Abstract:
A probabilistic map generator for indicating the probability of a chemical, biological or other agent in a structure or building. The building is mapped in to floors and several levels of cubes in each floor. The probability of an agent&#39;s presence is indicated for each cube. Sensors are placed in various locations on each floor of the building. Inputs from the sensors go to a data processor. The probabilities of an agent&#39;s presence may be calculated by the data processor in conjunction with a Kalman filter. The probabilities may be displayed in a diagram of cubes, each having a certain shading indicating a probability of the agent&#39;s presence for the respective cube.

Description:
BACKGROUND  
         [0001]    The invention pertains to detection of dangerous agents in the air. More particularly, the invention pertains to detecting the presence and movement of a chemical or biological agent in a building.  
         SUMMARY  
         [0002]    The invention provides a probabilistic map with the likelihood of a location and a concentration of a chemical or biological agent in various portions of a building or structure during and/or after an attack. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0003]    [0003]FIG. 1 is a three-dimensional representation of a building floor divided up into subvolumes or cubes;  
         [0004]    [0004]FIG. 2 a  shows a plan view of the floor of a building with an overlay of cube boundaries;  
         [0005]    [0005]FIG. 2 b  is a probabilistic map of the floor according to the cubes or subvolumes of the floor;  
         [0006]    [0006]FIG. 3 is a diagram of hardware used for the probabilistic map generator or system;  
         [0007]    [0007]FIG. 4 is a diagram of the hardware and Kalman filter of the map system; and  
         [0008]    [0008]FIG. 5 is a diagram of the system, measurement and Kalman filter aspects of the probabilistic map system. 
     
