**4.3. SPAN (Synchronized Position Attitude Navigation) technology: Bidirectional INS/GPS coupling to obtain the objectives positioning with an improved accuracy and continuity**

Inertial Measuring Systems – INS are used on land, at sea and in the air as well as in space to determine the dynamic properties and trajectory of a moving object. They are, also, used for navigation, guidance and control or stabilisation of objects.

GPS Positioning of Some Objectives Which are Situated at Great Distances from the Roads by Means of a "Mobile Slide Monitor – MSM" 167

**Figure 13.** The components of the Mobile Slide Monitor

166 Cartography – A Tool for Spatial Analysis

**4.2. Tightly coupled GPS/INS** 

(Moafipoor S. et al., 2004)

**improved accuracy and continuity** 

receivers with two frequencies (Stoica, 2008);

data, the data regarding the Universal Time – UTC;

connected through the Internet network, to a reference GPS station, at which it is subscribed and from which it can take the differential corrections. In relation to this, it is mentioned that the National Romanian Service ROMPOS – DGNSS provides corrections for the real time kinematic applications with a positioning accuracy evaluated at the interval between 3.0 and 0.5 meters for the receiver with a single frequency. The ROMPOS – RTK service delivers corrections for the real time kinematic applications with a positioning accuracy value situated between 0.5 and 2.0 cm for the



The integrated GPS/INS solution produces continuous, smooth position and orientation of the system even when the GPS signals are lost due to obstructions such as bridges, trees,

Taking into account of the functioning details described here, the figure 13 presents the

**Bidirectional INS/GPS coupling to obtain the objectives positioning with an** 

Inertial Measuring Systems – INS are used on land, at sea and in the air as well as in space to determine the dynamic properties and trajectory of a moving object. They are, also, used for

tunnels, mountains, high-rise buildings or limited and sporadic satellite coverage.

**4.3. SPAN (Synchronized Position Attitude Navigation) technology:** 

complete set of devices which compose our Mobile Slide Monitor.

navigation, guidance and control or stabilisation of objects.

In general, an INS system uses forces and rotations measured by an IMU (Inertial Measuring Unit) to calculate position, velocity and attitude. Forces are measured by accelerometers in three perpendicular axes within the IMU and the gyros measure angular rotation rates around those axes. Over short periods of time, inertial navigation gives very accurate acceleration, velocity and attitude output. The INS must have prior knowledge of its initial position, initial velocity, initial attitude, Earth rotation rate and gravity field. Since the IMU measures changes in orientation and acceleration, the INS determines changes in position and attitude, but the initial values for these parameters must be provided from an external source. Once these parameters are known, an INS is capable provide an autonomous solution with no external inputs. However, because of errors in the IMU measurements that accumulate over time, an inertial-only solution degrades in time unless external updates such as position, velocity or attitude are supplied.

GPS Positioning of Some Objectives Which are Situated

at Great Distances from the Roads by Means of a "Mobile Slide Monitor – MSM" 169

cases in which the geographic positioning of some objectives which are at some distance from the surveying vehicle, an optimal variant in the case of an aircraft can be constituted by IMU unit mounting above the video camera in the mode presented in the following

**Figure 15.** The reciprocal orientation of the IMU unit and the carrying vehicle.

**Figure 16.** The mounting variant of the IMU unit in a surveying aircraft. (Novatel, Inertial Explorer,

The lever arm (offset) between IMU and GPS antenna has to be measured in the IMU coordinate system and with an accuracy better than 1 centimeter. Even slight deviations in the measurement of the lever arm may lead to significant position errors and will degrade

schema:

(IMAR - iTraceRT-F200, 2008)

2009)

the total system performance (Fig.17).

The GPS receiver provides auxiliary information for the INS, and it is reciprocally aided by feedback from the INS to improve signal tracking. The feedback from the INS to the GPS engine is the deeply coupled aspect of the system (Fig. 14).

