Improvements in or relating to pedestrian collision forensics

Abstract

A method for estimating forensic details of vehicle-pedestrian collisions comprises determining a set of parameters of the collision including the position where the pedestrian’s 10 head impacted the

Description

Technical Field of the Invention The present invention relates to pedestrian collision forensics. Particularly, but not exclusively, the invention relates to determining the forensic details of collisions involving pedestrians and vehicles using the known outcomes of collisions. Background to the Invention Collisions between pedestrians and vehicles are extremely common, with over 5,500 pedestrian fatalities or serious injuries occurring in road traffic accidents in 2021 alone. It is difficult, and often impossible, to establish the exact conditions in which the crash occurred after the fact, despite the importance of this for various purposes, such as determining liability for insurance claims, improving road safety and for use in any potential criminal investigations arising from such collisions. Whilst there are some methods used to ascertain details of a crash these often have significant drawbacks and are thus generally unreliable. Common non-empirical methods include taking eyewitness statements, which are prone to untrustworthiness and failing memories clouding the actual details of the crash. A more reliable (though still imperfect) method is to use video evidence, but in many road traffic collisions there is either no video evidence, or insufficient video evidence to properly determine the details of the crash. There are some more analytical techniques, such as the Searle technique, which take empirical data from the collision in order to determine the vehicles speed at time of the collision. However, this method (and the Appel method, a variant of the Searle technique) rely upon numerous mathematical assumptions, and therefore have a significant margin of error. Particularly, the Searle technique only evaluates the range of the impact speed based on the projection of the pedestrian from witness marks left on the road to the resting place of the pedestrian victim. This technique ignores the shape of the vehicle profile, the height, weight, gait, crossing direction, crossing speed, and struck leg of the pedestrian, thereby making it a coarse estimation of the vehicle collision speed, which is also amplified with increasing speed. A more reliable alternative to physical forensic analysis techniques has been a topic of intense research interest in recent years. Simulation-based software packages such as PC Crash rely heavily on the initial and final positions of the involved parties for an accurate reconstruction, which might not be possible in cases of hit-and-run or if the pedestrian hits another infrastructure. It is an objection of the present invention to overcome and / or ameliorate the above issues in known crash forensic techniques. Summary of the Invention According to a first aspect of the present invention, there is provided a method for estimating forensic details of vehicle-pedestrian collisions comprising: determining a set of parameters of the collision, the parameters including the position where the pedestrians head impacted the vehicle, inputting said parameters into a collision model, estimating forensic details of the collision using the collision model in a first spatial dimension using the position where the pedestrians head impacted the vehicle with respect to the first spatial dimension, estimating forensic details of the collision using the collision model in a second spatial dimension using the position where the pedestrians head impacted the vehicle with respect to the second spatial dimension, and averaging the results of the estimated forensic details from the first spatial dimension and the second spatial dimension to arrive at a final estimation of the forensic details of the collision. The use of such a method enables the speed of the vehicle to be estimated using only parameters available after the collision in a more accurate manner than conventional methods. This allows for better determination of liability and / or criminality in collision investigations, such as those performed by insurers and / or police. In addition, the use of independent estimations in respect of each of the at least two spatial dimensions of the head impact position provides improved accuracy whilst requiring less processing power than estimating using a single multi-output model. The position where the pedestrians head impacted the vehicle, may be defined with reference to a co-ordinate system. Typically, the co-ordinate system comprises three mutually perpendicular linear axes, the axes having an origin defined as a bottom, front side corner of a vehicle. In one particular example, the origin may be defined as the bottom front left corner of the vehicle (when looking at the vehicle from in front of the vehicle). Spatial dimensions may be defined about this origin. In one such embodiment, the spatial dimensions define an X-axis parallel to the longitudinal axis of the vehicle, a Y-axis parallel to a transverse axis of the vehicle and an upright Z-axis. The position where the pedestrians head impacted the vehicle (‘head impact coordinates’) may be defined in relation to the origin. In one embodiment, the first and second spatial dimensions for which forensic details are estimated may be the length (X-axis) and width (Y-axis) dimensions. In embodiments which use such a co-ordinate system, vehicle velocity may be in the -X direction. In such embodiments, pedestrian velocity may be in the +Y or -Y direction, depending upon the direction of the pedestrian. The vehicle may be any suitable road vehicle. In particular embodiments, the vehicle may be a car, lorry, van, scooter, electric scooter, bicycle, electric bicycle or the like. In a particular embodiment, the vehicle is a car or similarly configured vehicle, and the following parameters: vehicle height, vehicle length width, ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height and roof angle) are collectively defined as “the vehicle profile”. The parameters input into the collision model may comprise the vehicle profile. The parameters may include any combination from the following list: • Vehicle profile; • Pedestrian speed; • Pedestrian impact angle; • Pedestrian impact width; • Pedestrian height; • Pedestrian weight; and • Pedestrian gait. Where