Adjusting multiple model neural filter for the needs of marine radar target tracking

Transcription

1 International Radar Symposium IRS Adjusting multiple model neural filter for the needs of marine radar target tracking Witold Kazimierski *, Andrzej Stateczny * * Maritime University of Szczecin, Chair of Geoinformatics Waly Chrobrego Street 1-2, 7- Szczecin, POLAND w.kazimierski@am.szczecin.pl, a.stateczny@am.szczecin.pl Abstract: The paper presents the research on establishing neural models of target movement. The models are to be adjusted to General Regression Neural Network, as such a filter is a base for multiple model neural filter, which is currently under development. The research presented are a part of the research project Development of radar target tracking methods with the use of multiple model neural filtering financed by Polish Ministry of Science and the paper is one of the series. The main goal of the presented research was to examine if different manoeuvring dynamics can be defined as a neural model by a network parameters. The research was conducted with Monte Carlo simulation. 1. Introduction Multiple model tracking is one of the most popular approaches used for tracking a manoeuvring target. This is one of popular solution of classical tracking problem to find a perfect compromise between tracking sensitivity and track smoothness. The idea is to estimate state vector in a few independent elementary filters and combine their output into one state vector. Each of the filters represents one movement model of the target. Many different methods of mixing elementary filters are use with the decision-based method being the simplest of them. In this method the decision is made in which of the modelled states the target is, and output from the appropriate filter is chosen [1]. Neural networks as well as other artificial intelligence methods can be used for target tracking in maritime radars. A research on this has been carried out in Maritime University of Szczecin for last years. The idea is to use a non-linear tool like neural networks for estimating state vector, especially during non-linear movement, like during manoeuvres. Particularly interesting research results were obtained with the use of General Regression Neural Network. Such a filters have been presented on IRS since 2. In the last years the idea of building multiple model filter based on GRNN has been developed. This led to a multiple model neural filter in which different neural networks represents different movement states of the targets. Assuming that such states have been defined and related to movement dynamics, the question arise how to implement these states into respective networks. Answering this question is the scope of this paper. First a few words about multiple model neural filter are said, then about parameters possible for adjusting in GRNN filters. At the end the results of numerical experiment based on simulation are presented. 2. Multiple model neural filter for target tracking The significant grown in the number of neural networks applications and important evolution of artificial intelligence technology could have been observed in 8 s of XX century. It was also that time when idea of using neural networks for radar target tracking arose. One of the possible network to use is General Regression Neural Network (GRNN). The concept of such a filter was shown in [2], [4], [], [12]. The filter proposed in these papers consists of two parallel GRNNs. One of them is to estimate Vx and the other Vy. Second filtration stage for additional smoothing of signal is enabled. To ensure proper functioning of the filter, since the

2 618 International Radar Symposium IRS 211 beginning of observation, the dynamic increase or decrease of number of radial neuron in hidden layer and elements of teaching sequence is introduced. Observed (measured) values of movement vectors are used as input and teaching values while estimated movement vector is the output. General Regression Neural Network itself has been invented by D. F. Specht [7] and from the mathematical point of view is basically neural implementation of kernel regression algorithms from the sixties. GRNN performs kernel regression, resulting in computing weighted average of teaching vectors. The weights are the values of Gaussian kernel function for the distances of input vector to teaching vector [4]. Multiple model approach is the development of so called decision based filters. The The filter consists of a few elementary filters, each of them for tracking targets in unique movement stage, called model. They are running simultaneously. The final estimation can be a chosen output of one of elementary filters (in the decision based methods) or a combination of elementary estimates (in multiple model approach). There are several particular algorithms of multiple model tracking, in which different interaction methods between elementary filters is used. These can be found for example in [1] and [6]. The idea of creating multiple model neural filter, which can be implemented as decision based filter as well has finally arrived. Main problem in such an approach is to tune elementary filters for suitable movement model. This of course shows the need of defining such a models and translating them then to neuron language.. GRNN parameters for maneuvering target tracking In the theory of neural networks main parameters that has to be defined and that can be adjusted are the weights of the links between layers and the threshold values In each neuron. Additionally a network structure can be threaded as parameter, however it is usually set once at the beginning in the project phase. General Regression Neural Network is trained without any teacher. It s structure is thoroughly known and strictly defined. As it is related to teaching sequence length, the structure is this time variable. The links between networks has the value of teaching cases. Thus there are three main parameters to be adjusted in GRNN: length of teaching sequence activation function of radial neurons (kernel function) smoothing factor. All the parameters can be adjusted separately. The length of teaching sequence is the parameter, which decides about the network structure. Each element of teaching sequence is represented by one teaching neuron (radial neuron in radial layer). This means that the more elements there is in teaching sequence, the more neurons is needed in hidden layer. Activation function and the smoothing factor are the parameters influencing the work of each and every particular neuron, however the same values are used for all the neurons in radial layer. Activation function is usually gaussian or hyperbolic and the smoothing factor is in fact the parameter of this function, which decides of generalization level of estimated vector. The aim of the research is to find an answer for the question how this parameters shall be adjusted for the best modelling of one of the movement states. Suitable scenario have been prepared and the network parameters have been examined. The research has been made with PC-based simulator by an author.

