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The problem of fault detection and isolation (FDI) on inertial measurement units (IMUs) has received great attention in the last years, mainly with growing use of
IMU strapdown platforms using fiber optic gyros (FOG) or micro electro mechanical systems (MEMSs). A way to solve this problem makes use of sensor redundancy and parity vector (PV) analysis. However, the actual sensor outputs can include some anomalies, as impulsive noise which can be associated with the sensors itself or data acquisition process, committing the elementary threshold criteria as commonly used. Therefore, to overcome this problem, in this work, it is proposed an algorithm based on median filter (MF) for prefiltering and chi-square cumulative sum (

The design of a FDI algorithm for applications on IMUs can, in general, be divided in two types.The first one, named analytical redundancy, takes into account a mathematical model of the system in which the IMU is used. This method generates a residue vector as a result of the state observer [

The geometrical arrangement used in this work considers four gyros mounted on the faces of a tetrahedral structure (tetrad), and three accelerometers in a triad configuration internally fixed in the tetrahedral. The analysis performed here takes into account the gyros only, and the extension for accelerometers is straightforward. The tetradconfiguration and the reference frame are shown in Figure

Tetrahedral base.

Equation (

The sensor equation considered in (

In the image processing field, it is very common to employ filters that preserve edges or abrupt transitions between distinct parts of the image or remove salt and pepper noise. These filters generally compare the pixel under observation with its neighbors at certain window and take a decision based on a statistical or threshold criteria. The simplest filter that meets these requirements is the median filter (MF). Being the MF not an optimal filter, it preserves discontinuities as jumps [

In the time sequence processing by MF, it is possible to process the samples in the filter window in two ways. (a) Process the samples in the window to obtain the output at discrete time (

The recursive form of the MF presents an expressive noise attenuation capacity comparing with the nonrecursive form, this property leads the signal to a fast convergence [

The appropriate size of the MF can be defined comparing the variance of the signal filtered with the variance of the same signal filtered by an average filter. In this work it was chosen the exponentially weighted moving average (EWMA) filter [

The absolute value of the difference between variances is defined as

The cumulative sum (CUSUM) algorithm is widely used to detect changes in the mean value of an independent Gaussian sequence. This algorithm is based on log-likelihood ratio and defined as follows [

Before a change, the parameter

Considering (

The alarm time (

Considering the prior knowledge about

As a consequence of the previous derivation,

The detection of faults in a IMU with redundant sensors can be performed by PV analysis. Under normal conditions, that is, bias and faults with null values, the PV should present a normal distribution

Gyro processing and fault detection block diagram. MF: median filter (MF

Absolute value of the difference between variances of the

For the actual sensor matrix (this matrix is obtained from calibration process) (

The filtering block in the Figure

The calibration of the FD algorithm was performed offline by using a time series extracted from the IMU movement on a 2DOF rotating table. The first parameter to be determined is the threshold (

Of course, the parameters

Tuning parameters for

0.022 | 0.002 | 0.1 to 5 | 30 |

Ratios for

After the calibration phase, it was injected a step bias fault of magnitude 0.15 deg/s into one of sensors for the sample 10000. This fault generated a step variation in the PV according to Figures

Fault detection delay as a function of fault magnitude given in number of samples with respect to the parameters

Step fault | 1st MF delay | 2nd MF delay | Detection | Total delay |
---|---|---|---|---|

(°/s) | (MF3) | (MF11) | delay | ( |

0.10 | 1 | 5 | 430 | 436 |

0.15 | 1 | 5 | 54 | 60 |

0.20 | 1 | 5 | 9 | 15 |

0.30 | 1 | 5 | 4 | 10 |

PV with step fault for sample 10000. (a) PV nonfiltered (red) and filtered by MF of size 11 (blue); (b) PV filtered by MF of size 11 (blue) and by FExp with

In this paper, a method based on