one or more of the above listed parameters are unavailable after the crash, the method of the present invention may be able to estimate one or more of the unknown parameters or each parameter at the time of the collision. In cases where more than one unknown parameter is estimated, the present invention offers further improved performance over single parameter estimations. In a particular embodiment, the method is able to estimate the vehicle speed and / or pedestrian speed at the time of the collision using the following parameters: • Vehicle profile; • Pedestrian height; and • Pedestrian weight. In this embodiment, the above listed parameters may be input into the collision model. The collision model may comprise at least one multibody model. The collision model may comprise a multibody model of the pedestrian (‘the pedestrian model’). The collision model may comprise a multibody model of the vehicle (‘the vehicle model’). Preferably, the collision model comprises both a pedestrian model and a vehicle model. The or each model may be generated in conventional dynamic modelling software. Alternatively, the collision model may comprise conventional computer aided engineering software instead of or in addition to the at least multibody model. The pedestrian model may comprise multiple ellipsoids connected to form a model of the pedestrian. The multibody model of the pedestrian may be altered by the pedestrian height and / or weight parameters, where these are known. The pedestrian model may be scaled so as to accurately reflect the pedestrian height and / or weight in line with existing Body Mass Index (BMI) data. In such embodiments, the BMI data may be taken from existing databases, such as the NHS BMI database. The pedestrian model may comprise information as to the gait of the pedestrian at the time of the collision. The gait information may include stance / posture classification taken from a discrete pedestrian gait stance model as known in the art. In a specific embodiment, the vehicle model may comprise a series of rectangular planes connected to model the vehicle in the collision. The vehicle model may comprise information on any of the following parameters: vehicle height, vehicle length width, ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height and roof angle, of the vehicle in the collision. In particular embodiments, the vehicle model may comprise information on select parameters from those collectively defined as the vehicle profile. In such embodiments, the vehicle model may comprise information on the ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height and roof angle, of the vehicle. The collision model may be configured to simulate a collision based upon the parameters input into the model. The collision model may be configured to simulate the collision using the input parameters and provide estimated forensic details of the collision based upon the simulation. The collision model may be based upon one or more machine learning algorithms trained using real-life collision data. The collision model may be based upon one or more machine learning algorithms trained using simulated collision data. In some embodiments, the collision model may be based upon one or more machine learning algorithms trained using both real-life and simulated collision data. The simulated data may be that obtained from the collision model. As above, the collision model may use multibody models or conventional computer aided engineering software. Alternatively, the model may be trained using purely real-life collision data. In embodiments where the collision model is based upon one or more machine learning algorithms trained using simulated collision data, the collision model may be validated using real-life collision data. The collision model may be configured to iteratively optimise the estimated forensic details. The collision model may use Bayesian optimisation to estimate the forensic details of the collision. The estimation model may be configured to iterate the estimate the forensic details until the error in said estimation is below a threshold level. The error threshold may be tied to the value of the estimated forensic detail. For example, the threshold error may be a percentage of the estimated forensic detail or a specific dimension / s. It will be understood by the skilled person that there are many suitable error thresholds which could be used. The position where the pedestrians head impacted the vehicle (referred to hereinafter as ‘head impact co-ordinates’) may be defined in relation to the vehicle. The head impact co-ordinates may be in the form of 3-dimensional Euclidean co-ordinates. In some embodiments, the head impact co-ordinates input into the collision model may only be input as 2-dimensional co-ordinates, for example x and y co-ordinates. The X value could be estimated also in Euclidean coordinates as well as a wraparound distance passing through the head strike position on the windscreen to the ground along the vehicle front profile in the +X direction. In such embodiment the collision model may be used to determine the third dimension using the vehicle model within the collision model. The averaging of the independently estimated forensic details may be performed using a dedicated model averaging algorithm. The estimated forensic details may comprise vehicle speed at the time of collision. The estimated forensic details may comprise the pedestrian speed at the time of collision. The estimated forensic details may comprise the pedestrian’s gait at the time of collision. In a particular embodiment, the method may be configured to estimate the vehicle and pedestrian speeds at the time of the collision, where the input parameters comprise the vehicle profile and head impact position. In another particular embodiment, the invention may include estimation of the severity of any injuries sustained by the pedestrian in the collision. In such embodiments, the injury estimation step may be based on an estimate of the vehicle velocity at the time of collision. It will be understood by the skilled person that the vehicle velocity at the time of collision will necessarily be the pedestrian impact velocity. It will also be understood by the skilled person that the vehicle velocity is composed of an orthogonal component and a tangential component. In particular embodiments, the injury estimation step may comprise mapping the orthogonal component of the estimated vehicle velocity at