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The question whether barometric altimeters can be applied to accurately track human motions is still debated, since their measurement performance are rather poor due to either coarse resolution or drifting behavior problems. As a step toward accurate short-time tracking of changes in height (up to few minutes), we develop a stochastic model that attempts to capture some statistical properties of the barometric altimeter noise. The barometric altimeter noise is decomposed in three components with different physical origin and properties: a deterministic time-varying mean, mainly correlated with global environment changes, and a first-order Gauss-Markov (GM) random process, mainly accounting for short-term, local environment changes, the effects of which are prominent, respectively, for long-time and short-time motion tracking; an uncorrelated random process, mainly due to wideband electronic noise, including quantization noise. Autoregressive-moving average (ARMA) system identification techniques are used to capture the correlation structure of the piecewise stationary GM component, and to estimate its standard deviation, together with the standard deviation of the uncorrelated component.

Barometric altimeters can be used for measuring the height of an object above a given reference level, e.g., the sea level—a popularly used term for this height is pressure altitude. Common applications are, e.g., in avionics, where barometric altimeters can help in stabilizing the vertical position and velocity of a flying object [

Recent advances in MEMS sensing technologies have led to the availability of barometric altimeters that are well suited for integration in mobile and portable systems. The most popular barometric altimeters for human-centric applications are manufactured by Bosch Sensortec (Reutlingen, Germany) [

In this paper we develop a method for capturing salient statistical properties of the noise that affects barometric altimeters (stochastic approach to noise modeling). Using the developed model we intend to assess the short-time tracking performance of small-amplitude, low-frequency motions. By the term short-time motion tracking we refer to motions with durations up to few minutes, in which relative changes of altitude are to be tracked. Conversely, long-time motion tracking involves accurate tracking of absolute altitude over long time intervals. In human-centric applications, both tracking modes are involved: short-time tracking, e.g., fall detection; long-time tracking, e.g., personal navigation. Under conditions of short-time motion tracking, the time-varying mean is expected to vary very slowly, contributing an offset in the measured pressure altitude with no practical effect on the tracking accuracy. In those applications where accurate absolute altitude is needed, barometric altimeters in differential mode are perhaps the best option available to deal with slow changes of atmospheric pressure [

The proposed method of analysis decomposes the noise in three additive components with different physical origin and properties: a deterministic time-varying mean, correlated with slow pressure changes that can be involved in, e.g., local weather forecasting [

Experimental results obtained when the barometric altimeter is either motionless (for model identification) or moving (for tracking performance assessment) are presented. To this aim

The International Standard Atmosphere (ISA) model can be used to calculate the altitude from the output of an air pressure sensor [^{2}), ^{−1}, in conditions of dry air). The ISA model prescribes that the standard pressure at sea level is _{o} = 1,013.25 hPa, and the standard temperature is _{o} = 15 °C (288.15 K).

The assumption of constant gravity is not crucial in solving

The ISA model fails to accurately describe the real atmosphere in many ways. The assumption of hydrostatic equilibrium is generally valid, provided that the effects of short-term winds can be tolerated. In the real atmosphere significant variations are also observed in pressure, temperature and even lapse rate. Moreover, although the ideal gas assumption is highly accurate for air, the behavior of an ideal gas is influenced by

Absolute altitude information cannot be easily obtained; in particular, it is necessary to know,

In this paper the noise _{c}_{u}

_{c}

The standard deviation σ_{c}

_{u}

The standard deviation _{u}

Applying the spectral factorization technique to the additive combination of the spectral densities of _{c}_{u}

Since the pressure altitude samples from the barometric altimeter are available only at discrete times that are integer multiples of the sampling interval _{s}

_{c}_{u}_{o}

Using autoregressive moving average (ARMA) system identification techniques, _{o}

Under the assumption that the shaping filter _{e}_{e}

The estimates returned by the prediction-error approach are known to be asymptotically normally distributed as the number _{c}_{u}_{o}_{c}_{u}

The experimental distribution of

The experiments described in this paper were performed using a battery-powered wearable inertial measurement unit (WIMU) whose development is undergoing in our lab for applications in human motion ambulatory monitoring and assessment. The WIMU is endowed with a 32-bit ARM Cortex processor (LPC1768, NXP Semiconductors, Eindhoven, the Netherlands) and a Bluetooth transceiver for data communication with an Android-based smart-phone (Samsung Galaxy SII, GT-I9100, Samsung, Seoul, South Korea). The WIMU sensors are a digital tri-axial gyro (ITG-3200, InvenSense, San Jose, CA, USA), a digital tri-axial accelerometer (BMA180, Bosch, Reutlingen, Germany), a digitaltri-axial magnetic sensor (HMC5843, Honeywell, Morristown, NJ, USA), and a digital pressure sensor (Bosch BMP085).

