Research on the Rapid and Accurate Positioning and Orientation Approach for Land Missile-Launching Vehicle

Getting a land vehicle’s accurate position, azimuth and attitude rapidly is significant for vehicle based weapons’ combat effectiveness. In this paper, a new approach to acquire vehicle’s accurate position and orientation is proposed. It uses biaxial optical detection platform (BODP) to aim at and lock in no less than three pre-set cooperative targets, whose accurate positions are measured beforehand. Then, it calculates the vehicle’s accurate position, azimuth and attitudes by the rough position and orientation provided by vehicle based navigation systems and no less than three couples of azimuth and pitch angles measured by BODP. The proposed approach does not depend on Global Navigation Satellite System (GNSS), thus it is autonomous and difficult to interfere. Meanwhile, it only needs a rough position and orientation as algorithm’s iterative initial value, consequently, it does not have high performance requirement for Inertial Navigation System (INS), odometer and other vehicle based navigation systems, even in high precise applications. This paper described the system’s working procedure, presented theoretical deviation of the algorithm, and then verified its effectiveness through simulation and vehicle experiments. The simulation and experimental results indicate that the proposed approach can achieve positioning and orientation accuracy of 0.2 m and 20″ respectively in less than 3 min.


Introduction
Modern war is having increasingly higher requirements for weapon launching systems. To improve the weapon's survival capability in the battlefield, it needs weapon launching systems not only to be capable of accurate aiming at the objects, but also to be able to quickly respond and to have high flexibility, agility, and reliability [1]. This means that a weapon launching system must be capable of acquiring its accurate position, attitudes and orientation rapidly [2]. Consequently, designing an approach which can obtain the accurate launching reference information rapidly for launch of weapons is of great significance and value for improvement of ground artillery's survival capability, rapid response capability and maneuvering capability.
To achieve this goal, lots of work has been done in the past. Theodolite, Inertial Navigation System (INS), odometer, land markers correct, zero-velocity correct, Global Navigation Satellite System (GNSS) are the most commonly used methods and equipment [3][4][5][6]. Some multiple integrated approaches such as INS/GNSS integration, INS and odometer integration (INS/DR) are also studied and applied [7][8][9].
Theodolite can provide high performance orientation information by itself [3], but its operation is usually laborious and needs relatively long time, thus it is not beneficial for battlefield survival. INS is autonomous, which does not need external measuring information and has strong anti-interference ability [10]. However, INS's positioning and orientation errors increase with time [11]. If INS has been working for a relatively long time, its reference information is hard to satisfy accurate launching requirements. GNSS can achieve high positioning results, and its navigation errors do not divergent with time, but during wartime, it has the risk of being interfered and cannot provide high precision orientation and attitude reference [12]. Integration of INS and GNSS can combine both systems' advantages [13,14]. However, it would lose some autonomy since GNSS is involved in real-time.
Odometer is used to measure speed and distance of the vehicle moving on the ground. It cannot be used independently for positioning but can be used with INS for Dead Reckoning (DR) [15]. INS/DR integration approach is widely used in land weapon launching applications since it can provide relatively high precision reference information as well as keep autonomy [16]. However, for most approaches mentioned above, if precise orientation and attitudes are needed, high performance INS is necessary, which is always expensive and needs much preparation time.
Based on this background, the paper proposed a new solution. The approach only needs land vehicle based INS or INS/DR to provide rough position and orientation as iterative initial value, thus it does not have high performance requirements even in high precision applications. The new solution uses a vehicle based BODP to aim at and lock no less than three pre-set cooperative targets. Since the cooperative targets are set beforehand, their accurate coordinates can be measured by differential GNSS (DGNSS). After acquiring measurements from BODP, the vehicle's accurate position and orientation can be calculated. The proposed approach does not depend on GNSS and is autonomous. This paper described the basic principle of the system. Section 2 describes the system working procedure, and presents theoretical deviation of the algorithm. Simulations results under different conditions are given in Section 3. Vehicle experiments are carried out and experiment results are presented and analyzed in Section 4, and conclusions are drawn in Section 5.

System Working Procedure
The vehicle positioning and orientation system contains several subsystems, including INS/DR integration system, a vehicle based BODP, and several cooperative targets arranged around the launching areas. The vehicle starts from home and stops at any point and to any direction in the selected launching areas. The system uses the targets' coordinates and vehicle's coordinates provided by INS/DR to calculate targets' rough azimuth and pitch angle relative to vehicle. Then, it rotates BODP to search and lock the targets, and output the targets' precise azimuth and pitch angles relative to vehicle. After acquiring no less than three couples of azimuth and pitch angles, the system could calculate vehicle's accurate horizontal position and orientation, and then, the vehicle's accurate height and attitudes. The following section would give detailed positioning, orientation and attitudes determination algorithms that proposed.