the time of collision against an injury risk curve. In some such embodiments, the injury estimation step may comprise mapping the orthogonal component of the estimated vehicle velocity at the time of collision against a dedicated injury risk curve for each body region which impacts the vehicle. Based on the mapping between the orthogonal component of the estimated vehicle velocity at the time of collision and the injury risk curve an injury risk estimation may be output. The injury risk estimation may comprise a numerical source or may comprise a potential injury classification (e.g. moderate, significant, severe, etc). Dedicated injury risk curves may be provided for each vehicle model or each type of vehicle, as desired or as appropriate. Injury risk curve data may be obtained from the collision model, another model or trained using purely real-life collision data. The or each body region may be selected from the following list: head, thorax, shoulder, arm, leg. In a particular embodiment, the invention may comprise additional data acquisition steps. The data acquisition steps may acquire data for use in the estimation of the forensic details of the collision. The information relating to the collision may be selected from any of the parameters in the following list: • Area of most significant damage to vehicle; • Area type of the collision; • Bonnet status; • Bumper status; • Driver age; • Driver avoidance action (i.e. action taken by the driver to avoid the collision); • Driver gender; • Driver intoxication; • Footway condition; • Humidity; • Impact condition; • Injury agent (i.e. what specifically injured the pedestrian); • Junction type; • Land use; • Lighting condition; • Pedestrian age; • Pedestrian avoidance action (i.e. action taken by the pedestrian to avoid the collision); • Pedestrian consciousness; • Pedestrian gender; • Pedestrian height (in cm); • Pedestrian impacted another vehicle (i.e. did this occur?); • Pedestrian inconspicuousness; • Pedestrian intoxication; • Pedestrian movement direction (at time of collision); • Pedestrian movement direction (post collision); • Pedestrian throw distance (post collision); • Pedestrian speed (at time of collision); • Pedestrian stance (at time of collision); • Pedestrian weight; • Point of initial impact; • Precipitation; • Rear windscreen status; • Road camber; • Road horizontal geometry; • Road surface condition; • Road surface defect; • Road surface friction; • Roof status; • Was the pedestrian runover on their: o Arms? o Head? o Legs? o Torso? • Road signage; • Speed limit; • Status of underside of vehicle; • Vehicle body type; • Vehicle location; • Vehicle manoeuvre; • Vehicle speed; • Vehicle weight; • Vehicle width; • Vehicle profile; • Vision obscured; • Wind speed; • Wind direction; and • Windscreen status. The data acquisition steps may comprise acquiring data from a look-up table. The data acquisition steps may comprise using image recognition techniques on one or more images taken at the scene of the collision to acquire data on the collisions. The image recognition techniques may be configured to determined one or more of the parameters in the above list. The image recognition techniques may comprise using machine learning (for example convolution neural networks) and / or artificial intelligence. The image recognition techniques may comprise the step of extracting the vehicle profile from the one or more images. The extraction of the vehicle profile may utilise known vehicle detection models such as YOLO, Faster R-CNN and SSD. The image recognition techniques may comprise vehicle profile classification. This classification may be configured to determine the broad classification of the vehicle (such as ‘car’, ‘truck’, ‘van’ etc.). Alternatively, the vehicle profile classification may be configured to determine the make and model of the vehicle. The ‘vehicle profile’ parameters discussed above can then be determined therefrom. In an alternative embodiment, the vehicle profile classification may comprise identifying the license plate of the vehicle and subsequently determining the ‘vehicle profile’ using a look up table or by referencing an external data source. The licence plate identification may be performed by models such as Tesseract OCR, a Convolution Recurrent Neural Network or the like. The image recognition techniques may comprise damage detection. The damage detection may comprise identifying damaged areas of the vehicle. The damage detection may comprise identifying the type of damage for any identified damage. The damage detection may comprise damage severity estimation. The damage detection may comprise damage localisation. The damage localisation may be configured to specify which aspect of the ‘vehicle profile’ is damaged (for example, bonnet, roof, bumper etc.). The data acquisition steps may comprise using one or more application programming interfaces (APIs) to retrieve data from one or more external sources. One example of such an external source is the collision-specific database into which one or more witnesses, the driver, the pedestrian and / or any people otherwise involved in the collision have inputted data to. The data acquisition steps may comprise any of the exemplary APIs set out in the below list (and any combination thereof): • A ‘weather data’ API configured to acquire the humidity, precipitation, wind speed and wind direction at the time of the collision; • A ‘road surface condition’ API configured to acquire the road surface condition at the time of the collision; • An ‘infrastructure’ API configured to acquire the area type, footway condition, land use, lighting condition, nearby infrastructure, road horizontal geometry, junction type, road camber, road signage, road surface defect / s and speed limit; • A ‘pedestrian biometrics’ API configured to acquire the pedestrian height and weight; • A ‘pedestrian visibility’ API configured to acquire the pedestrian inconspicuousness at the time of the collision; • A ‘road surface friction’ API configured to acquire the road surface friction; • A ‘vehicle profile’ API configured to acquire the vehicle weight, vehicle width and vehicle body type, in addition to the ‘vehicle profile’ parameters as defined above; • A ‘vehicle condition’ API configured to acquire the area of most significant damage, bonnet status, bumper status, roof status, rear windscreen status, status of underside of vehicle and point of initial impact. The ‘weather data’ API may be configured