**Figure 14.** Bidirectional INS/GPS Coupling

The combined GPS/INS solution of the SPAN (Synchronized Position Attitude Navigation) integrates the raw inertial measurements with all available GPS information to provide the optimum solution possible in any situation. By using the high accuracy GPS solution, the IMU errors can be modelled and mitigated. Conversely, the continuity and the relative accuracy of the INS solution enable faster GPS signal reacquisition and RTK solution convergence.

GPS signal reacquisition is dramatically improved when running SPAN. This is a key performance feature in restricted coverage environments, such as urban canyons, where the user may have only a few seconds of satellite visibility before another blockage occurs. With SPAN technology, the user will be able to get GPS measurements in that small window of visibility. That means the INS will have shorter periods of free navigation and smaller errors, since the GPS is available more often for aiding (Kennedy and Rossi, 2005).

#### *4.3.1. The IMU unit montage conditions*

It is necessary to mount the IMU unit in a fixed location where the distance from the IMU to the GPS antenna phase center is constant. Also, the use must ensure that the orientation, with respect to the vehicle and antenna, is also constant. For the attitude output to be meaningful, the IMU should be mounted such that the positive Z-axis marked on the IMU enclosure points up and the Y-axis points forward through the front of the vehicle, in the direction of track and X pointing to right. (IMAR-iTraceRT-F200, 2008).

The body coordinate system is defined as given in figure 15:

#### *4.3.2. GPS antenna montage conditions*

Mount the GPS antenna close to the IMU housing. It is recommended to mount the antenna in top of the IMU if the system is mounted on a car, truck, ship or aircraft. In the cases in which the geographic positioning of some objectives which are at some distance from the surveying vehicle, an optimal variant in the case of an aircraft can be constituted by IMU unit mounting above the video camera in the mode presented in the following schema:

**Figure 15.** The reciprocal orientation of the IMU unit and the carrying vehicle. (IMAR - iTraceRT-F200, 2008)

168 Cartography – A Tool for Spatial Analysis

such as position, velocity or attitude are supplied.

**Figure 14.** Bidirectional INS/GPS Coupling

*4.3.1. The IMU unit montage conditions* 

*4.3.2. GPS antenna montage conditions* 

convergence.

engine is the deeply coupled aspect of the system (Fig. 14).

measures changes in orientation and acceleration, the INS determines changes in position and attitude, but the initial values for these parameters must be provided from an external source. Once these parameters are known, an INS is capable provide an autonomous solution with no external inputs. However, because of errors in the IMU measurements that accumulate over time, an inertial-only solution degrades in time unless external updates

The GPS receiver provides auxiliary information for the INS, and it is reciprocally aided by feedback from the INS to improve signal tracking. The feedback from the INS to the GPS

**Output RTK-GPS INS**

The combined GPS/INS solution of the SPAN (Synchronized Position Attitude Navigation) integrates the raw inertial measurements with all available GPS information to provide the optimum solution possible in any situation. By using the high accuracy GPS solution, the IMU errors can be modelled and mitigated. Conversely, the continuity and the relative accuracy of the INS solution enable faster GPS signal reacquisition and RTK solution

GPS signal reacquisition is dramatically improved when running SPAN. This is a key performance feature in restricted coverage environments, such as urban canyons, where the user may have only a few seconds of satellite visibility before another blockage occurs. With SPAN technology, the user will be able to get GPS measurements in that small window of visibility. That means the INS will have shorter periods of free navigation and smaller

It is necessary to mount the IMU unit in a fixed location where the distance from the IMU to the GPS antenna phase center is constant. Also, the use must ensure that the orientation, with respect to the vehicle and antenna, is also constant. For the attitude output to be meaningful, the IMU should be mounted such that the positive Z-axis marked on the IMU enclosure points up and the Y-axis points forward through the front of the vehicle, in the

Mount the GPS antenna close to the IMU housing. It is recommended to mount the antenna in top of the IMU if the system is mounted on a car, truck, ship or aircraft. In the

errors, since the GPS is available more often for aiding (Kennedy and Rossi, 2005).

direction of track and X pointing to right. (IMAR-iTraceRT-F200, 2008).

