A multi-resolution image alignment technique based on direct methods for pose estimation of aerial vehicles

In this paper, we seek to expand the use of direct methods in real-time applications by proposing a vision-based strategy for pose estimation of aerial vehicles. The vast majority of approaches make use of features to estimate motion. Conversely, the strategy we propose is based on a MR (Multi- Resolution) implementation of an image registration technique (Inverse Compositional Image Alignment ICIA) using direct methods. An on-board camera in a downwards-looking configuration, and the assumption of planar scenes, are the bases of the algorithm. The motion between frames (rotation and translation) is recovered by decomposing the frame-to-frame homography obtained by the ICIA algorithm applied to a patch that covers around the 80% of the image. When the visual estimation is required (e.g. GPS drop-out), this motion is integrated with the previous known estimation of the vehicles’ state, obtained from the on-board sensors (GPS/IMU), and the subsequent estimations are based only on the vision-based motion estimations. The proposed strategy is tested with real flight data in representative stages of a flight: cruise, landing, and take-off, being two of those stages considered critical: take-off and landing. The performance of the pose estimation strategy is analyzed by comparing it with the GPS/IMU estimations. Results show correlation between the visual estimation obtained with the MR-ICIA and the GPS/IMU data, that demonstrate that the visual estimation can be used to provide a good approximation of the vehicle’s state when it is required (e.g. GPS drop-outs). In terms of performance, the proposed strategy is able to maintain an estimation of the vehicle’s state for more than one minute, at real-time frame rates based, only on visual information.

Vision based control for fixed wing UAVs inspecting locally linear infrastructure using skid-to-turn maneuvers

The following paper proposes a novel application of Skid-to-Turn maneuvers for fixed wing Unmanned Aerial Vehicles (UAVs) inspecting locally linear infrastructure. Fixed wing UAVs, following the design of manned aircraft, traditionally employ Bank-to-Turn maneuvers to change heading and thus direction of travel. Commonly overlooked is the effect these maneuvers have on downward facing body fixed sensors, which as a result of bank, point away from the feature during turns. By adopting Skid-to-Turn maneuvers, the aircraft is able change heading whilst maintaining wings level flight, thus allowing body fixed sensors to maintain a downward facing orientation. Eliminating roll also helps to improve data quality, as sensors are no longer subjected to the swinging motion induced as they pivot about an axis perpendicular to their line of sight. Traditional tracking controllers that apply an indirect approach of capturing ground based data by flying directly overhead can also see the feature off center due to steady state pitch and roll required to stay on course. An Image Based Visual Servo controller is developed to address this issue, allowing features to be directly tracked within the image plane. Performance of the proposed controller is tested against that of a Bank-to-Turn tracking controller driven by GPS derived cross track error in a simulation environment developed to simulate the field of view of a body fixed camera.

Using cooperative vehicle systems to collect near collision incidents events : a simulation study

On the road, near collision events (also close calls or near-miss incidents) largely outnumber actual crashes, yet most of them can never be recorded by current traffic data collection technologies or crashes analysis tools. The analysis of near collisions data is an important step in the process of reducing the crash rate. There have been several studies that have investigated near collisions; to our knowledge, this is the first study that uses the functionalities provided by cooperative vehicles to collect near misses information. We use the VISSIM traffic simulator and a custom C++ engine to simulate cooperative vehicles and their ability to detect near collision events. Our results showed that, within a simple simulated environment, adequate information on near collision events can be collected using the functionalities of cooperative perception systems. The relationship between the ratio of detected events and the ratio of equipped vehicle was shown to closely follow a squared law, and the largest source of nondetection was packet loss instead of packet delays and GPS imprecision.

Adherence, adaptation and acceptance of elderly chronic heart failure patients to receiving healthcare via telephone-monitoring

Background: Although the potential to reduce hospitalisation and mortality in chronic heart failure (CHF) is well reported, the feasibility of receiving healthcare by structured telephone support or telemonitoring is not. Aims: To determine; adherence, adaptation and acceptability to a national nurse-coordinated telephone-monitoring CHF management strategy. The Chronic Heart Failure Assistance by Telephone Study (CHAT). Methods: Triangulation of descriptive statistics, feedback surveys and qualitative analysis of clinical notes. Cohort comprised of standard care plus intervention (SC + I) participants who completed the first year of the study. Results: 30 GPs (70% rural) randomised to SC + I recruited 79 eligible participants, of whom 60 (76%) completed the full 12 month follow-up period. During this time 3619 calls were made into the CHAT system (mean 45.81 SD ± 79.26, range 0-369), Overall there was an adherence to the study protocol of 65.8% (95% CI 0.54-0.75; p = 0.001) however, of the 60 participants who completed the 12 month follow-up period the adherence was significantly higher at 92.3% (95% CI 0.82-0.97, p ≤ 0.001). Only 3% of this elderly group (mean age 74.7 ±9.3 years) were unable to learn or competently use the technology. Participants rated CHAT with a total acceptability rate of 76.45%. Conclusion: This study shows that elderly CHF patients can adapt quickly, find telephone-monitoring an acceptable part of their healthcare routine, and are able to maintain good adherence for a least 12 months. © 2007.