    
     DESCRIPTION  
       [0009]    A probabilistic map shows regions with high to low probability indications of a presence of a chemical or biological agent or other substance or agent in a building or structure. The map is three dimensional in scope and may include information about building levels, ductwork and other building components. The map is updated continuously in time and space so as to provide information for a timely and targeted control response. It contains information noting the randomness of the sensor readings due to air movement, different points of attack, inaccurate sensor readings and the discrete nature of sensor locations in the building. The probabilities indicated by the map may be continuous in space to provide safe evacuation routes for the building inhabitants. The probability map may be stored to provide forensic material by observing the evolution of the map in time and space. The map may provide information for optimal placement of additional sensors in areas where the map does not provide full information. It may be based on first principles of building models. The map may provide information for computational reduction for fluid dynamic calculations by specifying special areas of concern.  
         [0010]    During a chemical or biological attack, measurements by sensors used to collect information always introduce randomness, due to reasons of air movement, different points of attack, inaccurate sensor readings and due to the discrete nature of sensor location. In the event of such an attack, it would be useful to create a probability map of the building and estimate the agent concentration and location.  
         [0011]    The driving mechanism of the map would be an application of an extended Kalman filter. The outcomes of the filter are the state estimates of location and concentration of the agent in the building. A good structural model of the building environment, as well as measurement data and a measurement model, needs to be available. The filter uses a mix between “continuous” state updates and “discrete” Kalman filter/measurement updates that occur when useful new measurements come in.  
         [0012]    There are various forms of dynamic building models currently available that can be used to continuously simulate/update the building states. Those states should include pressures, flow, agent concentration and agent location. Parameters that describe the building model are the geometry of the building, outside conditions, sensor location and number of sensors, agent properties, as well as agent release location and agent amount. Control inputs to the Kalman filter include the changing HVAC system settings, i.e., opening and closing dampers, fan speeds, and so forth. During the period of time where there are not any measurements available, the Kalman filter propagates and predicts its states continuously using the dynamic building model. As soon as there are sensor measurement data available, the Kalman filter updates its state estimates using the new measurement data.  
         [0013]    An advantage of using the Kalman filter is its use for online estimation and prediction of the model states. It can be updated continuously in time and space, to provide information for a timely and targeted control response. The Kalman filter describes regions of high to low probability indicating the presence of a chemical or biological agent by displaying information of the error and measurement covariance matrices of the Kalman filter. The map incorporates information indicating the randomness mentioned in the introduction by calculating standard deviations that are a direct outcome of the state estimate updates. The evolution of the Kalman filter states and covariance matrices in time and space should be stored to provide forensic material.  
         [0014]    [0014]FIG. 1 is a schematic of an illustrative floor  101  of a building that a probabilistic map of agent distribution will represent. The volume of floor  101  is divided into cubes or subvolumes  102 . The cube density may be changed. There may be as many levels of cubes  102  and as many cubes in a layer as desired. A pattern  103  at the bottom of floor  101  may reveal the various features, stairwells, vents, sensors  105  and so forth in floor  101 . A plan view or pattern  103  of the floor  101  is also shown in FIG. 2 a . A particular floor  101  of a building along with a particular level of cubes is represented in FIG. 2 a . Cubes  102  are indicated by the dashed lines. FIG. 2 b  is an example of a probabilistic map  106  of floor  101  at a selected level of cubes  102 . The various shades of the block indicate the level of likelihood of the presence of an agent in a particular cube. The darker shading  107  indicates a greater probability of the presence of an agent than a lighter shading  108 .  
         [0015]    An agent release, for an illustrative example, is shown by symbol  104  in FIG. 2 a . A block  102  in probabilistic map  106  corresponding to block  102  in FIG. 2 a  corresponding to the same volume, is black and represents a high probability of the presence of an agent. Probabilistic map  106  may be configured to indicate, besides location, the concentration of the agent. Probabilistic map  106  may represent cubes in a side view as desired. Map  106  may be a three-dimensional representation of cubes  102  for one level of cubes  102  in a floor  101  or all levels of cubes  102  of floor  101 , or all cubes  102  for the whole building.  
         [0016]    [0016]FIG. 3 shows an illustrative example of the basic hardware used to implement the invention. A digital computer  201  is used for processing input signals from sensors or sensor suite  105  via an interface  202 . Computer  201 , in FIG. 3, contains not just a processing mechanism, but also a database which includes the building and transport models. Also, processor  201  of this figure contains Kalman filter  407 , a data processing algorithm. A probabilistic map  106  output is provided to display indicator  203  for observation by an operator. Control or recommended action signals  204  may be output of the probabilistic map  106  system.  
         [0017]    [0017]FIG. 4 is like FIG. 3 except Kalman filter  407  and data bus and database  302  are delineated from digital computer or data processor  301 . Processor  301  may have a database connected to it. Data  303  from specialty sensors or sensor mechanism  105  may go to data bus  302 . Control signals  303  may go to control various aspects of sensors  105 . Sensors  105  may sense pressure, flow, temperature, agent composition and concentration, and other things. A structure model  305  having parameters is connected to data bus/database  302 . Data bus  302  is like an interface between data processor  301  and sensors  105 . Data processor  301  passes building systems information  304  to Kalman filter  407  and filter  407  provides filter-processed information  304  to data processor  301 . Kalman filter  407  algorithmically processes out probabilistic information  305  for a probabilistic map  106  to be displayed on computer screen or display  203 . Computer screen or display  203  may have a console or keyboard proximate to it for controlling data processor or computer  201 .  
         [0018]    A continuous-discrete extended Kalman filter is utilized for the probabilistic map. The system model equation is:  
             {dot over (x)}   ( t )=   f   (   x   ( t ), t )+   w   ( t ), where    w t˜N ( 0   ,Q ( t )  
         [0019]    The system model    {dot over (x)}   (t) is a state space representation of the building model and an agent transport model. Transport of the agent is affected by the building model and the transport model.  f (x(t)) is a portion of the equation that is the essence of the system model which includes the building and transport models.  f  incorporates parameters of the building model such as the dimensions of the building.  w (t) is process noise. It represents other conditions or external influences like weather. More accurate models should reduce  w (t). However, with more accurate models the computation time increases.  w (t) follows N(0,Q(t)) where N indicates a normal distribution of the noise model.  
         [0020]    The equation for the measurement model is:  
             z     k   = h     k ( x ( t   k ))+   v     k , where  K= 1, 2, . . . and    v     k   ˜N ( 0   ,R   k ).  
         [0021]    The measurement model involves measurements of the agent (what kind is indicated by a chemical sensor), location and concentration of the agent, the pressure and/or flow, and the temperature. X(t k ) indicates measurements made at time t at discrete instances k. V k  indicates the noise on the measurements. The noise is integrated into the Kalman filter calculations. The measurement noise V   k     ˜N ( 0 , R   k ) follows a normal distribution.  
         [0022]    The equation for the initial conditions is  x (0)˜N( {circumflex over (x)}   0 , P 0 ).  x (0) is the initialization of the states. N( {circumflex over (x)}   0 , P 0 ) indicates the certainty of the initial estimate. The initial values of measurements involve pressure and/or flow, temperature, agent location which indicates no agent to be present, and a zero agent concentration. The other assumptions are stated as E[ w (t) v   k   T ]=0 for all k and all t, i.e., measurement noise and process noise are independent from each other.  
         [0023]    The state estimate propagation or system model continuous update is indicated by  {circumflex over (x)} (t)= f ( {circumflex over (x)} (t),t). The error covariance propagation is indicated by:  
           {dot over (P)} ( t )= F (   {circumflex over (x)}   ( t ), t ) P ( t )+ P ( t ) F   T ( {circumflex over (x)} ( t ), t )+ Q ( t ).  
         [0024]    F( {circumflex over (x)} (t),t) is a linearized representation of the system model. It is a Jacobian matrix as shown by the following equation evaluated at previous state estimates.  
         F        (         x   ^          (   t   )       ,   t     )       =         ∂       f   _          (         x   _          (   t   )       ,   t     )           ∂       x   _          (   t   )                |         x   _          (   t   )       =         x   _     ^          (   t   )                                   
 