The body coordinate system is defined as given in figure 15:

**Figure 16.** The mounting variant of the IMU unit in a surveying aircraft. (Novatel, Inertial Explorer, 2009)

The lever arm (offset) between IMU and GPS antenna has to be measured in the IMU coordinate system and with an accuracy better than 1 centimeter. Even slight deviations in the measurement of the lever arm may lead to significant position errors and will degrade the total system performance (Fig.17).

GPS Positioning of Some Objectives Which are Situated

*xV* 

*xV* 

*x'C*

*f* sinΨ*<sup>C</sup>*cosΘ*<sup>C</sup>*

*f*sinΘ*<sup>C</sup>*

*xC*

*L*

at Great Distances from the Roads by Means of a "Mobile Slide Monitor – MSM" 171

network of fixed reference base stations as it is the **ROMPOS network** in Romania, which is

**4.4. Determination of the offset values between the GPS positioning point of the Inertial Measuring Unit and the central reference point "L" of the video camera** 

*4.4.1. The offset linear components in relation to the reference system (xV, yV, zV) of the lab* 


> *zV*

**Figure 19.** The relative positioning between the Inertial Measuring Unit (IMU) and the Video Camera

*n*

*f* cosΨ*<sup>C</sup>*cosΘ*<sup>C</sup>*

*f*

Ψ*<sup>C</sup>*

*m*

*p*

*C*

*IMU*

able to transmit to its customers differential correction data.

*zV yV*

*yV* Θ*<sup>C</sup>*

Measuring Unit is placed (Fig.19);

*vehicle* 

coordinate systems

**Figure 17.** Fig.17 Body Frame Definition for Lever Arm Offset (Novatel Inertial Explorer 8.20, 2009) The IMU is the local origin of the system and the measurements are defined as follows: **X**: The measured lateral distance in the vehicle body frame from the IMU to the GNSS antenna; **Y**: The measured distance along the longitudinal axis of the vehicle from the IMU to the GNSS antenna. **Z**: The measured height change from the IMU to the GNSS antenna (Fig.18).

**Figure 18.** The definition of the offsets between the IMU unit and the GPS antenna (IMAR iTrace-F200, 2008)

#### *4.3.3. Complex positioning equipment for the slide monitoring*

In the same time it is very important to mention that the necessary accuracies of some centimetres can be obtained due to the capability of a device such as Novatel GPS which is to function in a differential RTK (Real Time Kinematic) regime. (Kennedy S. et al., 2007). This type of operation is obtained by connecting the Novatel GPS receiver via Internet to a network of fixed reference base stations as it is the **ROMPOS network** in Romania, which is able to transmit to its customers differential correction data.

170 Cartography – A Tool for Spatial Analysis

**Figure 17.** Fig.17 Body Frame Definition for Lever Arm Offset (Novatel Inertial Explorer 8.20, 2009)

The IMU is the local origin of the system and the measurements are defined as follows: **X**: The measured lateral distance in the vehicle body frame from the IMU to the GNSS antenna; **Y**: The measured distance along the longitudinal axis of the vehicle from the IMU to the GNSS antenna.

**Z**: The measured height change from the IMU to the GNSS antenna (Fig.18).

**Figure 18.** The definition of the offsets between the IMU unit and the GPS antenna

In the same time it is very important to mention that the necessary accuracies of some centimetres can be obtained due to the capability of a device such as Novatel GPS which is to function in a differential RTK (Real Time Kinematic) regime. (Kennedy S. et al., 2007). This type of operation is obtained by connecting the Novatel GPS receiver via Internet to a

*4.3.3. Complex positioning equipment for the slide monitoring* 

(IMAR iTrace-F200, 2008)

#### **4.4. Determination of the offset values between the GPS positioning point of the Inertial Measuring Unit and the central reference point "L" of the video camera**

*4.4.1. The offset linear components in relation to the reference system (xV, yV, zV) of the lab vehicle* 