to acquire the relevant data from a suitable external data source, for example a website containing a record of weather conditions. The ‘weather data’ API may be configured in response to the input of the location (for example as expressed via latitude and longitude) and the time of the collision to rettieve the relevant data at the time of collision. The ’road surface condition’ API may be configured in response to the input of the latitude and longitude of the collision and the time of the collision to retrieve the relevant data at the time of collision. The ‘road surface condition’ API may comprise an intermediate API used to acquire air temperature, relative humidity, wind speed, precipitation, incoming long wave radiation and incoming short wave radiation data at the time of the collision. The data acquired in this intermediate API may then be used in a dedicated API configured to determine the road surface condition (i.e. dry, wet or damp) when input with the data acquired by the intermediate API. The ‘infrastructure’ API may be configured to acquire the relevant data from a suitable external data source, for example a mapping website containing up to date data on the road upon which the collision occurred at the point of collision. The ‘infrastructure’ API may be configured in response to the input of the location (for example as expressed via latitude and longitude) and the time of the collision to retrieve the relevant data at the time of collision. The ‘pedestrian biometrics’ API may be configured to acquire the relevant data from a suitable external data source, for example the collision specific database. In the event that the data is not available in the collision specific database, the ‘pedestrian biometrics’ API is configured to estimate the pedestrian's height and weight using the pedestrian's age. The ‘pedestrian biometrics’ API may be configured to refer to a statistical database collating the height, age weight and gender data for a population. For example, this may be the NHS adult BMI statistics, or a UN report on child growth statistics, dependent upon the age of the pedestrian involved in the crash. Where the pedestrian’s height is known (but not their weight) the ‘pedestrian biometrics’ API is configured to determine the weight that corresponds to the 50th percentile of the pedestrian's age and gender. In the inverse scenario, where the pedestrian’s weight is known and height is not, the ‘pedestrian biometrics’ API operates in the inverse manner. If neither the pedestrian height or weight are known, the ‘pedestrian biometrics’ API uses the average height and weight for the pedestrian's age and gender. The ‘pedestrian visibility’ API may be configured in response to the input of the time of the collision to data on whether or not it was light at the time of the collision, and then use this data to determine if the pedestrian was inconspicuous (or not) at the time of the collision. The ‘road surface friction’ API may be configured in response to the input of the road surface data either from the collision specific database or a retrieved from a suitable external data source, for example a mapping website containing up to date data on the road upon which the collision occurred at the point of collision. The ‘road surface friction’ API may then be configured to estimate the friction of the road surface via reference to a look-up table. The ‘vehicle profile’ API may be configured in response to the input of the vehicle make, model and year to retrieve the relevant data. The ‘vehicle profile’ API may be configured to retrieve the relevant data retrieved from a suitable external data source. The ‘vehicle condition' API may be configured to retrieve the relevant data either from the collision specific database or by performing image recognition upon a photograph / s of the vehicle post collision. The external sources may be external databases containing information relating to the collision. The external sources may include a collision-specific database. The collision specific database may comprise data relating to the collision which has been input thereto by one or more witnesses, the driver, the pedestrian and / or any people otherwise involved in the collision (for example any police officers investigating the collision, or doctors / nurses treating the driver / pedestrian) into. The data acquisition steps may only be used to acquire data not already available i.e. ‘missing data’. It will be understood that the method of the present invention may include any of the optional features presented herein, including any combinations thereof, as required or as desired. Detailed Description of the Invention In order that the invention may be more clearly understood one or more embodiments thereof will now be described, by way of example only, with reference to the accompanying drawings, of which: Figure 1 shows a diagram of a pedestrian gait classification of a multibody model of a pedestrian. Figure 2 shows a cross-section diagram of a multibody model of a vehicle. Figure 3 shows a diagram of the initial conditions of a simulated collision between multibody models of a pedestrian and vehicle. Figure 4 shows a simplified flow diagram of the process of training a collision model for use in the present invention. Figure 5 shows a box diagram of a method of estimating forensic details of vehicle-pedestrian collision. Figure 6a shows a graph plotting injury risk against impact velocity in respect of collisions where a pedestrian’s head is impacted by the vehicle. Figure 6b shows a graph plotting injury risk against impact velocity in respect of collisions generally. Referring to figure 1, there is schematically illustrated a multibody model of a pedestrian (“the pedestrian model” 10). The pedestrian model 10 comprises multiple connected ellipsoids arranged to form a model of a pedestrian. Each ellipsoid can be adapted in length and width, so as to accurately model pedestrians of varying heights and weights. In particular, the heights and weights are able to vary between 1.45-1.97m and weights of 39-119kg respectively, with four different BMI classifications (underweight, ideal, overweight and obese) used to ensure that the pedestrian model 10 scales correctly in line with the relevant height and weight of pedestrian. The ellipsoids are each connected such that impacts on one ellipsoid have corresponding effects on the neighbouring ellipsoids, which provides a more accurate simulation of