2d bimodal distribution filter

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First, some infos about my goal:
I'm trying to create a model for somekind of a occupancy grid, which is more or less a matrix. Each cell describes a quadratic area (e.g. 1m²)



Now we have a station which measures a certain distance to an object, e.g. d and we assume that the station is in the middle of the grid. So normally we would "occupy" each cell that fits into the distance, which gives us somekind of a "marked box" in the occupancy grid.



Since d is not that accurate, we want to apply a probability using a normal distribution. Searching into this direction gives me the idea of a gaussian filter matrix (like it is often used in image processing), which could be applied to the grid by multiplying the grid-matrix with the gaussian filter matrix (which is filled with zeros to match the grid's dimensions). Thus, we don't need a convolution here, but only a possibilty to calculate the probability for a certain cell using the 2d gaussian kernel function.



But the gaussian filter doesn't not fit, because the expected value would only be a single cell in the grid (obviously the station itself instead of the object). Looking at the probability distribution the expected value would be the distance d and -d as well. Or figuratively speaking: We don't need a bell, but rather a ring.



So, is there any common filter or kernel function for such a bimodal distribution and/or are we in a totally wrong direction?




probability probability-distributions signal-processing




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    First, some infos about my goal:
    I'm trying to create a model for somekind of a occupancy grid, which is more or less a matrix. Each cell describes a quadratic area (e.g. 1m²)



    Now we have a station which measures a certain distance to an object, e.g. d and we assume that the station is in the middle of the grid. So normally we would "occupy" each cell that fits into the distance, which gives us somekind of a "marked box" in the occupancy grid.



    Since d is not that accurate, we want to apply a probability using a normal distribution. Searching into this direction gives me the idea of a gaussian filter matrix (like it is often used in image processing), which could be applied to the grid by multiplying the grid-matrix with the gaussian filter matrix (which is filled with zeros to match the grid's dimensions). Thus, we don't need a convolution here, but only a possibilty to calculate the probability for a certain cell using the 2d gaussian kernel function.



    But the gaussian filter doesn't not fit, because the expected value would only be a single cell in the grid (obviously the station itself instead of the object). Looking at the probability distribution the expected value would be the distance d and -d as well. Or figuratively speaking: We don't need a bell, but rather a ring.



    So, is there any common filter or kernel function for such a bimodal distribution and/or are we in a totally wrong direction?




    probability probability-distributions signal-processing




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      First, some infos about my goal:
      I'm trying to create a model for somekind of a occupancy grid, which is more or less a matrix. Each cell describes a quadratic area (e.g. 1m²)



      Now we have a station which measures a certain distance to an object, e.g. d and we assume that the station is in the middle of the grid. So normally we would "occupy" each cell that fits into the distance, which gives us somekind of a "marked box" in the occupancy grid.



      Since d is not that accurate, we want to apply a probability using a normal distribution. Searching into this direction gives me the idea of a gaussian filter matrix (like it is often used in image processing), which could be applied to the grid by multiplying the grid-matrix with the gaussian filter matrix (which is filled with zeros to match the grid's dimensions). Thus, we don't need a convolution here, but only a possibilty to calculate the probability for a certain cell using the 2d gaussian kernel function.



      But the gaussian filter doesn't not fit, because the expected value would only be a single cell in the grid (obviously the station itself instead of the object). Looking at the probability distribution the expected value would be the distance d and -d as well. Or figuratively speaking: We don't need a bell, but rather a ring.



      So, is there any common filter or kernel function for such a bimodal distribution and/or are we in a totally wrong direction?




      probability probability-distributions signal-processing




      share|cite|improve this question













      First, some infos about my goal:
      I'm trying to create a model for somekind of a occupancy grid, which is more or less a matrix. Each cell describes a quadratic area (e.g. 1m²)



      Now we have a station which measures a certain distance to an object, e.g. d and we assume that the station is in the middle of the grid. So normally we would "occupy" each cell that fits into the distance, which gives us somekind of a "marked box" in the occupancy grid.



      Since d is not that accurate, we want to apply a probability using a normal distribution. Searching into this direction gives me the idea of a gaussian filter matrix (like it is often used in image processing), which could be applied to the grid by multiplying the grid-matrix with the gaussian filter matrix (which is filled with zeros to match the grid's dimensions). Thus, we don't need a convolution here, but only a possibilty to calculate the probability for a certain cell using the 2d gaussian kernel function.



      But the gaussian filter doesn't not fit, because the expected value would only be a single cell in the grid (obviously the station itself instead of the object). Looking at the probability distribution the expected value would be the distance d and -d as well. Or figuratively speaking: We don't need a bell, but rather a ring.



      So, is there any common filter or kernel function for such a bimodal distribution and/or are we in a totally wrong direction?





      probability probability-distributions signal-processing





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