Experimental studies of wireless communication and GNSS kinematic positioning performance in high-mobility vehicle environments

In order to support intelligent transportation system (ITS) road safety applications such as collision avoidance, lane departure warnings and lane keeping, Global Navigation Satellite Systems (GNSS) based vehicle positioning system has to provide lane-level (0.5 to 1 m) or even in-lane-level (0.1 to 0.3 m) accurate and reliable positioning information to vehicle users. However, current vehicle navigation systems equipped with a single frequency GPS receiver can only provide road-level accuracy at 5-10 meters. The positioning accuracy can be improved to sub-meter or higher with the augmented GNSS techniques such as Real Time Kinematic (RTK) and Precise Point Positioning (PPP) which have been traditionally used in land surveying and or in slowly moving environment. In these techniques, GNSS corrections data generated from a local or regional or global network of GNSS ground stations are broadcast to the users via various communication data links, mostly 3G cellular networks and communication satellites. This research aimed to investigate the precise positioning system performances when operating in the high mobility environments. This involves evaluation of the performances of both RTK and PPP techniques using: i) the state-of-art dual frequency GPS receiver; and ii) low-cost single frequency GNSS receiver. Additionally, this research evaluates the effectiveness of several operational strategies in reducing the load on data communication networks due to correction data transmission, which may be problematic for the future wide-area ITS services deployment. These strategies include the use of different data transmission protocols, different correction data format standards, and correction data transmission at the less-frequent interval. A series of field experiments were designed and conducted for each research task. Firstly, the performances of RTK and PPP techniques were evaluated in both static and kinematic (highway with speed exceed 80km) experiments. RTK solutions achieved the RMS precision of 0.09 to 0.2 meter accuracy in static and 0.2 to 0.3 meter in kinematic tests, while PPP reported 0.5 to 1.5 meters in static and 1 to 1.8 meter in kinematic tests by using the RTKlib software. These RMS precision values could be further improved if the better RTK and PPP algorithms are adopted. The tests results also showed that RTK may be more suitable in the lane-level accuracy vehicle positioning. The professional grade (dual frequency) and mass-market grade (single frequency) GNSS receivers were tested for their performance using RTK in static and kinematic modes. The analysis has shown that mass-market grade receivers provide the good solution continuity, although the overall positioning accuracy is worse than the professional grade receivers. In an attempt to reduce the load on data communication network, we firstly evaluate the use of different correction data format standards, namely RTCM version 2.x and RTCM version 3.0 format. A 24 hours transmission test was conducted to compare the network throughput. The results have shown that 66% of network throughput reduction can be achieved by using the newer RTCM version 3.0, comparing to the older RTCM version 2.x format. Secondly, experiments were conducted to examine the use of two data transmission protocols, TCP and UDP, for correction data transmission through the Telstra 3G cellular network. The performance of each transmission method was analysed in terms of packet transmission latency, packet dropout, packet throughput, packet retransmission rate etc. The overall network throughput and latency of UDP data transmission are 76.5% and 83.6% of TCP data transmission, while the overall accuracy of positioning solutions remains in the same level. Additionally, due to the nature of UDP transmission, it is also found that 0.17% of UDP packets were lost during the kinematic tests, but this loss doesn't lead to significant reduction of the quality of positioning results. The experimental results from the static and the kinematic field tests have also shown that the mobile network communication may be blocked for a couple of seconds, but the positioning solutions can be kept at the required accuracy level by setting of the Age of Differential. Finally, we investigate the effects of using less-frequent correction data (transmitted at 1, 5, 10, 15, 20, 30 and 60 seconds interval) on the precise positioning system. As the time interval increasing, the percentage of ambiguity fixed solutions gradually decreases, while the positioning error increases from 0.1 to 0.5 meter. The results showed the position accuracy could still be kept at the in-lane-level (0.1 to 0.3 m) when using up to 20 seconds interval correction data transmission.