Orientation and Horizontal Position Determination Algorithm
Establish a rectangular coordinate system shown in Figure 1A  From geometric relations shown in Figure 1, we can get the following equation: x y x y as follows: tmi tmi tmi tmi tri tmi tri tri tri x y x y x y x y x y x y r r tri tri tmi tmi x y x y x y x y tri tri x y x y x y x y where tmi tmi x y x y , i = 1, 2, 3, and Since coordinates of the cooperative targets A, B and C are acquired by precise measurement, compared to 0 δx and 0 δy , δ tmi x and δ tmi y can be ignored. Then, Equation (2) can be simplified as follows: If three cooperative targets are measured, the corresponding equations can be written as following: Then, the initial horizontal position and orientation errors can be calculated by the following Equation: 1 ( ) After calculating , use it to update and correct INS/DR positioning result (x0,y0) and orientation error δψ , recalculate each target's true azimuth ψ tmi relative to vehicle, and then use the corrected positioning and orientation results to do the same procedure, until each iteration correction is within the expected accuracy. By finishing the iteration, the horizontal position and orientation of the vehicle is accurately determined.

Attitudes and Height Determination Algorithm
In the proposed approach, the vehicle's accurate attitudes and height determination algorithm is on the basis of orientation and horizontal position determination results. After acquiring the accurate horizontal position and orientation results in the previous section, their errors are assumed to be negligible when determining the vehicle's attitudes and height.
The relationship of vehicle and targets' position and angles measurements are shown in Figure 2: From the Euler angles rotation relationship and Figure 2, the following equation can be derived: ( , ) sin sin γ sin ψ cos γ sin θ cos ψ ri r r r In land vehicle missile-launching applications, usually relatively firm and flat areas are selected as launching point, and the attitudes of the vehicle are usually small angles. If attitudes errors provided by INS/DR are θ Δ and γ Δ , that is, θ θ θ, γ γ γ r r = +Δ = + Δ , then Equation (7) can be simplified as: The BODP measured ( , )ri θ γ φ is denoted by ( , )mi θ γ φ , which is given by: θ cos ψ γsin ψ From Equations (8)- (10), it can be seen that: , where the pitch angle ri φ is measured by BODP, then the following equation can be derived: tan tan tan( ) tan( ) 1 tan tan Since tan θ cos ψ γsin ψ , thus the following equation can be derived: If three cooperative targets are measured, the corresponding equations can be written as following: where, 2  2  2  2  2  2  2   3  0  3  0  3  3  3  3  3  3  3   1  1  tan  cos  1  tan  sin   1  1  tan  cos  1  tan  sin   1  1 tan Then, the initial height and attitudes errors can be calculated by the following equation: After calculating V E Δ , use it to update and correct INS/DR height and attitudes errors. And then use the corrected results to do the same procedure, until each iteration correction V E Δ is within the expected accuracy. By finishing the iteration, the vehicle's height and attitudes can be accurately determined.

Orientation and Horizontal Position Determination Simulation
Consider the orientation and horizontal position determination algorithm simulation first. Establish the measurement rectangular coordinate system as shown in      Figure 6 indicates that azimuth error of the vehicle is within ±40″, and the standard deviation is 11.1″. assumed to be zero. However, the horizontal position and orientation errors are inevitable. Consequently, in vehicle's attitudes and height determination simulations here, we add horizontal position errors of 0.3 m (1σ) and orientation error of 20″ (1σ), which is the same accuracy as previous simulation results. Apply the proposed attitudes and height determination algorithm under the above conditions and simulate 100 times. The simulation results are shown in Figures 7-9.

Attitudes and Height Determination Simulation
It can be seen from Figures 7 and 8 that the vehicle's attitudes determination errors are within ±30″ (Standard deviation of pitch and roll errors are 7.9″ and 8.8″ respectively). The Figure 9 indicates that vehicle's height determination error is within ±0.3 m, and the standard deviation is 0.1 m.