3 International Radar Symposium IRS Numerical experiment The simulator used in research is a PC-based application, prepared by the author in MS Visual Studio. The idea of radar target simulation used in the simulator derives from [] and is based on adding to non-cluttered measurement process noise. Thus the position of simulated target is obtained. The noise is calculated as a product of maximum sensor noise and pseudorandom value. Start point of random numbers is changing, which allows carrying out Monte Carlo simulation. Own ship movement is also simulated and typical errors of gyrocompass (, ) and log (, kn) are included. The auto-correlation function factors were established based on [] and [9]. The simulator has also other possibilities and functionalities, which were not used for the research for this paper, however they can be used for many other purposes. Table 1. Research scenario Scenario no 1 Own ship course Own ship speed Initial distance kn 8 Nm Initial bearing Initial target course 18 Initial target speed Start of manoeuvre Manoeuvre Manoeuvre dynamics kn 24 sek 8 stbd 2 /min, 4 / min, 6 / min The idea of the research was to examine if different manoeuvring dynamics can be defined as a neural model by a network parameters. To achieve this, influence of different dynamics for adjusting teaching length and smoothing factor was examined. The research scenario assumed course manoeuvre of a target with different rate of turn, which was the indicator of ship s dynamics. The details of scenario are shown in table 1. The research was done with Monte Carlo simulation method for runs. Two parameters have been examined, namely length of teaching sequence (number of radial neurons) and the smoothing factor, so the research had two stages. As for another parameter activation function, the most popular Gaussian function, calculated with formula 1 was used. It is presented in Figure 1. 2 u μ i ( u) = exp 2 (1) 2σ where: u = x - t, t central point (in GRNN t is teaching sample) σ smoothing factor, σ >.

4 62 International Radar Symposium IRS Figure 1. Gaussian activation function used in GRNN filter [8]. Results In the first part of experiment the use of different smoothing factor sequence for different manoeuvre dynamics has been examined. The results of an experiment can be seen in figure 2. a) b) course error [º] 8 1 c) Figure 2. Course estimation error during course manoeuvre for different smoothing factors and rates of turn ah, a 2 º/min, b 4 º/min, c- 6 / min The error of estimated course have been shown for different smoothing factor values. The same manoeuvre was examined, but with different dynamics three different turn rates have been included. The smoothing factors to be used have been established based on earlier research eight values from the range 2 have been tested. Only four of them are included due to figure readability. Presented values are the averages for Monte Carlo simulations. From the figure 2 two main conclusions can be stated. Firstly is that the smaller the smoothing factor is the smaller are the mean errors of course estimation, but the values achieved are more variable. This conclusion is independent from rate of turn and confirms

