Patent Application
20170108612
1. Field of the Invention
The present invention relates to airborne gravimetry, and particularly to an inertial system for gravity difference measurement that uses a global navigation satellite system (GNSS) in combination with a strapdown inertial measurement unit (IMU) on an airborne platform to measure differences in the earth's gravitational field.
2. Description of the Related Art
Airborne gravimetry technology using strap-down IMU/GPS methods has been heavily researched at the University of Calgary over a 10+ year period. More recently, IMU/GPS gravimetry research has also been conducted at Ohio State University.
All major airborne gravimeter solutions today use gimbaled systems to isolate the precision accelerometers from the attitude motion of the aircraft and require that the aircraft fly in light turbulence to achieve the necessary quiet environment for gravimetry sensing.
Generally, these traditional methods use extensions of the ground-based accelerometer methods and attempt to place the airborne sensors into a ground-like motion-isolated environment.
Conventional systems for gravity difference measurement use proprietary accelerometer designs built in-house that are usually bulky, expensive, and not easily upgradable.
Thus, an inertial system for gravity difference measurement solving the aforementioned problems is desired.
The inertial system for gravity difference measurement uses commercial-off-the-shelf (COTS) nano accelerometers and strap-down Global Navigation Satellite System (GNSS)-aided inertial measurement units (IMU). The former has low measurement noise density, while the latter is used to analytically stabilize the platform. Stochastic modeling of the gravity anomaly is utilized (as opposed to the deterministic modeling of causes and effects) to simplify the algorithm. The algorithm aims at finding relative changes between points, as opposed to absolute values at the points, which allows for high relative precision required in many applications.
These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.
Similar reference characters denote corresponding features consistently throughout the attached drawings.
As shown in
A DC power source 112 is connected to a communal power and interface board 110, which connects to and powers the single board computer 108. The DC power source 112 is also connected to a second interface board 114, which is connected to and powers the GNSS 106, IMU 104 and accelerometer 102.
The IMU 104 and accelerometer 102 are housed separately from the system enclosure, but are connected to the single-board computer 108 via a communal cable. The IMU 104 is preferably a commercial-off-the-shelf (COTS) strap-down unit. The accelerometer 102 is preferably a COTS nano accelerometer. The connection of the GNSS antenna 116 to the GNSS 106, the connection of input DC power 112 to the interface boards 110, 114, and the connection of data storage 118 (a generic USB disk that also contains startup configuration scripts for the system) to the computer 108 are considered to be peripheral connections of the system 100. The COTS hardware is outlined in Table 1 (sensor head) and Table 2 (control box).
The single-board computer 108 is equipped with a 1 GHz Vortex processor and 256 MB memory with Linux as the operating system. The single-board computer 108 also features multiple I/O peripherals, among which one RS-232 port, one RS-422 port, six analog channels, and one external trigger pin are utilized in the operation of acquiring data from the GNSS receiver board 106, the IMU 104, and the accelerometer 102. All data acquired are stored in the USB disk 118.
The GNSS receiver board 106 is configured to output GNSS data (L1 and L2 range measurements and navigation data from satellites in both Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS) systems) in Radio Technical Commission (RTCM)-3 format at 20 Hz to the RS-232 port with baud rate 115200 bps on the single-board computer 108. The GNSS receiver board 106 also outputs a pulsing signal at 1 Hz to the external trigger pin for generating timestamps for acquired data. Additionally, means are provided in which the GNSS receiver board 106 also receives a pulsing signal at 1 Hz from the IMU 104 through its event marker for the purpose of generating timestamps for the IMU data. In addition, there is a bi-color LED indicator from the GNSS receiver board 106 provided as means for indicating the number of satellites tracked by the receiver, wherein a number of green flashes indicates how many GPS satellites are tracked, and a number of yellow flashes indicates how many GLONASS satellites are tracked.