The measurements by the BMP085 digital pressure sensor are noisy, including a significant amount of quantization noise due to a coarse resolution of about 1 Pa (corresponding to about 8.43 cm). The BMP085 was used in the ultra-low power mode (no oversampling was performed internally to the sensor). The ANSI C code by the sensor manufacturer was used to implement the compensation algorithm for pressure and temperature measurement using the integrated thermal sensor [

The barometric altimeter was tested in static and motion conditions. The barometric altimeter was motionless on a table while six data acquisition trials, each of one lasting 10 min, were performed in different day hours, either in a household environment or outdoors (tests in static conditions). The testing procedure was repeated a second time, days later, in similar environmental conditions as above. Static tests allowed ARMA model identification and validation. Based on the ARMA model parameters, a whitening filter was also designed by inverting and discretizing the shaping filter

Two motion tracking experiments were also performed (tests in motion conditions). These experiments with a moving barometric altimeter were used to test few methods of signal processing: Method A (no filtering); Method B (4-point moving average filtering); Method C (4-point moving average filtering cascaded with the designed whitening filter). In the first experiment, the WIMU was mounted at the waist of a person who walked indoors along stairs spanning 1.7 m for each floor in a series of three distinct floors from ground level (

During motion tracking experiments, the relative pressure altitude was computed by taking the average value of the absolute pressure altitude _{o}_{o}

Data processing was carried out using MATLAB. Piecewise constant fitting of raw data from static tests was performed using data windows of fixed size (1 min), and data were locally detrended by subtracting the constant level (detrended raw data). After applying a 4-point moving average filter, the filtered data were downsampled by 5 (_{s}

ARMA model parameters were then estimated for each non-overlapping data window of

The sampling interval and the window length were chosen with the aim to reduce the model parameter uncertainty while preserving the short-term stationarity of the processed data. The short-term stationarity was assessed using the spectral error measure approach [_{e}_{e}_{u}_{o}

_{c}_{u}_{s}

The standard deviation of the correlated noise component took higher values than in relatively unperturbed conditions, while the standard deviation of the uncorrelated noise component was relatively unchanged.

A one-way analysis of variance was performed for comparing the means of the six groups of point estimates of _{e}_{e}

Surrogate data were generated by applying the whitening filter to the detrended raw data from both days. Surrogate data were submitted to ARMA identification after 4-point moving average filtering and time decimation, as described above. Zero-pole cancellation took place, even when the whitening filter was applied to data from the second day, which means that the whitening filter was effective in removing serial correlation from surrogate data, _{s}

Detrended raw data from static tests were also submitted to ARMA identification when

Finally, the results of the experiments in motion conditions are presented in

One important result from using the method of analysis developed in this paper is that the generic prescription that several seconds of averaging of barometric altimeter data are necessary to achieve accuracy in the order of 0.1 m is quite misleading. The correlated noise component should be accounted when assessing the benefits of averaging. In all performed static tests, either indoors or outdoors, the correlated noise component turned out to have a greater standard deviation than the uncorrelated noise component,

The correlated noise component was virtually unaffected by an

The whitening filter was a highly effective tool for filtering the correlated noise component, as shown by the results reported in

The results of the

In this paper we have developed a method of analysis of barometric altimeter noise based on system identification techniques. Beside the slowly time-varying mean, which was outside our scope in the present context, the noise-like fluctuations on barometric altimeter output were interpreted as the superposition of a GM random process that explained short-term temperature and pressure changes (environment-dependent) and an uncorrelated noise component with relatively time-invariant statistics, which accounted for electronics noise. Based on the ARMA model parameters, a whitening filter was also designed and tested, together with standard

Because of their limited accuracy, it is presently a matter of debate whether barometric altimeters can be effectively used in human-centric applications, e.g., fall detection. It is likely that they will find their role as aiding sensors in systems where multi-sensor fusion methods for motion tracking and event detection are implemented. Oftentimes, these methods are optimal when the sensor noise is white, and their robustness may be an issue when the whiteness assumption is not valid [

This work was partly supported by the Italian Ministry of Education and Research (MIUR) through the relevant interest national project (PRIN) “A quantitative and multi-factorial approach for estimating and preventing the risk of falls in the elderly people”, and by the EC funded project I-DONT-FALL “Integrated prevention and Detection sOlutioNs Tailored to the population and Risk Factors associated with FALLs” (CIP-ICT-PSP-2011-5-297225). The views expressed in this paper are not necessarily those of the I-DONT-FALL consortium. The authors are grateful to Andrea Mannini for his valuable help in setting up the

The authors declare no conflict of interest.

Pressure altitude noise spectrum from a barometric altimeter.

Tested methods of signal processing.

Pressure altitude noise pre-processing (modeling task).

Pressure altitude recorded from the barometric altimeter (outdoors static test).