Vehicle Experiments and Analysis
The proposed positioning and orientation system mainly consist of vehicle based equipment and cooperative targets. The vehicle-based equipment includes INS/DR integration system, a DGNSS receiver and a BODP. The experimental vehicle and relative equipment are shown in Figure 10.  The experimental vehicle is driven to the parking point from the starting point several kilometers away. Then, use the vehicle based DGNSS receiver to measure the vehicle's precise position as reference. The DGNSS position measuring results of the targets and the vehicle parking point are given in Table 1. After the BODP aims at and lock the targets, it would output azimuth and pitch angles relative to vehicle. Apply the proposed positioning and orientation approach to the equipment measurements, and then give the calculation results. In the experiment, the targets no. 2, 5, 7 were selected and the same experiment procedure was done seven times. Every time a new set of measuring parameters were acquired. Then, apply the proposed approach to seven sets of measurements and the results are given in Table 2. It can be seen from Table 2 that in the seven experiments, the standard deviation of horizontal positioning and height errors are about 0.1 m and 0.3 m, and attitudes (pitch and roll) and orientation errors are about 8″ and 20″ respectively. The statistical results indicate that the proposed approach displays good repeatability. To further verify the effectiveness of the proposed approach, five different sets of targets were selected to form different groups of measurements. The five groups of targets combinations are targets no. 2,5,7 combination, targets no. 1,4,6 combination, targets no. 3,4,7 combination, targets no. 1,3,5 combination, and targets no. 2,4,6 combination respectively. The proposed approach was applied to the five combinations of targets, and the calculation results are given in Table 3. In Table 3, the vehicle's position provided by DGNSS is listed as reference. It can be seen that compared to the reference, the approach can achieve positioning accuracy of about 0.3 m maximum offset by using different sets of targets. Since there isn't any other high performance azimuth and attitude measuring equipment in the vehicle during the experiments, the true azimuth and attitude reference are not acquired. In this circumstance, the mean attitude determination results are used as reference and only repeatability when using different groups of targets are evaluated. In addition, the results show that the azimuth maximum offset relative to mean value is 38.5″, and the maximum pitch and roll angles offset are 19.8″ and 15.5″, respectively.
In the verification experiments mentioned above, only three targets are selected for calculation. It takes about 40 s average to aim at and lock one target. If three cooperative targets are used and locked, the total time needed is about 2 min, but if more than three targets are used, it would take more time. In fact, if more preparing time is allowed, the system could aim at and lock more targets, and this approach could achieve better results.
Compared with other methods listed in the introduction, the vehicle experiments' results proved that the proposed approach in this paper has many advantages. By using theodolite, it can acquire quite high orientation information (20″), but the operation of theodolite requires long duration (usually more than 20 min), and theodolite cannot provide position information either; however, the proposed approach in this paper is easy to operate and can obtain the same orientation accuracy as theodolite within 3 min as well as high accuracy positioning information.
The positioning accuracy of medium-accuracy of INS/DR is about several hundred meters while the orientation accuracy is about 3′. Compared to the INS/DR integration, the proposed approach improves the positioning and orientation accuracy significantly, with positioning error of less than 1 m and orientation error of about 20″. If the same positioning and orientation accuracy were to be acquired by INS/DR, the drifts of gyros employed in INS must be less than 0.001°/h, which will greatly increase the cost. However, the proposed approach only needs a rough position and orientation as an algorithm's iterative initial value by INS/DR, so the cost can be reduced substantially.
The positioning accuracy of GNSS can be less than 1 m, but the GNSS signals are easy to interfere with and are requested not to be used during wartime. In addition, in order to achieve 20″ orientation information by GNSS, multiple GNSS antennas and long base line (several decameters) are needed; it is not easy to operate in practical situation. Therefore, the proposed approach has obvious advantages in positioning and orientation accuracy, rapidity, autonomy and cost; consequently, the approach has considerable potential in rapid and accurate positioning and orientation applications for land missile-launching vehicles.

Conclusions
The paper presented a new approach to get the land vehicle's accurate position, azimuth and attitude rapidly. It uses a BODP to aim at and lock no less than three pre-set cooperative targets, whose accurate position coordinates are measured beforehand. The vehicle's accurate position and orientation through the rough position and orientation provided by vehicle based INS/DR and at least three couples of azimuth and pitch angles measured by BODP while aiming at and locking cooperative targets are then calculated. It does not have high performance requirements for vehicle-based INS. Meanwhile, it does not depend on GNSS when determining vehicle's position, attitudes and azimuth; thus, it is autonomous and difficult to interfere. The approach's effectiveness is verified and evaluated by both simulation and vehicle experiments. The results indicate that it can achieve positioning and orientation accuracy of 0.2 m and 20″ respectively in 3 min; thus, it has high potential engineering values. Still, it has lots of work to do, including the influence of targets and vehicle distribution analysis, influence of vehicle based INS/DR error on the results analysis, et al. These are the next projects for our team to accomplish in the near future.