Evolutionary placement of continuously operating reference stations of network Real-Time Kinematic

Network RTK (Real-Time Kinematic) is a technology that is based on GPS (Global Positioning System) or more generally on GNSS (Global Navigation Satellite System) observations to achieve centimeter-level accuracy positioning in real time. It is enabled by a network of Continuously Operating Reference Stations (CORS). CORS placement is an important problem in the design of network RTK as it directly affects not only the installation and running costs of the network RTK, but also the Quality of Service (QoS) provided by the network RTK. In our preliminary research on the CORS placement, we proposed a polynomial heuristic algorithm for a so-called location-based CORS placement problem. From a computational point of view, the location-based CORS placement is a largescale combinatorial optimization problem. Thus, although the heuristic algorithm is efficient in computation time it may not be able to find an optimal or near optimal solution. Aiming at improving the quality of solutions, this paper proposes a repairing genetic algorithm (RGA) for the location-based CORS placement problem. The RGA has been implemented and compared to the heuristic algorithm by experiments. Experimental results have shown that the RGA produces better quality of solutions than the heuristic algorithm.

Learning in and beyond small business advisory programmes

The purpose of this paper is to analyse how participants learn in small business advisory programmes and to explore the impact of these learning programmes on the development of reflective learning dispositions in participants. The research involves two case studies of small business advisory programmes in Queensland, a state of Australia. One involves training in the use of GPS/GIS technology amongst rural SMEs and the other seeks to develop improved management and operational capabilities in regional and metropolitan manufacturing SMEs. Face to face semi-structured interviews were conducted throughout rural, regional and metropolitan Queensland with participants, trainers and senior executives in the administering organisations that ran the programmes. Learning in these programmes occurs through a combination of interaction with others and the adoption of practice-based and learner-centred processes. The impact of the programmes on participants includes the development of reflective learning dispositions, improved confidence in learning and appreciation of the value of new knowledge to their business. The research suggests that small business training programmes have the potential to affect the development of critical reflective learning dispositions in participants which is of fundamental importance to the development of a learning or knowledge economy.

Integrated vision-based attitude estimation

For many years, computer vision has lured researchers with promises of a low-cost, passive, lightweight and information-rich sensor suitable for navigation purposes. The prime difficulty in vision-based navigation is that the navigation solution will continually drift with time unless external information is available, whether it be cues from the appearance of the scene, a map of features (whether built online or known a priori), or from an externally-referenced sensor. It is not merely position that is of interest in the navigation problem. Attitude (i.e. the angular orientation of a body with respect to a reference frame) is integral to a visionbased navigation solution and is often of interest in its own right (e.g. flight control). This thesis examines vision-based attitude estimation in an aerospace environment, and two methods are proposed for constraining drift in the attitude solution; one through a novel integration of optical flow and the detection of the sky horizon, and the other through a loosely-coupled integration of Visual Odometry and GPS position measurements. In the first method, roll angle, pitch angle and the three aircraft body rates are recovered though a novel method of tracking the horizon over time and integrating the horizonderived attitude information with optical flow. An image processing front-end is used to select several candidate lines in a image that may or may not correspond to the true horizon, and the optical flow is calculated for each candidate line. Using an Extended Kalman Filter (EKF), the previously estimated aircraft state is propagated using a motion model and a candidate horizon line is associated using a statistical test based on the optical flow measurements and location of the horizon in the image. Once associated, the selected horizon line, along with the associated optical flow, is used as a measurement to the EKF. To evaluate the accuracy of the algorithm, two flights were conducted, one using a highly dynamic Uninhabited Airborne Vehicle (UAV) in clear flight conditions and the other in a human-piloted Cessna 172 in conditions where the horizon was partially obscured by terrain, haze and smoke. The UAV flight resulted in pitch and roll error standard deviations of 0.42° and 0.71° respectively when compared with a truth attitude source. The Cessna 172 flight resulted in pitch and roll error standard deviations of 1.79° and 1.75° respectively. In the second method for estimating attitude, a novel integrated GPS/Visual Odometry (GPS/VO) navigation filter is proposed, using a structure similar to a classic looselycoupled GPS/INS error-state navigation filter. Under such an arrangement, the error dynamics of the system are derived and a Kalman Filter is developed for estimating the errors in position and attitude. Through similar analysis to the GPS/INS problem, it is shown that the proposed filter is capable of recovering the complete attitude (i.e. pitch, roll and yaw) of the platform when subjected to acceleration not parallel to velocity for both the monocular and stereo variants of the filter. Furthermore, it is shown that under general straight line motion (e.g. constant velocity), only the component of attitude in the direction of motion is unobservable. Numerical simulations are performed to demonstrate the observability properties of the GPS/VO filter in both the monocular and stereo camera configurations. Furthermore, the proposed filter is tested on imagery collected using a Cessna 172 to demonstrate the observability properties on real-world data. The proposed GPS/VO filter does not require additional restrictions or assumptions such as platform-specific dynamics, map-matching, feature-tracking, visual loop-closing, gravity vector or additional sensors such as an IMU or magnetic compass. Since no platformspecific dynamics are required, the proposed filter is not limited to the aerospace domain and has the potential to be deployed in other platforms such as ground robots or mobile phones.