         [0025]    The state estimate update for the system model is a discrete update that is indicated by the following equation.  
             {circumflex over (x)}     k (+)=   {circumflex over (x)}     k (−)+ K   k   [ z     k   − h     k (   {circumflex over (x)}     k (−)].  
         [0026]    Z k− z, is truth minus estimate which equals the error. The Kalman filter is discretely updated with this error. Such updates may occur every several seconds or less. The error covariance update is:  
           P   k (+)=[ I−K   k   H   k (   {circumflex over (x)}     k (−))] P   k (−).  
         [0027]    P k  is a covariance matrix and K k  is a common gain matrix.  
         [0028]    K k  is represented by the following equation:  
         K   k     =         P   k          (   -   )                H   k   T          (           x   _     ^     K          (   -   )       )       [           H   k          (           x   _     ^     k          (   -   )       )              P   k          (   -   )              H   k   T          (           x   _     ^     k          (   -   )       )         +     R   k       ]                             
 
         [0029]    H k ( {circumflex over (x)}   k (−)) is a measurement matrix which is represented by the following equation—a linearized version of the measurement model.  
           H   k          (           x   ^     _     k          (   -   )       )       =         ∂         h   _     k          (       x   _          (     t   k     )       )           ∂       x   _          (     t   k     )                |         x   _          (     t   k     )       =           x   ^     _     k          (   -   )                                   
 
         [0030]    [0030]FIG. 5 is a block diagram depicting the system, measurement and estimator portions of the Kalman filter aspect of the probabilistic map generator for a building. System f(x t ) block  401  has system error sources w(t) input  402  to system  401 . An output  403  passes system state  x (t) information to measurement h k  block  404 . This information includes pressure and/or flow within the building, and the location and concentration of an agent within the building. Also, measurement error sources V k  information  405  passes on to block  404 . An output Z k    406  consists of observation  z (t) information that goes to Kalman filter  407 . A priori information goes to Kalman filter  407  via input  408 . An output  409  of Kalman filter  407  provides system state estimate  {circumflex over (x)} (t) information.  
         [0031]    Although the invention has been described with respect to at least one illustrative embodiment, many variations and modifications will become apparent to those skilled in the art upon reading the present specification. It is therefore the intention that the appended claims be interpreted as broadly as possible in view of the prior art to include all such variations and modifications.