collisions involving pedestrians. Figure 1 shows versions of the pedestrian model 10, which are each identical in form, but have different stances, as denoted by the stance classifications 0-9 below the relevant stance. Each classification 0-9 within figure 1 represents a different gait stance of the pedestrian model 10, in order to more accurately model the stance of the pedestrian at the point of collision. These gait stances are each represent a particular state within the typical walking motion of a pedestrian. Considering the gait of the pedestrian allows for more accurate results when compared to current methods, which do not consider the gait of the pedestrian. The use of a pedestrian model 10 formed of a multiplicity of connected ellipsoids allows for more sophisticated impacts to be modelled, particularly where there are no eye-witness accounts of the collision, which are relied upon by existing techniques. Figure 2 shows the parameters of the multibody model of the vehicle ("the vehicle model” 20) used in an embodiment of the present invention. In particular the vehicle can be modelled using the following parameters: vehicle width, vehicle height, vehicle length, ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height, roof angle. Figure 2 shows the following exemplary parameters of the model 20: bumper height 21, bumper angle 21a, bonnet leading edge height 22, bonnet leading edge angle 22a, bonnet height 23, bonnet angle 23a, windscreen height 24, windscreen angle 24a, roof height 25 and roof angle 25a. In this example, all angles are measured from the horizontal plane. The vehicle model may additionally include other parameters, not shown in figure 2 such as ride height, vehicle width, vehicle height and vehicle length. Setting appropriate values of these par ameters allows a simple geometric vehicle model to be generated for any vehicle. In many collisions, if the make and model of a vehicle is known, such parameters can be looked up to generate the vehicle model 20. This parameterisation of the vehicle allows of the specific vehicle profile of a vehicle involved in a collision to be modelled accurately, allowing for greater accuracy in the simulation of collisions, leading to more accurate estimates of the forensic details of collisions. The vehicle model 20 also defines a co-ordinate system. In this co-ordinate system, the origin is at the front bottom left corner of the vehicle, looking at the vehicle from the front. From the origin, the vehicle extends lengthwise along the +X-axis, widthwise along the +Y-axis, and height wise along the +Z-axis. Figure 3 shows a simplified collision model. To generate the collision model, the pedestrian and vehicle models 10, 20 are created and input into conventional mathematical dynamical modelling software. This collision model is then used to simulate multiple collisions (in this specific example, 3000 collisions were simulated in the training stage of the model building process). The simulated data from these collisions is then used to train an appropriate machine learning model for use in estimation of forensic details for collisions. For each simulation, the pedestrian model 10 was placed at a specific distance from the vehicle model 20. The vehicle velocity was in the negative -X direction, indicating that it was approaching the pedestrian model 10, while the pedestrian crossing speed was set in the direction the pedestrian 5 was facing (i.e. in the +Y or -Y direction accordingly), based on the side of the vehicle from which the pedestrian model 10 was crossing for the relevant simulation. Typically, the coefficients of friction between shoes and the ground and between a moving vehicle and a pedestrian were respectively 0.7 and 0.3. In order to sufficiently model collisions, a set of boundary conditions was 10 required for the collision model. An example of a set of suitable boundary conditions is illustrated in Table 1 below. Parameter Units Lower Bound Upper Bound Vehicle width mm 1833 0 1 Vehicle height mm 826 2697 Vehicle length mm 2944 3371 Ride height mm 130 383 Bumper height mm 381 677 Bumper angle degrees 55 90 BEL height mm 18 212 BEL angle degrees 41 85 Bonnet height mm 700 1200 Bonnet angle degrees 8 37 Windscreen height mm 703 859 Windscreen angle degrees 23 55 Roof height mm 1242 1518 Vehicle speed m / s 5.5 13.8 Pedestrian speed m / s 0 2.8 Pedestrian impact angle degrees -90 90 Pedestrian impact mm 0 Width of Car Pedestrian height mm 1450 1970 Pedestrian weight kg 39 119 Pedestrian gait - 0 9 Table 1: Boundary conditions for the collision model In order to develop a collision model capable of estimating the forensic details of collisions, a machine learning model (specifically Histogram-based Gradient 15 Boosting Regression) was used to build the collision model. The development of the model has three principal stages: model training, testing and validation. Considering the number of simulated collisions (3000), the dataset of the simulated collision data was randomly divided into training data (70%), test data (30%), with real collision data from Road Accident In-Depth Studies (RAIDS) used to validate the model. The training data was used to train the machine learning model, and the test data was used to evaluate the learning, and the hyperparameters of the trained machine learning model were appropriately tuned before performing validation. The random search method is used for hyperparameter optimisation, which permits evaluating the hyperparameter values with bigger impacts on model performance. The Coefficient of determination (R2) and the Root Mean Squared Error (RMSE) (both conventional statistical quantities) are used to assess the machine learning model predictive performance, as will be understood by the skilled person. To validate the machine learning model, the stratified k-fold cross-validation technique (a technique known in the art) is used. This method randomly divides the training dataset into k subsets, after which classes are characterised in roughly the same numbers as the full training data, and the incumbent model is applied to the remaining k-1 subsets. In this embodiment, the value of k used is 10. This technique reduces any bias introduced by the machine learning model. R2 is used to evaluate the model's performance. Once the collision model is validated using the RAIDS data, it is then trained to predict parameters of the collisions using Bayesian optimisation as discussed above. Whilst the collision