The neglected dimension of community liveability : impact on social connectedness and active ageing in higher density accommodation

Purpose This thesis is about liveability, place and ageing in the high density urban landscape of Brisbane, Australia. As with other major developed cities around the globe, Brisbane has adopted policies to increase urban residential densities to meet the main liveability and sustainability aim of decreasing car dependence and therefore pollution, as well as to minimise the loss of greenfield areas and habitats to developers. This objective hinges on urban neighbourhoods/communities being liveable places, which residents do not have to leave for everyday living. Community/neighbourhood liveability is an essential ingredient in healthy ageing in place and has a substantial impact upon the safety, independence and well-being of older adults. It is generally accepted that ageing in place is optimal for both older people and the state. The optimality of ageing in place generally assumes that there is a particular quality to environments or standard of liveability in which people successfully age in place. The aim of this thesis was to examine if there are particular environmental qualities or aspects of liveability that test optimality and to better understand the key liveability factors that contribute to successful ageing in place. Method A strength of this thesis is that it draws on two separate studies to address the research question of what makes high density liveable for older people. In Chapter 3, the two methods are identified and differentiated as Method 1 (used in Paper 1) and Method 2 (used in Papers 2, 3, 4 and 5). Method 1 involved qualitative interviews with 24 inner city high density Brisbane residents. The major strength of this thesis is the innovative methodology outlined in the thesis as Method 2. Method 2 involved a case study approach employing qualitative and quantitative methods. Qualitative data was collected using semi-structured, in-depth interviews and time-use diaries completed by participants during the week of tracking. The quantitative data was gathered using Global Positioning Systems for tracking and Geographical Information Systems for mapping and analysis of participants’ activities. The combination of quantitative and qualitative analysis captured both participants’ subjective perceptions of their neighbourhoods and their patterns of movement. This enhanced understanding of how neighbourhoods and communities function and of the various liveability dimensions that contribute to active ageing and ageing in place for older people living in high density environments. Both studies’ participants were inner-city high density residents of Brisbane. The study based on Method 1 drew on a wider age demographic than the study based on Method 2. Findings The five papers presented in this thesis by publication indicate a complex inter-relationship of the factors that make a place liveable. The first three papers identify what is comparable and different between the physical and social factors of high density communities/neighbourhoods. The last two papers explore relationships between social engagement and broader community variables such as infrastructure and the physical built environments that are risk or protective factors relevant to community liveability, active ageing and ageing in place in high density. The research highlights the importance of creating and/or maintaining a barrier-free environment and liveable community for ageing adults. Together, the papers promote liveability, social engagement and active ageing in high density neighbourhoods by identifying factors that constitute liveability and strategies that foster active ageing and ageing in place, social connections and well-being. Recommendations There is a strong need to offer more support for active ageing and ageing in place. While the data analyses of this research provide insight into the lived experience of high density residents, further research is warranted. Further qualitative and quantitative research is needed to explore in more depth, the urban experience and opinions of older people living in urban environments. In particular, more empirical research and theory-building is needed in order to expand understanding of the particular environmental qualities that enable successful ageing in place in our cities and to guide efforts aimed at meeting this objective. The results suggest that encouraging the presence of more inner city retail outlets, particularly services that are utilised frequently in people’s daily lives such as supermarkets, medical services and pharmacies, would potentially help ensure residents fully engage in their local community. The connectivity of streets, footpaths and their role in facilitating the reaching of destinations are well understood as an important dimension of liveability. To encourage uptake of sustainable transport, the built environment must provide easy, accessible connections between buildings, walkways, cycle paths and public transport nodes. Wider streets, given that they take more time to cross than narrow streets, tend to .compromise safety - especially for older people. Similarly, the width of footpaths, the level of buffering, the presence of trees, lighting, seating and design of and distance between pedestrian crossings significantly affects the pedestrian experience for older people and impacts upon their choice of transportation. High density neighbourhoods also require greater levels of street fixtures and furniture for everyday life to make places more useable and comfortable for regular use. The importance of making the public realm useful and habitable for older people cannot be over-emphasised. Originality/value While older people are attracted to high density settings, there has been little empirical evidence linking liveability satisfaction with older people’s use of urban neighbourhoods. The current study examined the relationships between community/neighbourhood liveability, place and ageing to better understand the implications for those adults who age in place. The five papers presented in this thesis add to the understanding of what high density liveable age-friendly communities/ neighbourhoods are and what makes them so for older Australians. Neighbourhood liveability for older people is about being able to age in place and remain active. Issues of ageing in Australia and other areas of the developed world will become more critical in the coming decades. Creating livable communities for all ages calls for partnerships across all levels of government agencies and among different sectors within communities. The increasing percentage of older people in the community will have increasing political influence and it will be a foolish government who ignores the needs of an older society.