**Figure 19.** The relative positioning between the Inertial Measuring Unit (IMU) and the Video Camera coordinate systems


$$D\_{x'\_V} = m + f \cdot \cos\Psi\_{\mathbb{C}} \cdot \cos\Theta\_{\mathbb{C}};\tag{1}$$

GPS Positioning of Some Objectives Which are Situated

*Dy , in circular arcs* 

at Great Distances from the Roads by Means of a "Mobile Slide Monitor – MSM" 173

 *meters* (5)

 *and respectively* 

. *D h <sup>z</sup>* (7)

. *<sup>L</sup> hhh* (8)

*Dx and V*

 *meters* (6)

*4.4.2. Transformation of the linear offset distances, V*

min. 360 60 2 cos *<sup>V</sup>*

*D R <sup>x</sup>*

constituted from the video camera objective centre, are obtained as follows:

**5. The computing relations group with which it is achieved the determination of the target T geographic position in the horizontal** 

equivalent sphere with a radius R = 6.367.472 km., as it is presented in the Fig. 20.

; *<sup>L</sup>*

 

min. 360 60 2 *<sup>V</sup> D R <sup>y</sup>*

direction.

On this basis, the geographical coordinates, *λ<sup>L</sup>*, *<sup>L</sup>*, *hL*, of the reference point L which is

At the computing of the linear distances, on the longitude and, respectively, on the latitude direction, between the video camera successive positions and, respectively, between the camera positions and the sighted target, it, also, takes account from the fact that this monocameral stereo-fotogrammetric system, permits the sighting of some objectives which are situated at distances of up to 200 – 300 meters from the lab vehicles. This way, it is possible to adopt the hypothesis consisting in the approximation of the terrestrial globe with an

The geographic position of the target T in the horizontal plane of the referential ellipsoid is achieved, by combining the determinations of the absolute angular coordinates,

positions, 1 *L* and, respectively, 2 *L* , of the video camera, positions which are obtained as a result of the lab vehicle displacement with a distance in limits of which the target T is

In the positioning scheme presented in Figure 20, the following notations were introduced:

, , *TTT* , of the sighted target, for two different

*, h,* represent the geographical coordinates supplied by the IMU for the point in

 ; *<sup>L</sup>* 

*corresponding to the angular coordinate segments:* 



**plane of the referential ellipsoid** 

, , *TTT* and respectively, 222

maintained in the video camera viewing field.

It is also adopted the notation:

where *λ,* 

111

which this is situated.

b. On the *Vy* axis of the vehicle coordinate system:

$$D\_{y\_V'} = \mathfrak{n} + f \cdot \sin \Psi\_{\mathbb{C}} \cdot \cos \Theta\_{\mathbb{C}} \,\,\,\,\,\tag{2}$$

c. On the *Vz* axis of the vehicle coordinate system:

$$D\_{z\_V'} = p + f \cdot \sin \Theta\_{\mathbb{C}}.\tag{3}$$

In the above-mentioned relations, by *m*, *n* and *p* were noted the components, on the axis , , *VVV xyz* , of the distance between the point IMU and the central point C of the video camera sensor.

By *C* and *C* were noted the video camera montage (fixed) angles in relation with the vehicle coordinate system.

$$D\_{x\_V}, D\_{y\_V}, D\_{z\_V}$$


$$\begin{split} D\_{x\_{\mathcal{V}}} &= D\_{x\_{\mathcal{V}}'} \cdot \left( \cos \Psi \cdot \cos \Phi - \sin \Theta \cdot \sin \Phi \cdot \sin \Psi \right) - D\_{y\_{\mathcal{V}}'} \cdot \\ & \cos \Theta \cdot \sin \Psi + D\_{z\_{\mathcal{V}}'} \cdot \left( \cos \Phi \cdot \sin \Psi \cdot \sin \Theta + \sin \Phi \cdot \cos \Psi \right) \\\\ D\_{y\_{\mathcal{V}}} &= D\_{x\_{\mathcal{V}}'} \cdot \left( \cos \Phi \cdot \sin \Psi + \sin \Theta \cdot \sin \Phi \cdot \cos \Psi \right) + D\_{y\_{\mathcal{V}\_{\mathcal{V}}}'} \cdot \\ & \cos \Theta \cdot \cos \Psi + D\_{z\_{\mathcal{V}}'} \cdot \left( \sin \Phi \cdot \sin \Psi - \sin \Theta \cdot \cos \Phi \cdot \cos \Psi \right) \\\\ D\_{z\_{\mathcal{V}}} &= -D\_{x\_{\mathcal{V}}'} \cdot \cos \Theta \cdot \sin \Phi + D\_{y\_{\mathcal{V}\_{\mathcal{V}}}'} \cdot \sin \Theta + D\_{z\_{\mathcal{V}\_{\mathcal{V}}}'} \cdot \cos \Theta \cdot \cos \Phi \end{split}$$