model can, in principle, predict any forensics details when given the appropriate parameters, the head-impact co-ordinates, vehicle velocity and pedestrian velocity are the key forensic details which are estimated using the model. In the case of head impact co-ordinate prediction, with the vehicle profile known, only two of the three axes need be predicted, as the third can be calculated using simple trigonometry. The collision model uses Bayesian optimisation in order to estimate the forensic details of the collision. Bayesian optimisation is a systematic technique based on the Bayes theorem for directing an efficient and successful solution to a global optimisation problem. Bayesian optimisation is known in the art. Initially, boundary conditions for the Bayesian optimisation were set to minimum and maximum values, and a single-axis model trained on the X axis alone was used to estimate vehicle velocity, using data from the original training dataset (including the vehicle profile, pedestrian height and weight and vehicle profile). For the present invention, Bayesian optimisation is used to estimate the input parameters, resulting in estimated head impact coordinates. In this embodiment, a single-output model, designed to estimate a single target, i.e., single axis X, Y, or Z, was trained. In such models, the input parameters are used to generate the required output. It is also possible to use multi-output models for the estimation. Multi-input, multi-output models are designed to estimate multiple targets simultaneously, in this case to estimate multiple axes simultaneously. For example, in the case of single-output models, only one axis could be estimated at any given instance, but in the case of multi-output models, all three axes can be estimated in a single run. It is important to note that the difference between these models is only the number of target variables they can estimate at any given run and does not represent the complexity of the model itself. The same algorithm, linear regression, for instance, can be used in both single- and multi-output configurations. The average diameter of a human head is between 100-150 mm, and under impact conditions, impact at any location on the head will cause similar damage to the vehicle. Therefore, when using Bayesian optimisation, an error threshold of 100mm was selected for the model error. To estimate the inputs in a single-axis model, at least two models must be optimised, as least two head-impact co-ordinates are required. To concatenate the estimated inputs, the estimated inputs of each optimisation are combined via model averaging. Ensemble models (i.e., model averaging) demonstrate a method for dealing with uncertainty. It accepts that there may be several models that might be used to represent data and develop distinct learning errors, which can be leveraged to improve the overall prediction by averaging the outputs of potential models. Confidence in each model’s performance can be expressed by weighing the averages. Unlike other inputs which are continuous variables, a pedestrians’ gait is a categorical variable, and the estimate of the gait cannot be evaluated in the same way. Thus, accuracy and Fl scores were used as substitutes. The accuracy of forecasts is the ratio of the sum of true positives and true negatives out of all the predictions. The Fl score is the weighted average of precision and recall where precision is the fraction of correctly predicted positives to the total number of positives, while recall is the fraction of correctly predicted positives to all positive predictions. R2 and RMSE were used to evaluate the estimated input parameters in the same way that they were used to evaluate the model used for continuous variables. As the collision model is inherently simplified model (i.e., it does not account for the influence of the various parameters that are not modelled), an error tolerance of 10%, which translates to around 1.5 m / s or 5 km / h, is used. To estimate unknown input parameters, Bayesian optimisation requires an initial search boundary within which the optimisation is performed. Various boundary thresholds are possible. Initially, boundaries were established for minimum and maximum values; for example, these were 5.5 and 13.9 m / s for vehicle speed, which are the boundary conditions set for the design space. In the next iteration, this boundary was set to 2.5 m / s (10 km / h) and 1.4 m / s (5 km / h) for the next. A similar method was adopted for pedestrian speed, where the pedestrian was either at a standstill, walking, or running speed. All ten gait stances were explored in each iteration, as it is difficult to determine the gait only based on other evidence. Once the estimation model is developed as above, it was used to replicate five RAIDS vehicle-to-pedestrian crashes for which all the required (real-life) forensic details were known. After the estimation model has been fully validated, the estimation model is now suitably trained to estimate forensic details of a pedestrian vehicle collision based upon the input of known parameters. From the dataset used previously for training, head impact coordinates were added, and vehicle velocity was removed (to reflect the fact that the head-impact co-ordinates are known after a collision, and the vehicle velocity at the time of the collision is not). In this manner, the known parameters of the collision (i.e. vehicle width, vehicle height, ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height, pedestrian height, and pedestrian weight) are input into the collision model, and a single-axis model trained on the X axis alone is used to estimate vehicle velocity. This process is then performed in respect of the Y axis alone, which also gives an estimated vehicle velocity. Referring to the below Table 2, it can be seen that the error margin is around 3.3 for the first iteration, and using a single axis alone is not sufficient to estimate the input parameters. In this case the coordinates are considered independently, and so a wide variety of input parameters can result in the head of the pedestrian landing on the given axis. Thus, to address this problem, model averaging was employed to combine the predictions of these individual axes, which will result in a more realistic estimation of the inputs. At first, equal weights were assigned to both models, which resulted in an RMSE of 2.2 and an R2 of 0.166. Although this is an improvement over the individual models, it is not the best strategy to apply equal weights because each model's performance is not entirely the same. An algorithm (specifically Voting Regressor) was used to investigate various weight distributions; this ensemble model outperformed all others during each iteration, with an RMSE of 1.7, 0.9 and 0.7 and an R2 of 0.273. 