5 International Radar Symposium IRS earlier research [], [11]. Secondly conclusion is that the bigger rate of turn is, course is estimated with the bigger error for the same smoothing factor. Thus the smaller smoothing factor shall be used for more dynamic manoeuvres to maintain the same level of accuracy. This confirms, that smoothing factor shall be one of the parameters of movement model for GRNN. In the second part of experiment the same situation has been tested with the difference that teaching sequence length was examined instead of smoothing factor. The results of an experiment can be seen in figure. The idea of presentation remains the same estimated course error for Monte Carlo runs is presented. This time also a few observations can be made based on the graphs. Firstly it can be noticed that if teaching sequence is too short, the results are very variable and target vector would be unstable. Secondly it can be stated that the shorter teaching sequence is, the more accurate is the estimation during the manoeuvre (in general, for reasonably small values). Third conclusion is quite similar to the one for smoothing factor namely that the bigger rate of turn is, course is estimated with the bigger error for the same length of teaching sequence. Thus shorter sequences shall be used more dynamic manoeuvres to obtain the same accuracy. a) 2 b) c) Figure. Course estimation error during course manoeuvre for different teaching length sequence and rates of turn a 2 º/min, b 4 º/min, c- 6 / min 6. Final remarks The paper presents the research, which aimed at finding which parameters of General Regression Neural Networks shall be used to model different target movement, while tracking with multiple model neural filter. First the idea of filter itself has been explained and then experiment has been presented and the result of the research has been shown.

6 622 International Radar Symposium IRS 211 Two of three GRNN parameters have been examined namely smoothing factor and length of teaching sequence, while choosing of activation function remains beyond scope of this paper. Presented results leads to three main conclusions movement with different dynamics (faster or slower maneuvers) shall be modeled with different neural filters smaller smoothing factors shall be used for more dynamic movement shorter teaching sequences shall be used for more dynamic movement. Summing up the paper it can be said that the multiple model neural filter can be built with having the research result in mind. If the movement models were defined with the use of rate of turn it should be possible to translate them to GRNN language with the use of smoothing factor and length of teaching sequence. References: [1] Y. Bar Shalom, X. R. Li, Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software, John Wiley & Sons, Inc., NY USA, 21 [2] W. Juszkiewicz, A. Stateczny, GRNN Cascade Neural Filter for Tracked Target Maneuver Estimation, Neural Networks and Soft Computing, Zakopane 2 [] T. Kantak, A. Stateczny, J. Urbaski, Basis of automation of navigation (in polish). AMW, Gdynia [4] W. Kazimierski, Two stage General Regression Neural network for radar target tracking, Polish Journal of Environmental Studies, Vol. 17, No B, 28. [] W. Kazimierski, Selection of General Regression Neural Net-work s Training Sequence in the process of Target Tracking in Maritime Navigational Radars, Polish Journal of Environmental Studies, Vol 16A., 27 [6] X. R. Li, V. P. Jilkov, A Survey of Maneuvering Target Tracking Part V: Multiple-Model Methods, IEEE Transactions on Aerospace and Electronic Eystems, Vol. 41, 2. [7] D. F. Specht, A General Regression Neural Network, IEEE Transactions on Neural Network, Vol. 2, No. 6, [8] A. Stateczny (ed.), Radar navigation, GTN, Gdansk 211 (in polish) [9] A. Stateczny, A. Felski, M. Krotowicz, Generating of correlated measurements in navigational research (in polish), Biuletyn WAT, 1987 [] A. Stateczny, W. Kazimierski, General Regression Neural Network (GRNN) in the Process of Tracking a Maneuvering Target in ARPA Devices, Proceedings of IRS 2, Berlin 2. [11] A. Stateczny, W. Kazimierski, Selection of GRNN Network Parameters for the Needs of State Vector Estimation of Manoeuvring Target in ARPA Devices, SPIE Proceedings 26 [12] A. Stateczny, W. Kazimierski, The Process of Radar Tracking by Means of GRNN Artificial Neural Network with Dynamically Adapted Teaching Sequence Length in Algorithmic Depiction, Proceedings of 7th International Symposium of Navigation TransNav27, Gdynia 27