Total standard deviation (●), standard deviation of the correlated (♦) and uncorrelated (▪) noise components. The line superimposed to the values of the standard deviation of the uncorrelated noise component indicates the theoretical scaling with the number of samples involved in the averaging process.

ARMA model parameters (10% trimmed mean ± SD)—first day.

_{c} |
_{u} |
_{s} | ||
---|---|---|---|---|

Indoors static tests | ||||

1 | 0.71 ± 0.27 | 0.26 ± 0.03 | 0.23 ± 0.01 | 0.33 ± 0.03 |

2 | 0.87 ± 0.34 | 0.27 ± 0.04 | 0.24 ± 0.01 | 0.34 ± 0.03 |

3 | 0.72 ± 0.21 | 0.26 ± 0.02 | 0.23 ± 0.01 | 0.33 ± 0.02 |

| ||||

Outdoors static tests | ||||

1 | 0.77 ± 0.30 | 0.26 ± 0.03 | 0.24 ± 0.01 | 0.34 ± 0.02 |

2 | 0.68 ± 0.32 | 0.29 ± 0.02 | 0.24 ± 0.01 | 0.36 ± 0.04 |

3 | 0.65 ± 0.23 | 0.27 ± 0.03 | 0.23 ± 0.01 | 0.34 ± 0.03 |

ARMA model parameters (10% trimmed mean ± SD)—second day.

_{c} |
_{u} |
_{s} | ||
---|---|---|---|---|

Indoors static tests | ||||

1 | 0.69 ± 0.32 | 0.27 ± 0.04 | 0.24 ± 0.01 | 0.35 ± 0.04 |

2 | 0.82 ± 0.23 | 0.27 ± 0.05 | 0.25 ± 0.01 | 0.35 ± 0.04 |

3 | 0.78 ± 0.36 | 0.29 ± 0.05 | 0.27 ± 0.01 | 0.38 ± 0.05 |

| ||||

Outdoors static tests | ||||

1 | 0.75 ± 0.34 | 0.24 ± 0.03 | 0.22 ± 0.01 | 0.32 ± 0.03 |

2 | 1.26 ± 0.39 | 0.29 ± 0.03 | 0.23 ± 0.01 | 0.34 ± 0.04 |

3 | 0.98 ± 0.26 | 0.28 ± 0.04 | 0.25 ± 0.03 | 0.36 ± 0.05 |

ARMA model parameters (10% trimmed mean ± SD)—surrogate data, first day.

_{c} |
_{u} |
_{s} | ||
---|---|---|---|---|

Indoors static tests | ||||

1 | -- | -- | 0.22 ± 0.02 | 0.24 ± 0.01 |

2 | -- | -- | 0.23 ± 0.02 | 0.24 ± 0.01 |

3 | -- | -- | 0.22 ± 0.02 | 0.23 ± 0.01 |

| ||||

Outdoors static tests | ||||

1 | -- | -- | 0.22 ± 0.03 | 0.25 ± 0.01 |

2 | -- | -- | 0.23 ± 0.02 | 0.25 ± 0.01 |

3 | -- | -- | 0.21 ± 0.03 | 0.24 ± 0.01 |

ARMA model parameters (10% trimmed mean ± SD)—surrogate data, second day.

_{c} |
_{u} |
_{s} | ||
---|---|---|---|---|

Indoors static tests | ||||

1 | -- | -- | 0.23 ± 0.02 | 0.25 ± 0.01 |

2 | -- | -- | 0.24 ± 0.01 | 0.25 ± 0.02 |

3 | -- | -- | 0.26 ± 0.04 | 0.27 ± 0.02 |

| ||||

Outdoors | ||||

1 | -- | -- | 0.21 ± 0.03 | 0.22 ± 0.01 |

2 | -- | -- | 0.20 ± 0.03 | 0.23 ± 0.01 |

3 | -- | -- | 0.25 ± 0.03 | 0.25 ± 0.03 |

Mean value ± SD of the pressure altitude, expressed in meters. Statistics computed using signal plateaus for each floor, including ground floor (

Reference | 0.00 | 1.70 | 3.40 | 5.10 |

Method A | 0.32 ± 0.53 | 1.99 ± 0.49 | 3.97 ± 0.53 | 5.39 ± 0.53 |

Method B | 0.31 ± 0.31 | 1.99 ± 0.27 | 3.80 ± 0.33 | 5.41 ± 0.28 |

Method C | 0.07 ± 0.15 | 0.41 ± 0.12 | 0.79 ± 0.14 | 1.12 ± 0.12 |

RMSE between the pressure altitude and the reference vertical position, expressed in meters, for different values of motion frequency (

Method A | 0.53 | 0.53 | 0.50 | 0.52 |

Method B | 0.34 | 0.35 | 0.32 | 0.34 |

Method C | 0.20 | 0.18 | 0.18 | 0.19 |