained from actual sensors. Several methods can be used in both the steps, but most of the methods analyzed so far are offline computations where the parameters and model order are calculated once and then used in the navigation system [9]. It is well known that the stochastic models of MEMS sensors are temperature dependant [10] and thus the pre-calculated AR model parameters can produce erroneous results in field operations of sensors. The work presented here discusses a simple, recursive AR parameter estimation method which leads to an adaptive error model of the MEMS sensor. The AR model order is still determined offline with an initial set of parameters for the model. These parameters are then refined with each measurement obtained from the sensor to better reflect the current status of the sensor. In the following sections, we first discuss the time series least square estimation of the AR model parameters and then compare the results with a classical spectral estimation method. We then extend the method to recursive least squares in which the previous estimation of the AR model parameters are refined with each measurement. A fast update method is then discussed which results in simple equations that can be easily programmed in to a low cost DSP chip. The performance of the proposed method is then analyzed using both simulations and actual MEMS inertial sensor data. II. AR MODEL AND CLASSICAL PARAMETER ESTIMATION An auto-regressive process of order p represents a random process at the output of a linear time invariant system driven by stationary white Gaussian noise. The governing equation for the process is given by ሾሿ ൌ ෍  ௞ ሾ െ ሿ ௣ ௞ୀଵ ൅ ݓሾሿ ሺͳሻ where  ௞ are constant parameters of the process and ݓሾሿ is zero mean white Gaussian noise with variance ߪ ௪ ଶ . The D M W Abeywardena, S R Munasinghe Department of Electronic and Telecommunication Engineering University of Moratuwa, Sri Lanka Email: {dinuka,rohan}@ent.mrt.ac.lk Recursive Least Square based Estimation of MEMS Inertial Sensor Stochastic Models T 424