The use of amenities in high density neighbourhoods by older urban Australians residents

Like other major cities, Brisbane (Australia) has adopted policies to increase residential densities to meet the liveability goal of decreasing car dependence. This objective hinges on urban neighbourhoods being amenity-rich spaces, reducing the need for residents to leave their neighbourhood for everyday living. While older people are attracted to urban settings, there has been little empirical evidence linking liveability satisfaction with older people's use of urban neighbourhoods. Using a case study approach employing qualitative (diaries, in-depth interviews) and quantitative (Global Positioning Systems and Geographical Information Systems mapping) methods,this paper explores the effect of the neighbourhood environment and its influence on liveability for older urban people. Reliance on motor vehicles and issues with availability and access to local amenities inhibit local participation for older people. Highlighting these issues furthers our understanding of the landscape planning and design factors that make urban neighbourhoods more liveable for older residents.

Experiences of neighbourhood walkability among older Australians living in high density inner-city areas

Walking as an out-of-home mobility activity is recognised for its contribution to healthy and active ageing. The environment can have a powerful effect on the amount of walking activity undertaken by older people, thereby influencing their capacity to maintain their wellbeing and independence. This paper reports the findings from research examining the experiences of neighbourhood walking for 12 older people from six different inner-city high density suburbs, through analysis of data derived from travel diaries, individual time/space activity maps (created via GPS tracking over a seven-day period and GIS technology), and in-depth interviews. Reliance on motor vehicles, the competing interests of pedestrians and cyclists on shared pathways and problems associated with transit systems, public transport, and pedestrian infrastructure emerged as key barriers to older people venturing out of home on foot. GPS and GIS technology provide new opportunities for furthering understanding of the out-of-home mobility of older populations.

Individual dose and exposure of Italian children to ultrafine particles

Time-activity patterns and the airborne pollutant concentrations encountered by children each day are an important determinant of individual exposure to airborne particles. This is demonstrated in this work by using hand-held devices to measure the real-time individual exposure of more than 100 children aged 8-11 years to particle number concentrations and average particle diameter, as well as alveolar and tracheobronchial deposited surface area concentration. A GPS-logger and activity diaries were also used to give explanation to the measurement results. Children were divided in three sample groups: two groups comprised of urban schools (school time from 8:30 am to 1:30 pm) with lunch and dinner at home, and the third group of a rural school with only dinner at home. The mean individual exposure to particle number concentration was found to differ between the three groups, ranging from 6.2×104 part. cm-3 for children attending one urban school to 1.6×104 part. cm-3 for the rural school. The corresponding daily alveolar deposited surface area dose varied from about 1.7×103 mm2 for urban schools to 6.0×102 mm2 for the rural school. For all of the children monitored, the lowest particle number concentrations are found during sleeping time and the highest were found during eating time. With regard to alveolar deposited surface area dose, a child's home was the major contributor (about 70%), with school contributing about 17% for urban schools and 27% for the rural school. An important contribution arises from the cooking/eating time spent at home, which accounted for approximately 20% of overall exposure, corresponding to more than 200 mm2. These activities represent the highest dose received per time unit, with very high values also encountered by children with a fireplace at home, as well as those that spend considerable time stuck in traffic jams.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to Real-Time Kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least-squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance-covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio-test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.