0.734 and 0.863, respectively. Model X Model Y Ensemble Multi-Axis R2 RMSE R2 RMSE R2 RMSE R2 RMSE Iteration 1 0.007 3.3 0.271 2 0.273 1.7 0.248 2.1 Iteration 2 0.665 1.4 0.698 1.4 0.801 0.9 0.734 1.3 Iteration 3 0.863 0.9 0.844 0.9 0.885 0.7 0.863 0.9 Table 2: Vehicle velocity estimation evaluation To validate the collision models estimation capability, the five RAIDS cases used to validate the collision model generally were then used to validate the collision model’s ability to estimate the forensic details of collisions. To do this, each of the forensic details to be estimated (vehicle speed, pedestrian speed and gait) were removed from the input set, and the collision model was used to estimate the missing values. Table 3 below illustrates the performance of the collision model when estimating these forensic details for these 5 cases. The estimated inputs have an error of 1.2 m / s for vehicle speed and 0.2 m / s for pedestrian speed on average, with Case 5 being the bestperforming scenario and Case 1 being the worst. Vehicle Speed Pedestrian Speed Gait Actual Estimated Actual Estimated Actual Estimated Case I 15 12.8 0.8 0.4 1 0 Case 2 7.14 8.3 0.83 0.4 1 0 Case 3 6.47 5.9 1.86 1.8 0 9 Case 4 13.14 11.2 1.65 1.8 0 9 Case 5 17.4 17.6 I 1.1 9 9 Table 3: Collision model validation data Figure 4 shows a simplified box diagram setting out the process of creating the collision model. Initially, a pedestrian model 10 and vehicle model 20 are each created (steps 101a and 101b respectively). The pedestrian and vehicle models 10, 20 are then combined (step 102) to form a collision model. The collision model is then used to simulate multiple collisions in order to generate collation data (step 103). Next, the collision model is trained using a machine learning model (or multiple models) at step 104. The trained models are then tested (step 105) and validated using real-life collision data (step 106). Once the collision model is validated, it is then trained using Bayesian optimisation (step 107) to estimate forensic details of a collision using only parameters known after the collision. In this particular embodiment, the model is trained to estimate vehicle and pedestrian speed given the head impact co-ordinates, pedestrian height and weight and vehicle profile. Finally, turning to figure 5, a method of estimating forensic parameter of a pedestrian vehicle collision. At a first step 201, the parameters of the collision are determined, in so far as this is possible. Typically, after such a collision, the vehicle and pedestrian speed are not known, but several other parameters are, such a vehicle profile, pedestrian height and weight and the head impact co-ordinates. In a second step 202, the known parameters post collision are input into a collision model as discussed extensively above. Once the parameters have been input, the collision model estimates the vehicle and / or pedestrian speeds based upon the known parameters. The collision model separately estimates the forensic details in respect of two spatial dimensions 203, 204. Once the forensic details have been estimated separately, the two estimates are then averaged 205, and a final estimate 206 is output from the collision model. The use of separate estimations which are later averaged with each other provide greater accuracy than conventional methods, whilst also requiring less computational power than a single estimate which can incorporate both axes within a single estimation. The use of such a method as described above enables the speed of the vehicle to be estimated using only parameters available after the collision (such as vehicle profile information, head impact position and pedestrian height and weight) in a more accurate manner than other known methods. This allows for better determination of liability and / or criminality in collision investigations, such as those performed by insurers and / or police after collision have occurred. In addition to the increased accuracy, the use of independent estimations in respect of each of the at least two spatial dimensions of the head impact position requires less processing power than estimating using a multi-output model as mentioned above. In this specific embodiment, there is an additional, optional sub method which is capable of estimating the severity of any injuries sustained by the pedestrian in the collision. It will be understood by the skilled person that the vehicle velocity at the time of collision will necessarily be the pedestrian impact velocity, and that the vehicle velocity is composed of an orthogonal velocity and a tangential velocity. Once the vehicle velocity at the time of collision has been estimated at step 206, the estimated vehicle velocity is ‘split’ into its’ orthogonal and tangential components, each of which are calculated at step 207. At a next step 208, the orthogonal component of the vehicle velocity is mapped against an injury risk curve for the or each body region which impacts the vehicle in the collision. Figure 6a shows an exemplary injury risk curve for collision where the head impacts the windscreen of the vehicle, and Figure 6b shows a general injury risk curve for pedestrian-vehicle collisions. Based on a mapping between the orthogonal component of the vehicle velocity and the selected injury risk curve, an estimate of the 5 likely severity of any injuries in the collision can be generated. This output could be in the form of a numerical score or potential injury classification such as moderate, significant, severe etc. Whilst the above description has referred to a single machine learning model used to build the collision model, there are a variety of machine learning models which 10 could be used to build such a collision model. Such alternative models include, amongst others, Linear Regression, Support Vector Regressor, Decision Tree Regressor, Random Forest Regressor, Gradient Boosting Regressor, XGBoost Regressor, and Multilayer perceptron. The one or more embodiments are described above by way of example only. 15 Many variations are possible without departing from the scope of protection afforded by the appended claims.