The IMU 104 features three gyros, three accelerometers, three magnetometers, and one temperature sensor. The IMU 104 outputs binary concatenated data packets at 150 Hz to the RS-422 port with a baud rate of 115200 bps. The IMU 104 enables hardware time-synchronization by outputting a 1 Hz pulsing signal to the event marker input pin of GNSS receiver board 106 and incorporating the status of a predefined data hit (one or zero) in its packet to reflect the status of the pulsing signal (high or low). The GNSS receiver board 106 then generates a timestamp upon the arrival of each pulse.
The accelerometer 102 is a three-axis accelerometer with ultra-low noise in order to detect the anomaly of gravity signal at the level of micro-G. The accelerometer 102 outputs bipolar analog signals to the analog I/O ports on single-board computer 108. The single-board computer 108 provides dedicated 16-bit analog-to-digital conversion circuitry, a hardware buffer (FIFO, first-in-first-out), and interrupt-based software operations to acquire analog data with high precision.
The power and interface board 110 provides necessary power supply circuitry for all components and connections among them. The main power supply input 112 is required to be 12V DC. The 12V DC power supply 112 and interface boards 114, 110 form a power distribution system 200 that regulates and distributes power to all the components, as shown in
The firmware comprises the software program(s) running on the single-board computer 108 for acquiring data from the GNSS receiver board 106, the IMU 104, and the accelerometer 102, including the synchronization (time-stamping) mechanism of acquired data. Programs include an algorithm that utilizes single board computer 108 as a means to perform stochastic modeling of the gravity anomaly (as opposed to the deterministic modeling of causes and effects) to simplify the algorithm. The algorithm aims at finding relative changes between points as opposed to absolute values at the points which allows for high relative precision required in many applications. Table 3 shows the pseudocode of the key functions of the firmware.
After initialization, the main function installs an interrupt routine for acquiring data from the GNSS receiver board 106, the IMU 104, and the accelerometer 102. The interrupt routine is triggered externally by the 1 Hz pulsing signal from the GNSS receiver board 106. The firmware timestamps GNSS time, IMU frame count, and accelerometer data with computer time for further synchronization in post-processing. Then the firmware reads and saves all data from buffer to disk.
The post-processing software translates/converts the acquired data to readable format. The acquisition software saves data in binary format and keeps timestamps in computer time without actually performing synchronization between computer time, GNSS time, and IMU frame count in order to maintain high data rate in acquiring data. The processing software is then used to convert/translate binary data into readable format. The processing software contains the following functions shown in Table 4.
Accelerometer data is already saved in TEXT format and time-stamped with GNSS time. The output of the processing software is TEXT files that include GNSS range measurements in Receiver Independent Exchange (RINEX) format, IMU data time-stamped in GNSS time, and the accelerometer data time-stamped in GNSS time. In other words, at any given GNSS time, there are range values with the attitudes, which will be further processed to produce trajectory coordinates, along with the accelerometer data for recording gravity values.
The operation of the GravMap System includes the following steps, shown in Table 5.
The processing operation can be done through the following steps shown in Table 6.
The startup waiting period (default is 3 min) and the operation duration (default is 24 hr) can be adjusted by using any TEXT editor to modify two numbers in the startup script “startgm.sh” inside the folder “scripts” on the USB disk as shown in Table 7.