In these relations by Ψ, Θ and Φ, were noted the rotational angles of the lab vehicle, angles which were measured by the Inertial Unite IMU in relation with the reference system (*x*, *y* and *z*) of the current location.

*4.4.2. Transformation of the linear offset distances, V Dx and V Dy , in circular arcs corresponding to the angular coordinate segments: and respectively* 

$$
\Delta\lambda \boxed{\text{min.}} = \left( 360 \times 60 \times D\_{x\_V} \right) \left( 2 \cdot \pi \cdot R \cdot \cos \phi \right) \left[ meters \right] \tag{5}
$$


$$
\Delta\phi \Big[ \min.\right] = \left( \mathbf{360} \times 60 \times D\_{y\_V} \right) \Big/ \left( 2 \cdot \pi \cdot \mathbf{R} \right) \Big[ mets \,\mathbf{r} \,\mathbf{s} \,\tag{6}
$$


It is also adopted the notation:

172 Cartography – A Tool for Spatial Analysis

camera sensor.

vehicle coordinate system.

and *z*) of the current location.



In the above-mentioned relations, by *m*, *n* and *p* were noted the components, on the axis , , *VVV xyz* , of the distance between the point IMU and the central point C of the video

By *C* and *C* were noted the video camera montage (fixed) angles in relation with the

, , *VVV DDD xyz*


 

cos sin sin sin cos

*y x y*

cos sin sin cos cos *<sup>V</sup> V V <sup>V</sup> DD D D z x y z*

In these relations by Ψ, Θ and Φ, were noted the rotational angles of the lab vehicle, angles which were measured by the Inertial Unite IMU in relation with the reference system (*x*, *y*

 

cos cos sin sin sin

*x x y*

cos sin cos sin sin sin cos *V V V*

cos cos sin sin sin cos cos *V V V*

*D D D*

*D D D*

*V*

*V*

*z*

*D*

*z*

*D*

*D mf x C <sup>C</sup>* (1)

*D nf y C <sup>C</sup>* (2)

*D pf z C* (3)


is placed at the focal distance *f* from the video camera matrix sensor;

the basis of the same type of coordinates of the point IMU;

cos cos ; *<sup>V</sup>*

sin cos ; *<sup>V</sup>*

a. On the *Vx* axis of the vehicle coordinate system:

b. On the *Vy* axis of the vehicle coordinate system:

c. On the *Vz* axis of the vehicle coordinate system:

sin . *<sup>V</sup>*

$$D\_z = \Delta h.\tag{7}$$

On this basis, the geographical coordinates, *λ<sup>L</sup>*, *<sup>L</sup>*, *hL*, of the reference point L which is constituted from the video camera objective centre, are obtained as follows:

$$
\boldsymbol{\lambda}\_{\perp} = \boldsymbol{\lambda} + \boldsymbol{\Delta}\boldsymbol{\lambda}; \ \boldsymbol{\varrho}\_{\perp} = \boldsymbol{\varrho} + \boldsymbol{\Delta}\boldsymbol{\varrho}; \ \boldsymbol{h}\_{\perp} = \boldsymbol{h} + \boldsymbol{\Delta}\boldsymbol{h}.\tag{8}$$

where *λ, , h,* represent the geographical coordinates supplied by the IMU for the point in which this is situated.