Claims

1. A method for estimating forensic details of vehicle-pedestrian collisions comprising:determining a set of parameters of the collision, the parameters including the position where the pedestrians head impacted the vehicle,inputting said parameters into a collision model,estimating forensic details of the collision using the collision model in a first spatial dimension using the position where the pedestrians head impacted the vehicle with respect to the first spatial dimension,estimating forensic details of the collision using the collision model in a second spatial dimension using the position where the pedestrians head impacted the vehicle with respect to the second spatial dimensions, andaveraging the results of the estimated forensic details from the first spatial dimension and the second spatial dimension to arrive at a final estimation of the forensic details of the collision.

2. A method according to claim I wherein the method includes estimation of the seventy of any injuries obtained by the pedestrian m the collision.

3. A method according to claim 2 wherein the method comprises mapping the orthogonal component of the estimated vehicle velocity at the time of collision against an injury risk curve.

4. A method according to claim 3 wherein the orthogonal component of the estimated vehicle velocity at the time of collision against a dedicated injury risk curve for each body region which impacts the vehicle.

5. A method according to any preceding claim wherein the position where the pedestrians head impacted the vehicle is defined with reference to a co-ordinate system.

6. A method according to claim 5 wherein the co-ordinate system comprises three mutually perpendicular linear axes, the axes having an origin defined as a bottom, front side corner of a vehicle.

7. A method according to claim 6 wherein the spatial dimensions define an X-axis parallel to the longitudinal axis of the vehicle, a Y-axis parallel to a transverse axis of the vehicle and an upright Z-axis.

8. A method according io any preceding claim wherein the first and second spatial dimensions for which forensic details are estimated are the length and width dimensions.

9. A method according to any preceding claim wherein the parameters include any combination from the following list: vehicle width, vehicle height, vehicle length, ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height, roof angle, pedestrian speed, pedestrian impact angle, pedestrian impact width, pedestrian height, pedestrian weight, and pedestrian gait.

10. A method according to any preceding claim wherein the method is able to estimate the vehicle speed and / or pedestrian speed at the time of the collision using the following parameters: vehicle width, vehicle height, ride height, bumper height, bumper angle, bonnet leading edge height, bonnet leading edge angle, bonnet height, bonnet angle, windscreen height, windscreen angle, roof height, pedestrian height, and pedestrian weight.11, A method according to any preceding claim wherein the collision model comprises at least one multibody model.

12. A method according to claim 11 wherein the collision model comprises a multi body model of the pedestrian.

13. A method according to either claim 11 or 12 wherein the collision model comprises a multi body model of the vehicle.

14. A method according to any claims 11 to 13 wherein the collision model comprises both a pedestrian model and a vehicle model.

15. A method according to any preceding claim wherein the collision model is configured to simulate a collision based upon the parameters input into the collision model.

16. A method according to claim 15 wherein the model is configured to simulate the collision using the input parameters and provide the estimated forensic details of the collision based upon the simulation.

17. A method according to any preceding claim wherein the collision model is based upon one or machine learning algorithms trained using real-life collision data.

18. A method according to any preceding claim wherein the collision model is configured to iteratively optimise the estimated forensic details.

19. A method according to claim 18 wherein the collision model uses Bayesian optimisation to estimate the forensic details of the collision.

20. A method according to either claim 18 or 19 wherein the collision model is configured to iterate the estimated forensic details until the error in said estimation is below a threshold level.

21. A method according to any preceding claim wherein the averaging of the separately estimated forensic details is performed using a dedicated model averaging algorithm.

22. A method according to any preceding claim wherein the method comprises additional data acquisition steps.

23. A method according to claim 22 %'herein the data acquisition steps acquire data for use in the estimation of the forensic details of the collision.

24. A method according to claim 23 wherein the data acquisition steps comprise:acquiring da ta from a look-up tableusing image recognition techniques on one or more images taken at the scene of the collisionusing one or more application programming interfaces (APIs) to retriev data from one or more external sources.

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