With respect to the stochastic modeling of the gravity anomaly, the basic model used in the inertial system for gravity difference measurement is as follows:
δg=fu−au+Ec−γu, (1)
where δg is the upward component of the gravity disturbance, measured in mGal (milli Galileo) where 1 mGal˜1 μg=10−5 m/s2 and g is the average Earth's gravity acceleration (˜9.81 m/s2), fu is the upward component of the specific force, measured by the accelerometer, au is the upward component of the vehicle acceleration, derived from measured GPS position, γu is the upward component of the normal gravity vector at vehicle height, computed analytically using normal ellipsoidal model (e.g. WGS84), and Ec is the Eötvös correction due to Coriolis and centrifugal accelerations in the horizontal plane resulting from the relative motion of the vehicle with respect to the rotating Earth. The Eötvös correction is computed as follows:
where ωe is earth's rotation rate (˜15°/h=7.29×10−5 rad/s), vE and vN are east and north components of the vehicle's velocity, respectively, φ and h are vehicle latitude and ellipsoidal height, respectively, R1 and R2 are prime vertical and meridian radii of curvature (R˜6,378 km−WGS84 ellipsoid). 100331 In assessing the performance of the gravity disturbance estimation via the use of kinematic observables (Acceleration from the nano accelerometer and that derived from GPS positions), a distinction is made between the stochastic model of the disturbance and the estimation process itself. We model the gravity disturbance as a third-order Gauss-Markov process whose state variable representation is given as:
or in differential equation form as:
+3f0{umlaut over (x)}+3f02{dot over (x)}+f03x=w, (4)
where f0 is a process/filter bandwidth (natural frequency) [Hz]—highest frequency at which signal can be recovered (i.e. signal can be distinguished from noise) and is characterized by the relation:
where v is the vehicle velocity [e.g. 100 m/s], b is the process spatial resolution [e.g. 1000 m], and w is the driving white noise [mGal].
Moreover, Q is the power spectral density of the driving white noise [mGal2/Hz], and is characterized by the relation:
Gravity disturbance process generated by the driving white noise is x, while s is the gravity disturbance process standard deviation[mGal]. Thus Qx is the power spectral density of the gravity disturbance process x, and is characterized by the relation:
The angular velocity in [rad/s] is ω=2πf. The covariance function of the gravity disturbance process x [mGal2] is Cx(d). The sampling distance ratio (of the process spatial resolution) is ζ=d/b, where d is the sample distance [e.g. 100 m]. Alternatively, sample time T=d/v could be used. The correlation distance [m]—distance at which Qx reduces to one half of the zero-lag (Qx) is defined as 1=2.9033b. Additionally, the output gravity disturbance signal [mGal] is defined as x1=x. The output gravity disturbance rate signal [mGal/s] is defined as x2=The output gravity disturbance second rate signal [mGal/s2] is defined as x3={umlaut over (x)}.
Both the navigation state vector and the instrument error state vector of the navigation solution are augmented with the gravity disturbance states. As seen from the equations above, position (φ, h) and velocity (vE, vN) errors affect the computation of the disturbance. Optimal estimates of the error states are obtained through a Kalman filter process. In the Kalman filter setup, the differences between the inertial navigation solution and the GPS positions and velocities are used as updates.
Because the gravity disturbance is not observable in this setup, the Kalman design matrix coefficients for the disturbance states are set to zero. This means the a posteriori covariance estimates of the gravity disturbance and its rates are not affected by the update measurements. The estimates of the gravity disturbance itself, however, are affected by the measurements, since the filter gain values associated with these terms are nonzero. The gravity disturbance estimates benefit from the measurement updates, but their covariance does not, instead evolving solely according to the error model. In other words, the covariance does not reflect the correct confidence in the gravity disturbance state, unless the model used is representative of the actual phenomenon.
To simulate this phenomenon, synthetic positions and velocities representing those obtainable through GPS were generated, along with synthetic angular rate and specific force measurements obtainable from an IMU. The INS mechanization was run in the MATLAB environment along with a Kalman filter stage for incorporating the synthetic GPS measurement updates. Noise values for positions varied from 1 mm to 1 m, representing the positional uncertainty of the platform at any given time. Gyro and accelerometer noise was modeled using the power spectral density (PSD) information available from the IMU used. For convenience, the platform was simulated to be moving from a position of 0° N, 85° W directly West at a velocity of 100 m/s with 0° roll and pitch and 270° heading. The gravity spatial resolution was fixed at 1000 m.
Plot 300 of
The simulation results are shown in plot 4003b of
Apart from the covariance and simulation analyses, it is also instructive to examine the steady-state gain values of the disturbance state computed from the Kalman filter, and in particular, the gain terms mapping the positional and velocity errors to the disturbance state, which show the contribution of the updates to the state estimates. The elements of the gravity disturbance row (row 16) of the gain matrix are presented in graphs 500 and 600 of
A conclusion to be drawn from the graph data 500 and 600 of
It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.
